Kyber-768 | مرکز عملیات رمزنگاری و امنیت شبکه (ML-KEM)

شبیه‌ساز عملیاتی و محاسباتی رمزنگاری کایبر (Kyber-768 / ML-KEM-768)

پیاده‌سازی دقیق ریاضیات مشبکه مدولار بر اساس NIST FIPS 203 و کتاب A Gentle Introduction to Lattice-Based Cryptography

PARAMETERS: q=3329 | n=256 | k=3 | eta1=2 | eta2=2

مرحله اول - تولید کلید (Key Generation)

$t = A \cdot s + e \pmod{3329}$

در استاندارد Kyber-768 (ML-KEM-768)، ابعاد ماژول برابر با $$k=3$$ و درجه چندجمله‌ای‌ها برابر با $$n=256$$ در پیمانه $$q=3329$$ می‌باشد. باب ماتریس تصادفی $A \in R_q^{3 \times 3}$ را به همراه بردارهای خطای کوچک $s \in S_{\eta_1=2}^3$ (کلید خصوصی) و $e \in S_{\eta_1=2}^3$ از توزیع دوجمله‌ای مرکزیت‌یافته $$CBD_2$$ تولید می‌کند. سپس بردار کلید عمومی $t = As + e \pmod{3329}$ محاسبه می‌گردد.

$$ t = A \cdot s + e \pmod{3329} $$

۱. ماتریس تصادفی $A \in R_q^{3 \times 3}$ (شامل ۹ چندجمله‌ای درجه ۲۵۶ در $\mathbb{Z}_{3329}$ )

Row / Col	Column 1	Column 2	Column 3
Row 1	$\mathbf{A_{ 1, 1 }} = 139 - 615x + 960x^2 - 1232x^3 + 738x^4 - 383x^5 + 151x^6 + 312x^7 + 48x^8 - 621x^9 - 1391x^10 - 720x^11 - 120x^12 - 1328x^13 + 1209x^14 - 493x^15 - 1403x^16 - 413x^17 - 1537x^18 - 1302x^19 - 28x^20 + 1115x^21 - 182x^22 - 1608x^23 + 69x^24 + 1339x^25 - 719x^26 + 160x^27 - 938x^28 + 714x^29 - 39x^30 + 353x^31 - 630x^32 + 301x^33 - 968x^34 + 433x^35 - 1469x^36 - 888x^37 - 40x^38 + 607x^39 + 142x^40 + 857x^41 - 243x^42 - 159x^43 - 557x^44 + 1069x^45 + 94x^46 - 496x^47 + 187x^48 + 425x^49 - 665x^50 - 1037x^51 + 1547x^52 + 717x^53 + 693x^54 - 1353x^55 + 17x^56 - 439x^57 + 536x^58 - 47x^59 + 1329x^60 + 1488x^61 - 1142x^62 + 1624x^63 + 961x^64 + 928x^65 - 771x^66 + 1079x^67 - 705x^68 - 69x^69 + 146x^70 - 52x^71 + 1568x^72 + 707x^73 + 480x^74 + 855x^75 + 223x^76 - 334x^77 + 923x^78 + 810x^79 - 15x^80 - 53x^81 - 1076x^82 + 338x^83 + 1285x^84 + 1567x^85 - 1240x^86 - 513x^87 + 370x^88 - 116x^89 - 633x^90 + 1656x^91 + 424x^92 - 1045x^93 + 867x^94 - 640x^95 - 420x^96 - 1573x^97 + 957x^98 - 189x^99 - 690x^100 + 189x^101 + 988x^102 + 221x^103 - 1195x^104 + 442x^105 - 25x^106 + 201x^107 + 454x^108 + 477x^109 - 334x^110 + 550x^111 - 502x^112 + 650x^113 - 217x^114 - 144x^115 - 675x^116 + 1072x^117 + 1597x^118 + 342x^119 - 1586x^120 + 785x^121 + 466x^122 - 1248x^123 + 1221x^124 - 861x^125 + 750x^126 - 677x^127 + 528x^128 - 144x^129 + 523x^130 - 767x^131 - 869x^132 - 1120x^133 - 1027x^134 + 138x^135 - 723x^136 + 812x^137 + 1253x^138 + 361x^139 - 1026x^140 + 377x^141 + 1330x^142 + 211x^143 + 1481x^144 - 443x^145 - 131x^146 + 1630x^147 + 118x^148 - 857x^149 - 1195x^150 + 311x^151 + 215x^152 + 50x^153 - 1016x^154 - 988x^155 + 899x^156 - 1576x^157 + 850x^158 - 582x^159 + 1047x^160 + 684x^161 - 1128x^162 + 1572x^163 + 804x^164 + 487x^165 + 676x^166 + 1407x^167 + 613x^168 + 803x^169 + 356x^170 + 539x^171 - 360x^172 - 1335x^173 - 1470x^174 + 28x^175 - 1409x^176 + 1370x^177 + 596x^178 - 266x^179 + 1162x^180 + 1176x^181 - 507x^182 - 1041x^183 - 1027x^184 + 1334x^185 - 2x^186 + 758x^187 - 1111x^188 - 730x^189 + 413x^190 - 270x^191 - 1414x^192 + 42x^193 - 1379x^194 + 445x^195 + 403x^196 + 206x^197 - 1386x^198 + 650x^199 + 1450x^200 - 1578x^201 + 664x^202 + 589x^203 - 430x^204 - 659x^205 + 1633x^206 + 1314x^207 + 208x^208 - 1061x^209 + 360x^210 + 611x^211 + 337x^212 - 247x^213 - 366x^214 - 958x^215 - 1664x^216 - 1559x^217 + 986x^218 - 1159x^219 + 274x^220 + 965x^221 - 640x^222 + 115x^223 + 1386x^224 - 929x^225 - 975x^226 + 1511x^227 - 247x^228 + 1237x^229 + 1363x^230 + 1138x^231 - 1517x^232 - 888x^233 + 315x^234 - 1015x^235 + 378x^236 - 1638x^237 - 170x^238 - 985x^239 - 190x^240 + 1028x^241 - 1451x^242 + 849x^243 - 506x^244 - 1301x^245 - 1278x^246 - 1367x^247 - 1338x^248 - 1184x^249 - 68x^250 + 1207x^251 - 1259x^252 - 1648x^253 - 700x^254 + 1550x^255$	$\mathbf{A_{ 1, 2 }} = -272 - 534x - 1136x^2 - 1434x^3 + 303x^4 - 1263x^5 - 899x^6 - 1087x^7 - 1481x^8 - 1152x^9 + 863x^10 + 299x^11 - 1570x^12 - 408x^13 + 1013x^14 - 1326x^15 + 1341x^16 + x^17 + 98x^18 + 340x^19 - 590x^20 - 1358x^21 - 554x^22 + 539x^23 - 915x^24 - 562x^25 - 715x^26 - 1475x^27 + 1436x^28 - 1433x^29 + 12x^30 + 725x^31 + 150x^32 + 425x^33 + 1247x^34 - 9x^35 - 502x^36 - 722x^37 - 903x^38 + 252x^39 - 241x^40 - 383x^41 + 1471x^42 + 1460x^43 + 723x^44 + 1602x^45 - 1183x^46 - 794x^47 + 754x^48 + 783x^49 - 291x^50 + 1247x^51 + 511x^52 + 203x^53 - 330x^54 + 375x^55 + 1359x^56 - 1555x^57 - 1248x^58 - 792x^59 - 746x^60 - 448x^61 - 1582x^62 + 1154x^63 + 1095x^64 - 696x^65 - 212x^66 - 1329x^67 - 41x^68 + 1561x^69 - 1600x^70 + 429x^71 + 1233x^72 + 25x^73 - 664x^74 - 1531x^75 - 1475x^76 - 399x^77 - 189x^78 - 1128x^79 + 1323x^80 + 746x^81 + 537x^82 + 115x^83 - 1634x^84 + 343x^85 + 1421x^86 - 368x^87 - 1280x^88 + 1564x^89 + 263x^90 - 1608x^91 + 1407x^92 - 627x^93 - 454x^94 + 225x^95 - 351x^96 - 902x^97 + 1231x^98 - 1375x^99 - 919x^100 - 262x^101 - 1005x^102 + 1238x^103 - 313x^104 + 1047x^105 + 445x^106 + 288x^107 + 550x^108 - 603x^109 + 803x^110 - 664x^111 - 856x^112 + 237x^113 + 929x^114 + 1333x^115 + 997x^116 + 1620x^117 + 1603x^118 + 619x^119 - 1055x^120 + 673x^121 + 621x^122 + 1663x^123 + 249x^124 - 894x^125 - 88x^126 - 1118x^127 + 554x^128 - 1627x^129 - 1572x^130 + 580x^131 + 111x^132 + 340x^133 - 656x^134 + 1307x^135 - 1611x^136 + 481x^137 + 603x^138 - 10x^139 + 1655x^140 - 1514x^141 + 578x^142 + 611x^143 - 550x^144 - 709x^145 - 1017x^146 + 460x^147 + 426x^148 + 636x^149 + 1415x^150 + 378x^151 + 898x^152 + 423x^153 - 887x^154 + 907x^155 - 1019x^156 - 1621x^157 - 904x^158 + 182x^159 - 837x^160 + 296x^161 + 276x^162 - 153x^163 - 11x^164 - 1366x^165 - 426x^166 + 1535x^167 + 721x^168 + 1155x^169 - 1266x^170 - 1047x^171 - 1617x^172 - 1398x^173 + 255x^174 + 1141x^175 + 444x^176 - 224x^177 - 1150x^178 - 21x^179 + 955x^180 + 382x^181 + 1489x^182 + 1524x^183 + 441x^184 - 1074x^185 + 224x^186 + 718x^187 + 486x^188 - 274x^189 + 732x^190 + 156x^191 - 433x^192 + 153x^193 - 227x^194 + 1439x^195 - 1334x^196 + 1396x^197 + 764x^198 + 1646x^199 + 651x^200 - 720x^201 - 333x^202 + 459x^203 + 461x^204 + 1402x^205 - 101x^206 - 1563x^207 - 716x^208 + 330x^209 - 904x^210 - 935x^211 + 548x^212 + 710x^213 + 1421x^214 - 867x^215 - 1526x^216 - 1072x^217 + 136x^218 - 517x^219 - 791x^220 + 1444x^221 - 868x^222 + 398x^223 + 1488x^224 - 1510x^225 - 791x^226 + 787x^227 + 1242x^228 + 1332x^229 + 1463x^230 - 558x^231 + 358x^232 - 930x^233 - 1299x^234 - 924x^235 + 1130x^236 - 347x^237 + 298x^238 - 411x^239 - 1392x^240 + 167x^241 + 600x^242 + 1261x^243 + 431x^244 - 93x^245 - 1069x^246 + 906x^247 - 1197x^248 - 89x^249 - 73x^250 - 722x^251 + 1044x^252 + 706x^253 + 559x^254 - 145x^255$	$\mathbf{A_{ 1, 3 }} = 513 - 531x + 1477x^2 + 1385x^3 - 605x^4 + 321x^5 - 277x^6 - 254x^7 + 1573x^8 + 45x^9 + 1219x^10 + 1041x^11 - 1480x^12 - 738x^13 - 1218x^14 + 1570x^15 + 1065x^16 - 30x^17 + 917x^18 - 100x^19 + 538x^20 + 748x^21 - 1144x^22 + 5x^23 + 630x^24 + 1011x^25 + 961x^26 + 284x^27 - 884x^28 + 611x^29 + 971x^30 + 1240x^31 - 176x^32 + 771x^33 + 1052x^34 - 963x^35 + 1642x^36 + 714x^37 - 95x^38 + 1658x^39 - 703x^40 + 1049x^41 - 1458x^42 + 1620x^43 - 1280x^44 - 1521x^45 + 1281x^46 + 153x^47 + 1422x^48 - 1080x^49 + 999x^50 + 136x^51 + 93x^52 + 1066x^53 - 245x^54 + 1446x^55 + 498x^56 + 419x^57 + 125x^58 - 464x^59 - 343x^60 - 790x^61 + 1067x^62 + 312x^63 - 1031x^64 - 1147x^65 + 1460x^66 + 433x^67 + 436x^68 - 770x^69 - 608x^70 + 1049x^71 - 1594x^72 - 1096x^73 + 501x^74 - 1464x^75 + 623x^76 + 905x^77 - 736x^78 - 438x^79 + 901x^80 - 827x^81 - 166x^82 + 1587x^83 - 1345x^84 - 1659x^85 + 866x^86 + 854x^87 + 711x^88 + 645x^89 - 1037x^90 - 482x^91 - 13x^92 - 626x^93 + 1495x^94 - 510x^95 - 269x^96 - 1400x^97 + 1283x^98 + 1585x^99 - 390x^100 - 1314x^101 - 582x^102 + 981x^103 + 615x^104 - 1119x^105 - 133x^106 + 1400x^107 + 88x^108 + 543x^109 + 819x^110 - 275x^111 + 1568x^112 - 1436x^113 - 1572x^114 - 1120x^115 + 562x^116 + 712x^117 - 236x^118 + 827x^119 - 1048x^120 - 589x^121 + 626x^122 + 1262x^123 - 1116x^124 + 286x^125 + 1379x^126 - 142x^127 + 937x^128 - 299x^129 + 1266x^130 + 282x^131 - 621x^132 + 742x^133 + 1611x^134 + 108x^135 + 1437x^136 - 969x^137 - 907x^138 - 707x^139 - 1302x^140 - 937x^141 - 332x^142 + 1356x^143 + 1005x^144 + 1134x^145 - 561x^146 + 496x^147 - 474x^148 - 843x^149 - 1164x^150 - 833x^151 - 125x^152 - 366x^153 + 461x^154 - 1474x^155 + 396x^156 + 1426x^157 + 416x^158 + 1078x^159 + 565x^160 - 1402x^161 - 163x^162 - 1009x^163 - 161x^164 + 570x^165 + 1364x^166 - 1185x^167 - 70x^168 + 400x^169 - 369x^170 - 1217x^171 - 492x^172 - 1105x^173 - 1566x^174 - 317x^175 + 320x^176 + 947x^177 + 1097x^178 + 1130x^179 + 313x^180 - 119x^181 - 1036x^182 + 504x^183 - 1332x^184 - 1417x^185 - 834x^186 + 744x^187 + 514x^188 + 618x^189 - 1166x^190 - 1444x^191 - 1659x^192 + 866x^193 - 1297x^194 - 1268x^195 + 1348x^196 - 764x^197 + 629x^198 - 812x^199 + 1270x^200 - 946x^201 + 1181x^202 - 244x^203 - 597x^204 - 235x^205 + 401x^206 - 1407x^207 + 263x^208 + 129x^209 + 47x^210 - 1407x^211 - 388x^212 + 161x^213 - 871x^214 - 382x^215 + 841x^216 - 1454x^217 - 1006x^218 - 1396x^219 - 913x^220 + 395x^221 + 555x^222 - 1540x^223 + 931x^224 - 1134x^225 - 289x^226 + 22x^227 + 1380x^228 + 1154x^229 + 113x^230 + 332x^231 - 1157x^232 + 988x^233 + 690x^234 - 855x^235 - 835x^236 - 1092x^237 - 1109x^238 - 1282x^239 + 1201x^240 + 454x^241 - 596x^242 - 1170x^243 + 1011x^244 - 1335x^245 + 620x^246 - 871x^247 + 757x^248 + 408x^249 + 250x^250 + 1043x^251 + 180x^252 + 737x^253 - 441x^254 - 308x^255$
Row 2	$\mathbf{A_{ 2, 1 }} = -91 + 314x + 1418x^2 - 1013x^3 + 406x^4 + 470x^5 + 1303x^6 + 231x^7 + 30x^8 + 317x^9 + 61x^10 - 312x^11 - 1184x^12 + 159x^13 - 608x^14 + 837x^15 + 129x^16 + 794x^17 - 1376x^18 + 1530x^19 - 269x^20 - 1312x^21 - 1258x^22 + 637x^23 + 633x^24 + 650x^25 - 1136x^26 - 1342x^27 + 168x^28 + 995x^29 + 709x^30 + 87x^31 - 1217x^32 - 1055x^33 - 694x^34 + 1178x^35 + 721x^36 - 722x^37 - 1477x^38 + 1130x^39 + 1602x^40 + 994x^41 - 1629x^42 + 941x^43 - 384x^44 + 1101x^45 - 1419x^46 + 1371x^47 + 1583x^48 + 1327x^49 - 1092x^50 + 1646x^51 - 1303x^52 + 70x^53 + 649x^54 - 1579x^55 - 961x^56 - 441x^57 + 65x^58 - 1206x^59 - 1612x^60 + 207x^61 + 31x^62 - 878x^63 - 1582x^64 - 413x^65 - 350x^66 + 307x^67 - 954x^68 + 819x^69 + 1287x^70 + 711x^71 - 305x^72 - 896x^73 - 1583x^74 - 1442x^75 + 390x^76 + 309x^77 + 871x^78 - 1325x^79 - 238x^80 + 617x^81 - 1174x^82 - 1151x^83 - 217x^84 + 413x^85 + 401x^86 - 249x^87 - 1617x^88 - 19x^89 + 500x^90 + 789x^91 - 1180x^92 - 1050x^93 - 675x^94 + 672x^95 + 231x^96 + 285x^97 + 144x^98 + 466x^99 - 107x^100 - 598x^101 - 772x^102 + 768x^103 + 676x^104 + 69x^105 + 787x^106 - 160x^107 + 163x^108 + 1506x^109 + 384x^110 + 265x^111 + 995x^112 + 1098x^113 + 1205x^114 - 461x^115 + 1622x^116 + 1438x^117 + 1101x^118 - 1205x^119 + 441x^120 + 276x^121 + 377x^122 + 1050x^123 - 28x^124 - 148x^125 - 1260x^126 - 1581x^127 - 593x^128 - 1329x^129 + 934x^130 - 49x^131 - 669x^132 - 611x^133 + 240x^134 - 672x^135 - 1102x^136 + 783x^137 + 687x^138 + 1083x^139 + 1159x^140 - 207x^141 - 1151x^142 - 1646x^143 + 180x^144 + 202x^145 + 501x^146 + 520x^147 + 702x^148 + 245x^149 - 1412x^150 - 796x^151 + 1615x^152 - 320x^153 + 317x^154 - 905x^155 + 121x^156 - 1232x^157 + 1294x^158 - 1308x^159 + 575x^160 + 935x^161 + 893x^162 - 659x^163 - 1608x^164 + 597x^165 + 1548x^166 + 1242x^167 + 785x^168 + 53x^169 - 316x^170 - 856x^171 - 886x^172 - 372x^173 + 12x^174 + 1317x^175 - 1236x^176 + 800x^177 - 129x^178 + 592x^179 + 39x^180 + 1164x^181 + 544x^182 - 880x^183 + 710x^184 + 199x^185 + 910x^186 - 121x^187 + 979x^188 - 1024x^189 - 627x^190 + 954x^191 - 332x^192 + 879x^193 - 955x^194 - 497x^195 - 730x^196 + 818x^197 - 731x^198 + 564x^199 + 689x^200 + 1530x^201 + 756x^202 + 278x^203 + 342x^204 - 1551x^205 - 761x^206 - 1127x^207 + 331x^208 + 1421x^209 - 1663x^210 + 417x^211 - 1586x^212 + 350x^213 - 854x^214 - 630x^215 - 698x^216 - 1580x^217 + 60x^218 - 57x^219 - 459x^220 - 265x^221 + 563x^222 - 316x^223 + 66x^224 + 491x^225 + 1167x^226 - 850x^227 - 352x^228 + 432x^229 - 765x^230 + 517x^231 - 766x^232 - 66x^233 - 732x^234 + 455x^235 + 32x^236 - 210x^237 + 822x^238 - 173x^239 - 739x^240 + 1156x^241 + 928x^242 + 127x^243 + 427x^244 - 601x^245 - 499x^246 + 375x^247 - 1336x^248 + 446x^249 - 602x^250 + 334x^251 + 812x^252 + 257x^253 - 1653x^254 - 115x^255$	$\mathbf{A_{ 2, 2 }} = 749 + 179x + 1578x^2 + 453x^3 + 1135x^4 - 1018x^5 + 111x^6 - 449x^7 + 1374x^8 + 115x^9 - 1355x^10 - 1314x^11 + 1107x^12 - 1025x^13 + 1216x^14 + 1604x^15 - 1419x^16 - 803x^17 - 574x^18 - 1058x^19 + 1606x^20 + 604x^21 + 723x^22 + 1273x^23 - 924x^24 - 149x^25 - 207x^26 - 513x^27 + 1502x^28 + 145x^29 - 1403x^30 - 407x^31 + 366x^32 + 1217x^33 - 1006x^34 - 1500x^35 - 831x^36 + 746x^37 + 818x^38 - 75x^39 + 846x^40 + 23x^41 + 846x^42 - 55x^43 + 810x^44 + 1242x^45 + 1145x^46 - 1606x^47 - 886x^48 - 1004x^49 - 54x^50 - 906x^51 - 1132x^52 + 1045x^53 - 1139x^54 - 312x^55 - 1589x^56 + 509x^57 - 977x^58 + 1006x^59 + 542x^60 - 1640x^61 - 1402x^62 + 152x^63 - 1052x^64 + 634x^65 - 652x^66 + 877x^67 + 991x^68 + 765x^69 - 736x^70 + 1600x^71 - 1376x^72 + 1451x^73 - 1613x^74 - 1448x^75 + 159x^76 + 1421x^77 - 32x^78 + 1445x^79 - 296x^80 - 1151x^81 + 1274x^82 - 1328x^83 + 1365x^84 + 369x^85 - 272x^86 - 891x^87 - 225x^88 + 266x^89 + 232x^90 + 40x^91 + 197x^92 - 667x^93 + 1056x^94 - 215x^95 - 1502x^96 - 1438x^97 + 1484x^98 + 829x^99 + 1127x^100 - 1239x^101 + 820x^102 - 1374x^103 - 1177x^104 - 371x^105 + 583x^106 - 658x^107 - 1576x^108 + 813x^109 + 1430x^110 + 1177x^111 + 500x^112 + 444x^113 + 144x^114 - 623x^115 + 633x^116 - 180x^117 + 658x^118 + 1632x^119 + 689x^120 - 1143x^121 + 780x^122 + 826x^123 + 1239x^124 + 932x^125 - 879x^126 + 573x^127 + 457x^128 + 740x^129 - 1658x^130 - 1507x^131 + 750x^132 + 29x^133 + 66x^134 - 904x^135 + 1281x^136 - 1477x^137 + 1413x^138 - 797x^139 - 694x^140 - 1483x^141 - 684x^142 - 580x^143 - 765x^144 - 1095x^145 - 1377x^146 + 187x^147 + 1185x^148 + 1389x^149 - 383x^150 + 528x^151 - 287x^152 + 160x^153 + 1414x^154 + 1655x^155 - 373x^156 + 1399x^157 + 1038x^158 - 728x^159 - 554x^160 - 194x^161 - 1383x^162 - 944x^163 + 836x^164 - 452x^165 - 320x^166 - 364x^167 + 1143x^168 + 1278x^169 + 165x^170 + 723x^171 + 107x^172 - 18x^173 - 716x^174 + 1529x^175 - 861x^176 - 668x^177 + 71x^178 - 595x^179 - 1449x^180 + 1597x^181 + 437x^182 - 337x^183 + 1507x^184 - 812x^185 + 955x^186 + 1129x^187 + 852x^188 - 1052x^189 + 1435x^190 - 250x^191 - 504x^192 + 1277x^193 + 1304x^194 - 957x^195 - 1124x^196 - 710x^197 + 609x^198 - 1225x^199 - 1006x^200 + 1426x^201 + 1448x^202 + 206x^203 - 528x^204 - 855x^205 - 25x^206 - 1558x^207 - 1029x^208 - 1034x^209 - 73x^210 + 1608x^211 - 1107x^212 + 980x^213 - 1457x^214 + 897x^215 + 665x^216 - 834x^217 + 701x^218 - 819x^219 - 1116x^220 - 390x^221 - 795x^222 + 282x^223 + 1249x^224 - 1444x^225 - 1014x^226 + 376x^227 - 980x^228 - 1367x^229 + 992x^230 + 1345x^231 - 1076x^232 - 1366x^233 + 1051x^234 + 775x^235 + 744x^236 - 849x^237 + 90x^238 - 1257x^239 - 1601x^240 - 868x^241 - 1071x^242 + 1482x^243 + 1547x^244 - 912x^245 - 979x^246 - 167x^247 - 543x^248 + 728x^249 - 684x^250 - 764x^251 - 1006x^252 + 1186x^253 - 145x^254 - 918x^255$	$\mathbf{A_{ 2, 3 }} = 1485 - 1003x + 611x^2 + 1377x^3 + 376x^4 - 336x^5 - 1108x^6 + 247x^7 + 1624x^8 + 1347x^9 + 907x^10 - 1370x^11 - 1244x^12 + 82x^13 - 447x^14 - 1513x^15 - 1463x^16 - 322x^17 + 969x^18 - 1400x^19 + 21x^20 + 985x^21 - 737x^22 - 112x^23 - 584x^24 + 866x^25 + 1132x^26 + 1246x^27 + 1136x^28 + 104x^29 + 789x^30 - 159x^31 - 211x^32 - 998x^33 + 726x^34 + 773x^35 + 57x^36 + 264x^37 + 96x^38 + 1434x^39 - 857x^40 + 694x^41 - 1346x^42 - 769x^43 + 869x^44 + 310x^45 + 1461x^46 + 291x^47 + 430x^48 - 115x^49 - 921x^50 - 365x^51 + 1481x^52 + 1222x^53 + 370x^54 - 749x^55 + 821x^56 - 759x^57 - 1049x^58 - 48x^59 + 1597x^60 + 1173x^61 - 923x^62 + 1415x^63 + 1170x^64 - 1319x^65 + 49x^66 - 1524x^67 - 1572x^68 - 876x^69 - 828x^70 + 1525x^71 - 1534x^72 - 54x^73 + 1044x^74 + 1315x^75 - 384x^76 + 591x^77 + 1215x^78 - 1583x^79 - 684x^80 - 827x^81 + 751x^82 + 199x^83 - 1157x^84 + 370x^85 - 459x^86 + 751x^87 - 479x^88 - 38x^89 - 134x^90 - 1318x^91 + 1583x^92 - 1157x^93 - 316x^94 - 973x^95 + 1362x^96 + 1448x^97 - 844x^98 + 1592x^99 - 1225x^100 - 125x^101 + 520x^102 + 262x^103 - 1225x^104 + 440x^105 - 963x^106 - 1023x^107 + 1109x^108 + 431x^109 - 1019x^110 + 486x^111 - 1335x^112 - 19x^113 + 1372x^114 - 476x^115 - 923x^116 + 643x^117 + 863x^118 - 1619x^119 - 428x^120 - 1107x^121 + 983x^122 - 1088x^123 + 181x^124 + 1083x^125 - 1264x^126 + 755x^127 - 472x^128 + 701x^129 - 804x^130 + 1306x^131 - 495x^132 - 614x^133 - 1478x^134 + 390x^135 - 613x^136 - 1395x^137 + 1309x^138 - 1003x^139 + 1124x^140 + 5x^141 + 792x^142 + 1161x^143 - 1480x^144 + 304x^145 + 43x^146 - 571x^147 - 295x^148 - 1046x^149 + 1234x^150 + 1509x^151 - 1407x^152 - 1308x^153 - 471x^154 + 1271x^155 + 203x^156 - 1085x^157 + 1334x^158 + 145x^159 + 1108x^160 - 1421x^161 - 135x^162 - 1125x^163 - 1447x^164 + 496x^165 - 748x^166 + 11x^167 + 1261x^168 - 1492x^169 + 937x^170 + 1155x^171 + 1444x^172 + 476x^173 - 517x^174 - 979x^175 - 920x^176 - 701x^177 + 792x^178 + 1590x^179 + 642x^180 + 418x^181 - 700x^182 - 289x^183 + 1216x^184 + 958x^185 + 60x^186 + 38x^187 - 56x^188 - 1570x^189 - 1539x^190 + 749x^191 + 540x^192 - 1428x^193 - 147x^194 + 832x^195 + 7x^196 + 1572x^197 - 1004x^198 + 33x^199 + 1077x^200 + 1186x^201 - 185x^202 + 79x^203 + 969x^204 - 1080x^205 - 264x^206 - 466x^207 + 1618x^208 + 12x^209 - 684x^210 + 1290x^211 + 1557x^212 + 362x^213 + 1265x^214 + 1574x^215 - 1444x^216 + 580x^217 + 517x^218 + 40x^219 + 1388x^220 - 962x^221 + 1396x^222 - 120x^223 - 1552x^224 - 125x^225 + 444x^226 + 803x^227 + 1496x^228 - 7x^229 - 961x^230 + 7x^231 + 996x^232 - 601x^233 + 401x^234 + 970x^235 - 130x^236 + 611x^237 + 629x^238 - 1619x^239 + 389x^240 + 614x^241 + 722x^242 - 773x^243 + 781x^244 + 830x^245 + 1201x^246 + 890x^247 - 1441x^248 - 25x^249 - 1177x^250 - 832x^251 - 1220x^252 - 225x^253 + 210x^254 + 1265x^255$
Row 3	$\mathbf{A_{ 3, 1 }} = -1242 + 1595x + 1204x^2 - 37x^3 + 402x^4 + 416x^5 + 818x^6 + 1322x^7 - 1526x^8 - 318x^9 - 236x^10 - 1186x^11 + 987x^12 - 778x^13 - 1089x^14 - 334x^15 - 588x^16 + 88x^17 + 79x^18 + 1592x^19 + 1141x^20 + 39x^21 - 460x^22 - 105x^23 - 1022x^24 + 999x^25 - 1449x^26 - 151x^27 - 522x^28 + 427x^29 + 722x^30 - 281x^31 + 985x^32 + 935x^33 - 527x^34 + 1531x^35 + 838x^36 + 320x^37 + 356x^38 - 1326x^39 + 1285x^40 - 255x^41 + 231x^42 - 905x^43 + 1096x^44 + 392x^45 + 428x^46 + 970x^47 - 11x^48 - 367x^49 + 468x^50 - 485x^51 - 490x^52 + 1064x^53 + 312x^54 - 1157x^55 - 1143x^56 + 246x^57 - 483x^58 - 1613x^59 + 95x^60 + 164x^61 + 826x^62 + 948x^63 + 454x^64 + 430x^65 + 287x^66 - 1371x^67 - 1596x^68 - 1520x^69 + 1415x^70 - 373x^71 + 852x^72 - 549x^73 + 1000x^74 + 455x^75 + 1608x^76 + 1189x^77 + 1314x^78 - 1616x^79 + 569x^80 - 803x^81 - 77x^82 + 51x^83 + 1347x^84 - 431x^85 + 1558x^86 - 1038x^87 - 280x^88 + 684x^89 + 140x^90 + 1657x^91 - 454x^92 + 425x^93 + 798x^94 + 769x^95 - 1238x^96 - 1592x^97 + 579x^98 - 895x^99 - 378x^100 + 1568x^101 + 1282x^102 + 348x^103 - 480x^104 - 637x^105 + 836x^106 - 138x^107 + 780x^108 - 195x^109 - 1141x^110 + 34x^111 - 36x^112 - 1028x^113 + 870x^114 + 1436x^115 + 1157x^116 - 805x^117 + 1227x^118 + 549x^119 + 1627x^120 + 1259x^121 + 1582x^122 - 195x^123 - 755x^124 - 1371x^125 + 1584x^126 + 973x^127 + 685x^128 - 1226x^129 + 1262x^130 - 129x^131 + 1582x^132 + 1405x^133 + 147x^134 - 117x^135 - 398x^136 + 889x^137 + 876x^138 + 627x^139 - 287x^140 + 921x^141 - 1379x^142 + 159x^143 - 1583x^144 + 1622x^145 - 1450x^146 + 176x^147 + 152x^148 - 70x^149 - 455x^150 - 139x^151 - 794x^152 - 1432x^153 - 1501x^154 + 1041x^155 - 422x^156 + 484x^157 + 1252x^158 - 173x^159 - 1337x^160 - 1308x^161 - 529x^162 + 1265x^163 - 538x^164 - 1550x^165 - 1043x^166 + 1073x^167 + 1426x^168 + 371x^169 - 1023x^170 + 1409x^171 + 1183x^172 + 1241x^173 - 1528x^174 + 1625x^175 + 264x^176 - 1646x^177 + 1427x^178 - 1627x^179 + 547x^180 + 177x^181 - 1205x^182 + 946x^183 + 746x^184 - 644x^185 + 1011x^186 - 197x^187 + 1088x^188 + 452x^189 - 1554x^190 + 29x^191 - 1346x^192 - 938x^193 + 1543x^194 - 813x^195 - 950x^196 - 254x^197 - 746x^198 - 30x^199 - 1322x^200 + 397x^201 - 601x^202 - 721x^203 + 1217x^204 + 128x^205 + 452x^206 + 664x^207 + 1587x^208 + 1474x^209 + 950x^210 - 1323x^211 + 42x^212 - 918x^213 - 315x^214 - 1603x^215 - 911x^216 - 904x^217 + 1169x^218 + 955x^219 - 743x^220 + 719x^221 - 660x^222 + 244x^223 + 1347x^224 - 1332x^225 + 1616x^226 - 1384x^227 + 696x^228 + 7x^229 - 1523x^230 - 1619x^231 + 1568x^232 - 677x^233 + 1248x^234 - 874x^235 - 133x^236 - 51x^237 - 1654x^238 - 133x^239 + 529x^240 - 1092x^241 - 990x^242 - 1542x^243 - 1428x^244 + 694x^245 - 527x^246 - 1124x^247 - 1519x^248 - 802x^249 + 1424x^250 - 954x^251 - 693x^252 - 1422x^253 - 288x^254 + 1127x^255$	$\mathbf{A_{ 3, 2 }} = -1190 + 785x + 1279x^2 + 562x^3 + 1096x^4 - 1591x^5 - 314x^6 - 758x^7 + 74x^8 - 917x^9 - 1427x^10 - 134x^11 + 1102x^12 - 355x^13 + 1122x^14 - 173x^15 + 1647x^16 + 811x^17 - 145x^18 - 1296x^19 - 533x^20 - 684x^21 - 530x^22 - 1442x^23 - 677x^24 + 1402x^25 - 867x^26 - 539x^27 + 1014x^28 - 937x^29 - 594x^30 - 1067x^31 + 1237x^32 - 1489x^33 - 1154x^34 - 702x^35 + 1320x^36 - 274x^37 + 1428x^38 - 8x^39 + 1254x^40 - 1035x^41 + 52x^42 - 150x^43 + 73x^44 + 728x^45 - 391x^46 - 458x^47 - 1636x^48 + 483x^49 - 1280x^50 - 543x^51 - 832x^52 + 1239x^53 - 1645x^54 - 977x^55 + 1016x^56 + 151x^57 - 1351x^58 - 840x^59 + 493x^60 + 1206x^61 - 433x^62 - 1347x^63 + 1443x^64 + 739x^65 - 752x^66 - 883x^67 - 822x^68 + 56x^69 + 1557x^70 + 215x^71 + 9x^72 - 204x^73 - 655x^74 - 1619x^75 - 208x^76 + 1618x^77 - 178x^78 + 1400x^79 + 35x^80 - 5x^81 - 1125x^82 + 779x^83 + 172x^84 + 1066x^85 + 1519x^86 + 374x^87 - 1411x^88 - 799x^89 - 1017x^90 + 524x^91 - 903x^92 + 1524x^93 - 1173x^94 + 260x^95 + 473x^96 - 449x^97 - 988x^98 - 1095x^99 - 579x^100 - 1104x^101 + 1485x^102 - 830x^103 + 979x^104 - 1423x^105 - 918x^106 + 287x^107 + 983x^108 + 27x^109 + 461x^110 - 1523x^111 - 276x^112 + 395x^113 + 613x^114 + 670x^115 - 930x^116 + 588x^117 - 583x^118 + 1379x^119 + 1307x^120 + 446x^121 - 779x^122 - 748x^123 - 1077x^124 - 453x^125 + 864x^126 - 1251x^127 - 1212x^128 - 1472x^129 + 632x^130 + 576x^131 + 286x^132 + 1517x^133 + 604x^134 - 1116x^135 + 602x^136 + 1087x^137 - 1497x^138 + 116x^139 - 1500x^140 + 987x^141 + 987x^142 - 327x^143 - 1106x^144 + 502x^145 - 440x^146 + 620x^147 - 364x^148 + 1312x^149 - 722x^150 + 211x^151 + 575x^152 + 721x^153 - 1294x^154 - 580x^155 + 662x^156 + 1308x^157 - 181x^158 - 1221x^159 - 1155x^160 - 103x^161 - 245x^162 - 366x^163 + 308x^164 + 932x^165 - 840x^166 + 1566x^167 + 1444x^168 + 1101x^169 - 12x^170 + 787x^171 - 277x^172 + 1278x^173 + 1447x^174 - 584x^175 + 1064x^176 - 1413x^177 + 947x^178 + 489x^179 + 1352x^180 - 449x^181 - 885x^182 + 1438x^183 + 288x^184 + 592x^185 - 86x^186 - 1659x^187 + 912x^188 - 398x^189 - 703x^190 - 992x^191 - 1161x^192 - 1635x^193 + 1508x^194 - 767x^195 - 1533x^196 + 698x^197 - 751x^198 + 1101x^199 - 1200x^200 - 119x^201 - 1397x^202 + 136x^203 - 577x^204 - 777x^205 + 1189x^206 - 701x^207 + 810x^208 + 798x^209 - 683x^210 - 1654x^211 - 735x^212 - 1221x^213 - 1581x^214 - 909x^215 - 1522x^216 + 182x^217 - 1240x^218 + 316x^219 - 1304x^220 - 38x^221 + 1657x^222 + 809x^223 + 1533x^224 - 185x^225 + 6x^226 - 933x^227 - 983x^228 + 844x^229 + 235x^230 - 57x^231 + 1626x^232 + 862x^233 + 192x^234 + 482x^235 + 135x^236 + 1075x^237 + 1530x^238 + 996x^239 + 926x^240 + 162x^241 - 1377x^242 - 1481x^243 + 595x^244 + 186x^245 - 719x^246 - 725x^247 - 241x^248 + 270x^249 + 202x^250 - 421x^251 - 1175x^252 - 1437x^253 + 164x^254 - 534x^255$	$\mathbf{A_{ 3, 3 }} = 696 - 838x + 328x^2 - 18x^3 - 861x^4 + 931x^5 + 1107x^6 - 593x^7 + 896x^8 + 1417x^9 - 801x^10 + 918x^11 + 1547x^12 - 1485x^13 + 1067x^14 + 1421x^15 - 799x^16 - 330x^17 + 288x^18 + 87x^19 - 86x^20 - 103x^21 + 765x^22 + 1228x^23 + 2x^24 - 50x^25 + 559x^26 + 1411x^27 + 349x^28 + 945x^29 + 27x^30 + 658x^31 - 1172x^32 + 1626x^33 - 1438x^34 + 110x^35 - 972x^36 - 1473x^37 - 1130x^38 - 1207x^39 + 1652x^40 + 563x^41 + 1446x^42 + 680x^43 - 1558x^44 - 425x^45 - 313x^46 + 358x^47 + 1143x^48 + 1433x^49 + 1308x^50 + 1456x^51 - 188x^52 + 1258x^53 + 709x^54 - 1188x^55 - 759x^56 + 273x^57 - 1533x^58 + 343x^59 + 1121x^60 - 1400x^61 + 1537x^62 - 916x^63 - 562x^64 + 543x^65 - 1438x^66 + 1016x^67 - 1641x^68 - 1338x^69 + 97x^70 - 533x^71 - 46x^72 - 733x^73 - 287x^74 + 1435x^75 - 1116x^76 + 848x^77 - 1418x^78 - 759x^79 + 1249x^80 + 1527x^81 - 212x^82 - 326x^83 + 96x^84 + 1645x^85 + 1300x^86 + 1492x^87 - 1248x^88 + 519x^89 + 793x^90 - 12x^91 + 1243x^92 + 1434x^93 + 241x^94 + 602x^95 + 1508x^96 + 897x^97 - 1252x^98 + 1335x^99 + 299x^100 - 692x^101 - 1421x^102 + 1245x^103 + 272x^104 + 530x^105 + 1523x^106 - 1327x^107 + 1242x^108 - 266x^109 - 86x^110 + 445x^111 - 273x^112 + 205x^113 - 1126x^114 + 240x^115 - 575x^116 - 1189x^117 + 429x^118 - 221x^119 - 467x^120 + 1282x^121 + 1506x^122 + 810x^123 + 1001x^124 - 876x^125 - 1154x^126 + 1125x^127 - 480x^128 + 1425x^129 + 1277x^130 - 1270x^131 - 1525x^132 - 488x^133 - 233x^134 + 1489x^135 - 1518x^136 - 1028x^137 + 1208x^138 - 722x^139 - 286x^140 - 523x^141 - 462x^142 - 1337x^143 + 1639x^144 + 570x^145 - 275x^146 + 790x^147 - 1609x^148 - 1277x^149 - 380x^150 + 1413x^151 - 607x^152 - 304x^153 + 1510x^154 + 961x^155 + 97x^156 - 470x^157 - 700x^158 + 1393x^159 - 272x^160 + 354x^161 + 235x^162 + 413x^163 - 727x^164 - 831x^165 + 171x^166 - 1058x^167 + 819x^168 - 1367x^169 + 11x^170 - 1285x^171 + 1612x^172 + 1060x^173 + 509x^174 + 1620x^175 - 443x^176 - 956x^177 + 338x^178 + 192x^179 - 537x^180 - 103x^181 + 125x^182 - 822x^183 - 920x^184 + 1243x^185 + 789x^186 - 31x^187 + 1610x^188 + 968x^189 - 1344x^190 + 1469x^191 - 831x^192 + 370x^193 - 1481x^194 - 304x^195 + 1237x^196 - 1583x^197 + 340x^198 + 410x^199 + 1102x^200 - 729x^201 - 1616x^202 + 940x^203 + 1057x^204 - 75x^205 + 1585x^206 + 1643x^207 + 1586x^208 - 682x^209 + 404x^210 + 401x^211 + 64x^212 - 1137x^213 - 1284x^214 - 1602x^215 + 564x^216 - 814x^217 + 145x^218 - 633x^219 - 846x^220 + 192x^221 - 926x^222 + 81x^223 - 206x^224 - 984x^225 + 1616x^226 + 1061x^227 + 1132x^228 - 1341x^229 + 831x^230 + 1465x^231 - 1429x^232 - 259x^233 + 993x^234 - 1086x^235 - 994x^236 - 427x^237 - 359x^238 + 1301x^239 - 167x^240 + 392x^241 + 837x^242 + 197x^243 - 1294x^244 + 809x^245 + 607x^246 - 1442x^247 + 908x^248 - 933x^249 - 1017x^250 + 1130x^251 - 1084x^252 - 1029x^253 + 995x^254 - 70x^255$

بردار کلید خصوصی $s \in CBD_2^3$

$s_{ 1 } = -x - x^4 - 2x^6 - x^12 - 2x^14 - x^15 - x^16 + x^19 + x^20 - x^23 + 2x^24 + x^25 - x^27 - x^28 + x^29 + x^30 - x^32 + x^33 - x^34 - x^35 + x^36 + 2x^38 - x^39 + x^40 + x^43 - x^44 - x^49 - 2x^52 - x^53 + x^57 - x^58 - x^59 + x^60 - x^61 + x^63 - x^65 + x^66 + x^67 - x^68 - x^70 + 2x^73 + x^74 + 2x^76 + x^77 - x^79 - x^80 + x^83 - x^85 - 2x^86 + 2x^88 - 2x^90 - x^91 + x^92 - x^95 - x^96 - x^97 + x^98 - x^100 + x^101 - x^103 - x^104 - x^105 + 2x^108 + 2x^109 + x^110 - x^111 + x^113 - x^115 + x^117 - x^118 + x^119 - 2x^122 - x^123 + x^124 - x^126 - x^129 + 2x^130 - x^132 + x^134 + 2x^135 + x^138 - x^139 - 2x^141 + x^144 - x^145 - x^146 + x^147 - x^148 + x^149 - x^151 - x^152 + x^156 - x^157 + x^158 - x^159 + x^160 - x^161 + 2x^162 + x^164 + x^167 + 2x^169 - x^170 + 2x^171 + x^173 + x^175 - x^176 - x^177 + 2x^179 + x^181 - x^182 - x^185 + 2x^186 - x^189 + x^191 - x^192 + x^193 + x^194 - 2x^196 + x^197 - x^199 + x^201 - 2x^203 - x^204 + x^205 - 2x^206 + x^210 + x^211 - x^212 + 2x^214 + x^216 - x^217 + 2x^218 - 2x^219 + 2x^221 + x^222 + x^223 - 2x^224 - x^226 - x^230 - x^231 + x^232 - x^233 - x^234 + x^237 + x^238 + x^242 - x^244 - x^246 - x^247 - x^249 + x^250 - x^251 + 2x^253 - x^254 + x^255$

$s_{ 2 } = 2 + x - x^2 + x^3 + x^4 - x^5 + 2x^6 - x^7 + x^8 - 2x^9 + x^11 - x^13 + x^14 - x^16 + x^19 - 2x^21 - x^24 - x^26 + x^29 - x^32 + x^33 - 2x^36 - x^39 - x^40 - x^42 - x^43 - x^45 + x^48 - x^49 + x^51 + 2x^52 + x^53 + x^55 - 2x^57 + x^58 + x^59 + 2x^60 + 2x^61 + x^63 - x^64 + 2x^66 - x^68 - x^70 + x^71 + x^75 + x^76 + 2x^77 + 2x^78 + x^79 - x^82 + x^83 - x^84 + 2x^85 - x^86 - x^87 - x^88 + x^90 + x^93 - x^95 + x^98 - x^99 + 2x^101 - x^102 - 2x^103 + 2x^104 - x^105 - x^106 + x^107 - x^110 - 2x^111 - x^112 + x^114 - x^116 - x^117 - 2x^118 - x^121 + x^122 + x^124 - 2x^125 + 2x^126 + x^128 - 2x^130 + x^133 + x^137 - x^138 - x^139 - x^140 - x^141 + x^142 - 2x^143 + x^145 - x^146 + 2x^150 + x^151 - x^154 - x^155 + x^156 + 2x^157 - x^159 + x^161 + x^163 + x^164 - x^166 + x^167 + 2x^168 + x^170 - 2x^171 + x^173 + x^174 + x^177 - x^179 - x^180 + x^181 - x^182 - 2x^183 + x^184 - x^185 - x^187 - x^188 + x^191 - x^192 + x^194 + 2x^195 - x^198 - x^199 - x^200 - x^201 - x^202 + 2x^204 + x^207 + 2x^208 + x^210 + x^211 - 2x^212 - 2x^213 - x^215 + x^219 + x^221 - x^222 + 2x^223 - x^224 + x^230 + x^232 - x^233 + 2x^234 - 2x^235 + x^236 - 2x^238 - 2x^240 - 2x^241 + x^243 - x^246 + x^249 + x^252 - x^254$

$s_{ 3 } = -1 + 2x + x^2 - x^3 + x^4 + 2x^6 - x^7 - x^8 - x^9 - 2x^10 + x^11 + x^14 - x^16 + x^19 + 2x^23 - x^24 - 2x^25 - x^27 - x^28 + x^29 - x^31 - x^32 + x^33 - 2x^35 - x^40 - x^41 - x^43 - 2x^44 + x^45 + x^46 - 2x^47 - x^48 + 2x^49 - x^50 - x^51 + x^52 + 2x^57 - x^60 + x^61 + x^62 + x^64 + x^66 + 2x^67 + x^68 + x^69 - x^72 - x^73 - x^76 - x^77 - x^78 - x^79 - x^81 + 2x^83 + 2x^84 + x^85 - x^87 - x^88 + x^89 + x^90 - x^91 + x^92 + x^94 + 2x^95 + x^97 + x^98 - x^99 - x^100 - x^103 + x^105 - 2x^106 + x^109 + x^111 + x^112 + x^113 + x^117 - x^118 - x^119 - 2x^120 - x^121 + x^122 - x^125 - x^126 + 2x^128 - x^130 + 2x^131 + x^132 + x^133 - x^135 + 2x^136 + x^140 - x^142 + x^143 - x^144 - x^145 - x^146 - x^147 - x^149 + x^152 - x^154 - 2x^155 + 2x^156 - 2x^157 - x^158 - x^159 - x^160 + x^161 + x^171 - 2x^172 + x^173 + x^174 + x^175 - x^176 + x^180 - x^182 + x^183 - x^184 - x^185 - x^187 + x^189 + x^190 + 2x^192 + x^193 + 2x^196 - 2x^199 + x^200 - x^202 + 2x^203 + 2x^205 + x^210 + x^211 - x^212 + x^213 + 2x^214 - 2x^215 + x^217 - x^218 + x^219 + 2x^221 - x^222 + x^224 - 2x^227 + x^229 + x^231 + x^233 + x^234 + x^236 - x^241 + x^243 + x^244 - x^245 + x^246 - x^247 + x^248 + x^249 + x^250 + x^251 + x^253 + x^254 + x^255$

$\|s\|_\infty = 2 \le \eta_1 = 2$

بردار خطای تصادفی $e \in CBD_2^3$

$e_{ 1 } = -2 + 2x - x^2 - x^3 + x^4 + x^5 + x^6 + x^7 - x^8 - 2x^9 + 2x^10 + x^11 + x^14 - x^15 + x^16 + x^17 - x^19 - x^20 - 2x^21 - x^23 - x^24 + x^25 + x^27 + x^28 + x^30 + x^32 - x^34 - x^35 - x^36 - x^40 + x^41 + x^44 - x^45 + 2x^46 + x^47 - 2x^49 - 2x^50 - x^52 - x^53 + x^54 + 2x^55 + x^56 + 2x^57 + x^59 + x^60 + x^61 + x^62 + x^63 - x^64 + x^66 - x^67 + x^68 + x^70 + x^71 - x^72 - x^73 - x^74 - x^75 + x^76 + x^77 + x^79 - x^81 + x^83 - x^86 + x^89 - x^90 + x^91 - x^93 - x^94 + x^95 - x^96 + x^97 - 2x^98 - x^99 + x^100 - x^101 + x^102 - 2x^103 + x^106 + x^108 - x^110 + x^112 - 2x^114 - x^116 - x^117 + x^118 + x^119 - x^120 + 2x^121 - 2x^122 - x^124 - x^125 - x^127 + x^128 - x^130 + x^131 - x^134 - x^135 - x^138 - x^139 - x^141 - x^142 + x^143 - x^146 - 2x^147 - x^148 + x^149 + x^150 + x^153 - x^158 - x^159 - x^160 - x^161 - x^162 + x^163 + x^164 - x^166 + 2x^169 - 2x^171 - 2x^172 - x^174 - x^175 + x^176 - x^178 + x^179 + x^180 + x^182 - x^186 + x^188 - x^189 + x^191 - x^192 - x^193 + x^195 - x^196 - x^198 - x^199 + 2x^200 + 2x^203 - x^204 + x^205 + x^207 + x^210 + x^211 - x^213 + x^215 - x^217 - x^218 + 2x^221 + x^223 - x^224 + 2x^229 + x^235 - x^236 + x^238 - x^239 + x^240 - 2x^241 + x^243 + 2x^244 - x^245 + x^248 - x^249 + x^250 + x^252 + 2x^253 + 2x^254 - x^255$

$e_{ 2 } = 1 + x - x^3 + 2x^4 + 2x^7 - x^9 - x^10 - 2x^11 - x^12 - x^13 + x^14 + 2x^16 + x^18 + x^19 - x^20 + x^21 - 2x^24 + x^30 - x^31 + 2x^32 - x^34 - 2x^35 - x^36 - 2x^38 - 2x^40 + x^41 - x^42 + x^43 + x^44 - x^47 - 2x^48 - x^49 + x^50 - x^51 - x^54 + 2x^56 - x^58 - x^60 + 2x^61 + x^63 - x^64 - x^65 - x^66 + x^67 + x^68 - x^70 + x^74 + x^77 + 2x^79 + x^80 - x^81 + 2x^82 - x^85 + 2x^86 + x^88 - x^89 - x^90 + x^91 - x^93 - x^94 + x^95 - x^98 - x^100 + x^101 + x^102 + x^104 - x^107 + x^110 - x^116 + x^117 + 2x^118 - x^120 + x^121 - x^122 - x^124 - x^126 - 2x^128 - x^129 - x^130 + x^131 + x^133 + 2x^135 + x^136 + x^138 + x^139 - x^140 + x^142 + x^144 - x^147 + 2x^149 + 2x^150 - x^151 - x^154 + x^155 - x^156 + x^157 - x^159 - x^163 + x^165 + 2x^166 + x^167 + 2x^168 - x^170 + 2x^171 - x^172 - x^173 - x^174 + x^175 - 2x^178 - x^180 - x^184 - x^185 - 2x^186 + x^189 + x^191 + x^192 - x^195 + x^197 - x^198 + x^199 - x^200 + x^201 + x^202 - x^208 + x^209 + x^212 + x^216 - x^218 + x^221 + x^222 - x^223 - x^225 - x^226 - x^227 - x^228 - x^229 - x^230 + x^231 + x^235 + x^236 + x^237 + x^240 + x^241 - x^243 - x^244 - x^245 - x^247 + x^249 + 2x^250 + x^251 + 2x^254$

$e_{ 3 } = -2 + x^2 - x^3 + 2x^4 - x^6 + 2x^7 - x^8 + x^9 - x^10 - x^11 - x^12 + x^13 + x^17 - x^18 - x^19 + x^20 + x^21 - x^24 - 2x^25 + x^27 - x^28 - x^33 + x^34 + x^35 + x^37 - x^38 - x^39 + x^41 - x^42 + x^43 + x^44 + x^48 - x^52 - x^53 - x^54 + x^57 - 2x^58 - x^60 + x^61 + 2x^63 - x^64 - x^65 - x^66 + x^67 - x^70 - x^71 - x^72 + x^73 - x^75 - x^76 + 2x^77 - x^78 + x^80 - x^83 + x^84 + x^85 + x^89 + x^91 + x^92 - x^93 + x^95 - x^97 - 2x^101 - x^102 + x^104 - x^105 + x^107 + x^109 + x^111 + x^112 - x^113 + x^114 - x^117 - x^118 - x^120 - x^121 - x^124 - 2x^125 - x^126 - 2x^128 - x^129 - x^132 - x^133 - x^135 + 2x^136 - x^138 + 2x^139 - x^142 - x^143 - 2x^144 + x^150 + 2x^151 - 2x^153 - x^154 + x^155 + x^156 - 2x^157 + 2x^159 + x^161 + x^162 + x^164 + x^167 - x^169 + x^170 + x^179 + x^181 - x^182 - 2x^184 - x^186 + x^187 + x^188 + x^189 + x^190 + x^191 + x^193 + x^194 - x^196 - x^198 + 2x^199 - x^200 + x^203 + x^204 - x^205 - x^207 - x^210 + x^211 + x^212 + x^214 - x^215 + x^217 + x^219 + 2x^222 + x^223 + x^224 + x^225 + x^226 + x^228 + x^229 + x^230 - x^232 - 2x^234 + x^237 + x^239 - x^240 - 2x^244 - x^247 - x^249 - x^250 - 2x^251 - x^252 - x^253 + 2x^254 - x^255$

$\|e\|_\infty = 2 \le \eta_1 = 2$

۲. بردار کلید عمومی محاسبه‌شده $t = As + e \pmod{3329}$

$t_{ 1 } = -748 - 252x + 5x^2 + 601x^3 + 685x^4 - 1050x^5 + 14x^6 - 1407x^7 - 1233x^8 + 60x^9 + 1332x^10 + 801x^11 + 38x^12 + 184x^13 + 1611x^14 - 545x^15 - 638x^16 + 387x^17 - 1072x^18 + 706x^19 - 1391x^20 - 411x^21 + 291x^22 - 471x^23 - 545x^24 - 941x^25 - 1231x^26 - 1477x^27 - 1171x^28 + 1600x^29 + 1656x^30 - 314x^31 + 348x^32 - 1201x^33 - 226x^34 + 987x^35 + 640x^36 - 105x^37 + 525x^38 + 37x^39 + 131x^40 - 635x^41 - 214x^42 + 1142x^43 + 1036x^44 + 1266x^45 + 976x^46 - 932x^47 - 1081x^48 - 972x^49 + 881x^50 - 739x^51 - 1382x^52 - 530x^53 + 1581x^54 - 836x^55 - 402x^56 - 746x^57 + 911x^58 - 218x^59 + 1635x^60 - 1651x^61 + 1151x^62 + 410x^63 - 1471x^64 - 827x^65 - 1348x^66 - 110x^67 - 958x^68 - 367x^69 + 624x^70 + 97x^71 - 212x^72 - 1417x^73 + 26x^74 + 1207x^75 + 1513x^76 + 257x^77 + 167x^78 + 1155x^79 + 121x^80 + 1651x^81 - 715x^82 + 1193x^83 + 400x^84 - 257x^85 - 250x^86 + 159x^87 - 895x^88 + 656x^89 - 1541x^90 - 853x^91 + 666x^92 - 477x^93 - 1187x^94 - 833x^95 + 441x^96 - 917x^97 + 294x^98 - 692x^99 - 671x^100 + 1347x^101 + 175x^102 - 1005x^103 + 369x^104 - 7x^105 + 132x^106 + 406x^107 + 424x^108 + 1246x^109 + 302x^110 + 698x^111 - 48x^112 - 1233x^113 - 519x^114 + 1600x^115 + 133x^116 + 1152x^117 - 419x^118 + 1023x^119 + 1033x^120 - 557x^121 + 226x^122 + 1033x^123 + 560x^124 + 1500x^125 - 929x^126 + 290x^127 + 1020x^128 - 978x^129 + 1013x^130 + 750x^131 - 606x^132 + 1500x^133 - 457x^134 - 883x^135 - 280x^136 + 1127x^137 + 756x^138 + 1643x^139 + 692x^140 - 1110x^141 - 875x^142 + 1624x^143 - 1327x^144 - 221x^145 + 626x^146 - 158x^147 - 1115x^148 + 738x^149 + 947x^150 + 1121x^151 + 1024x^152 - 451x^153 - 368x^154 + 89x^155 - 530x^156 - 928x^157 + 1278x^158 + 241x^159 + 884x^160 + 944x^161 + x^162 + 889x^163 - 51x^164 - 732x^165 - 1479x^166 + 697x^167 + 1614x^168 + 189x^169 + 1386x^170 - 1120x^171 - 1018x^172 - 509x^173 - 773x^174 - 746x^175 - 348x^176 + 319x^177 - 32x^178 + 1409x^179 + 1083x^180 + 1461x^181 + 1486x^182 - 81x^183 - 469x^184 - 1453x^185 + 264x^186 + 416x^187 - 366x^188 + 1438x^189 + 1614x^190 - 160x^191 - 1636x^192 + 77x^193 - 832x^194 + 551x^195 - 1536x^196 + 1465x^197 - 246x^198 - 1632x^199 - 257x^200 - 1173x^201 + 732x^202 + 170x^203 - 573x^204 + 510x^205 + 1558x^206 - 382x^207 - 281x^208 - 1389x^209 + 864x^210 + 181x^211 - 492x^212 + 934x^213 + 1250x^214 + 201x^215 + 1463x^216 + 246x^217 + 655x^218 - 868x^219 + 116x^220 - 1358x^221 - 1178x^222 + 485x^223 + 1568x^224 + 1387x^225 - 294x^226 - 1620x^227 + 1482x^228 - 84x^229 - 80x^230 + 1474x^231 + 180x^232 + 841x^233 + 1255x^234 - 290x^235 + 197x^236 + 174x^237 + 552x^238 + 313x^239 - 595x^240 + 1042x^241 - 632x^242 + 1046x^243 + 551x^244 + 1027x^245 - 390x^246 + 1014x^247 + 59x^248 + 1632x^249 + 390x^250 + 1010x^251 - 1562x^252 + 770x^253 - 264x^254 + 1169x^255$

$t_{ 2 } = 826 + 1589x + 1129x^2 + 564x^3 - 751x^4 - 140x^5 + 598x^6 - 1473x^7 - 1307x^8 - 426x^9 + 821x^10 + 1089x^11 - 1184x^12 - 682x^13 - 579x^14 - 695x^15 - 1116x^16 + 628x^17 - 1600x^18 + 869x^19 - 597x^20 - 1485x^21 + 1072x^22 - 1416x^23 - 460x^24 - 194x^25 + 928x^26 + 1200x^27 - 16x^28 - 259x^29 - 1515x^30 + 516x^31 - 1324x^32 - 150x^33 - 126x^34 - 470x^35 - 1003x^36 - 506x^37 + 1273x^38 - 190x^39 - 1080x^40 - 180x^41 - 772x^42 + 1556x^43 - 887x^44 - 373x^45 - 667x^46 + 375x^47 + 35x^48 + 946x^49 + 989x^50 + 1151x^51 - 270x^52 - 1064x^53 - 1354x^54 + 1035x^55 - 841x^56 - 88x^57 + 111x^58 + 597x^59 - 1133x^60 - 1643x^61 + 153x^62 - 1088x^63 - 284x^64 + 152x^65 - 328x^66 + 855x^67 - 412x^68 + 76x^69 - 178x^70 - 1345x^71 + 363x^72 + 579x^73 - 1270x^74 + 1115x^75 + 1448x^76 + 954x^77 + 329x^78 + 900x^79 - 1533x^80 + 1607x^81 - 531x^82 - 1027x^83 + 865x^84 - 712x^85 + 1045x^86 + 236x^87 + 1019x^88 + 1287x^89 - 53x^90 - 1288x^91 + 1265x^92 + 30x^93 + 780x^94 - 527x^95 + 849x^96 - 327x^97 - 1035x^98 + 751x^99 + 1282x^100 + 162x^101 - 919x^102 - 1590x^103 - 580x^104 - 868x^105 + 1332x^106 + 160x^107 + 507x^108 - 834x^109 + 1543x^110 - 163x^111 + 1543x^112 + 1083x^113 - 138x^114 + 900x^115 - 1094x^116 + 1166x^117 - 568x^118 - 769x^119 - 1074x^120 + 223x^121 + 218x^122 + 1001x^123 - 1606x^124 - 346x^125 + 1648x^126 - 886x^127 + 1573x^128 + 1040x^129 + 1053x^130 - 97x^131 - 1362x^132 - 1630x^133 - 1030x^134 + 860x^135 - 1611x^136 + 1415x^137 + 91x^138 - 511x^139 - 1614x^140 - 1556x^141 - 1296x^142 - 1609x^143 + 718x^144 + 1160x^145 - 1434x^146 - 431x^147 + 1301x^148 - 40x^149 + 999x^150 + 50x^151 - 1398x^152 - 1139x^153 - 1446x^154 - 415x^155 + 45x^156 + 150x^157 - 793x^158 - 1254x^159 - 1203x^160 - 470x^161 - 1339x^162 + 1390x^163 + 488x^164 + 471x^165 - 751x^166 - 500x^167 + 1408x^168 - 228x^169 + 1559x^170 + 608x^171 - 1130x^172 + 296x^173 - 1539x^174 + 101x^175 + 937x^176 + 452x^177 + 750x^178 - 1489x^179 + 155x^180 - 638x^181 - 881x^182 + 599x^183 + 994x^184 - 200x^185 - 581x^186 - 183x^187 - 926x^188 - 1021x^189 + 1295x^190 - 560x^191 - 1199x^192 + 1301x^193 - 574x^194 + 751x^195 - 290x^196 - 1289x^197 - 1185x^198 + 943x^199 - 1442x^200 + 1512x^201 - 1342x^202 - 1661x^203 - 1132x^204 + 216x^205 + 1153x^206 - 306x^207 - 1373x^208 + 474x^209 + 427x^210 - 609x^211 - 564x^212 - 1067x^213 + 337x^214 - 549x^215 - 1435x^216 + 733x^217 - 1635x^218 + 815x^219 - 1469x^220 + 324x^221 + 426x^222 + 736x^223 + 961x^224 + 686x^225 - 1664x^226 - 672x^227 - 476x^228 - 1415x^229 - 479x^230 + 1309x^231 - 1313x^232 - 1231x^233 - 153x^234 - 1106x^235 + 837x^236 - 402x^237 + 1647x^238 + 1270x^239 - 1115x^240 + 713x^241 + 210x^242 - 468x^243 - 149x^244 - 785x^245 + 152x^246 - 1490x^247 - 173x^248 - 782x^249 + 769x^250 + 600x^251 + 1618x^252 + 373x^253 + 34x^254 - 854x^255$

$t_{ 3 } = 435 - 875x + 570x^2 + 1664x^3 + 938x^4 + 131x^5 - 53x^6 + 1494x^7 - 794x^8 - 1098x^9 + 372x^10 - 729x^11 - 1243x^12 + 1246x^13 + 582x^14 + 1035x^15 + 380x^16 + 373x^17 + 1462x^18 - 411x^19 + 667x^20 + 601x^21 + 539x^22 - 1541x^23 - 1142x^24 - 1261x^25 - 635x^26 + 278x^27 + 995x^28 - 662x^29 - 37x^30 + 444x^31 - 1486x^32 - 1553x^33 + 1204x^34 - 1074x^35 + 589x^36 + 816x^37 - 673x^38 + 1460x^39 + 1534x^40 + 954x^41 - 522x^42 - 1455x^43 - 1373x^44 - 1612x^45 - 1471x^46 + 1167x^47 + 40x^48 - 1494x^49 - 721x^50 + 713x^51 - 514x^52 - 648x^53 - 1450x^54 + 1494x^55 + 357x^56 + 518x^57 - 414x^58 - 1580x^59 + 340x^60 + 1522x^61 + 1207x^62 - 959x^63 + 126x^64 - 1595x^65 + 616x^66 + 957x^67 - 590x^68 + 659x^69 - 390x^70 + 1350x^71 - 1446x^72 + 1664x^73 - 1182x^74 + 235x^75 - 953x^76 - 1524x^77 - 715x^78 + 267x^79 - 328x^80 - 1584x^81 + 212x^82 - 1238x^83 + 580x^84 + 1352x^85 + 1635x^86 + 537x^87 - 918x^88 + 1067x^89 + 1538x^90 - 187x^91 - 1482x^92 + 1436x^93 - 202x^94 + 1025x^95 + 72x^96 - 219x^97 + 1535x^98 - 406x^99 - 315x^100 - 1585x^101 + 441x^102 - 958x^103 + 1265x^104 - 431x^105 - 362x^106 - 409x^107 + 1496x^108 - 1271x^109 + 1102x^110 + 358x^111 - 618x^112 + 352x^113 + 1651x^114 - 699x^115 + 727x^116 - 208x^117 - 1163x^118 + 1127x^119 - 463x^120 - 150x^121 - 23x^122 - 1012x^123 - 787x^124 + 179x^125 - 817x^126 - 892x^127 - 910x^128 - 396x^129 - 1147x^130 - 113x^131 + 884x^132 - 1610x^133 - 1311x^134 + 892x^135 - 709x^136 + 1310x^137 - 482x^138 + 637x^139 + 1577x^140 + 580x^141 + 464x^142 - 1313x^143 - 1113x^144 - 443x^145 + 1252x^146 + 1420x^147 - 22x^148 - 852x^149 + 442x^150 - 447x^151 + 1510x^152 + 1027x^153 + 1417x^154 - 1517x^155 - 333x^156 + 1008x^157 + 1105x^158 + 423x^159 + 845x^160 - 62x^161 + 1323x^162 + 945x^163 + 1629x^164 - 153x^165 + 458x^166 + 1105x^167 - 1318x^168 - 1453x^169 + 1403x^170 + 843x^171 + 867x^172 - 221x^173 + 232x^174 + 1327x^175 + 283x^176 - 1239x^177 + 928x^178 - 698x^179 + 912x^180 - 688x^181 + 1533x^182 + 105x^183 + 61x^184 + 195x^185 + 504x^186 - 1053x^187 + 1580x^188 - 1635x^189 + 479x^190 - 892x^191 + 265x^192 - 464x^193 + 1225x^194 + 1193x^195 + 1469x^196 + 573x^197 - 38x^198 + 588x^199 - 1243x^200 - 1166x^201 - 82x^202 + 1447x^203 + 1026x^204 - 135x^205 + 932x^206 + 1491x^207 + 1476x^208 - 317x^209 + 1118x^210 - 451x^211 + 573x^212 - 715x^213 - 671x^214 - 1054x^215 + 1290x^216 - 1011x^217 - 1107x^218 + 522x^219 - 1464x^220 - 341x^221 + 1401x^222 + 4x^223 + 1119x^224 - 818x^225 + 1078x^226 + 831x^227 + 824x^228 + 466x^229 + 49x^230 - 1149x^231 + 1550x^232 - 741x^233 + 1116x^234 - 959x^235 - 1649x^236 + 1635x^237 - 376x^238 + 882x^239 + 131x^240 + 1180x^241 + 1288x^242 + 679x^243 - 1260x^244 - 305x^245 - 894x^246 - 957x^247 - 50x^248 - 1233x^249 - 851x^250 - 70x^251 + 620x^252 - 29x^253 - 115x^254 + 221x^255$

قالب‌بندی کلیدهای خروجی سیستم (Key Pair)

Public Key (PK):

$$ PK = (A_{3 \times 3}, t_{3 \times 1}) $$

Secret Key (SK):

$$ SK = (s_{3 \times 1}) $$

مرحله دوم - رمزگذاری (Encryption)

$u = A^T r + e_1 \pmod{3329}$

متن پیام ورودی باب جهت ارسال به آلیس:

                "Advanced Cryptography Class, Dr. Najafi"
            

Bits Count: 312 | Bits Preview: 0100000101100100011101100110000101101110011000110110010101100100...

۱. بردارهای تصادفی و خطای رمزگذاری ( $$r, e_1, e_2$$ )

Random Vector $r \in CBD_2^3$:

$r_{ 1 } = 1 - x - 2x^3 + x^5 + 2x^7 + x^9 - x^10 - x^11 - x^13 + x^14 + x^16 + x^17 - x^19 + x^20 + x^21 + x^22 - x^23 - x^24 + x^25 - x^26 - x^27 - x^28 + x^30 + x^33 + x^35 - x^36 + 2x^37 + x^38 - 2x^39 + x^40 - x^42 + x^43 - x^45 + x^49 - x^50 - 2x^51 - 2x^52 - x^53 + x^55 - 2x^58 - 2x^60 - x^61 - x^63 - x^65 + x^66 + x^70 - x^71 + 2x^72 + x^73 - x^75 - x^79 - x^83 + x^84 - x^85 + x^86 + x^89 - x^91 - x^92 - x^93 - 2x^95 - x^97 + x^99 - x^100 - x^101 + x^102 - x^108 + 2x^109 + x^111 - x^112 - 2x^113 - x^114 + x^120 - 2x^121 - x^122 + x^124 + x^127 - x^128 + x^130 - x^132 + x^133 + 2x^134 - x^135 + x^136 - x^137 + x^138 - x^139 - x^141 - x^143 - x^146 + x^148 + x^149 - x^150 + x^151 - x^152 - x^153 + x^154 + x^155 + x^157 - x^158 - x^159 - x^165 - x^166 - x^167 - x^168 + x^170 + x^171 + 2x^172 - x^173 - 2x^175 - x^177 - x^178 - x^181 - x^183 - x^184 - x^187 + x^188 + x^191 - x^192 + x^193 - x^197 + x^198 + x^202 + x^208 - 2x^209 + 2x^210 + x^211 + x^212 - x^213 + x^214 - x^218 + 2x^219 - 2x^220 + x^221 + x^224 + x^225 + x^226 - 2x^227 - x^228 + x^229 - x^230 + x^231 - x^232 - x^234 - x^235 + x^237 + x^239 + x^241 - x^242 - x^244 + x^245 + 2x^246 - x^249 + x^250 - x^251 + 2x^252 - x^254 - x^255$

$r_{ 2 } = -x^4 - 2x^5 + 2x^6 - x^7 + x^8 + x^9 + 2x^10 - x^12 - 2x^14 - 2x^15 + x^16 - x^17 - x^19 - 2x^22 - x^23 + x^28 + x^31 + 2x^32 + x^33 - x^34 + x^38 - x^39 - 2x^40 - 2x^41 + x^42 + x^43 + 2x^44 + x^49 + x^50 + x^51 + x^52 - x^54 - x^55 - x^56 + x^57 + x^59 - x^60 + x^61 - x^62 + 2x^65 - x^66 - x^67 - x^68 + x^70 - x^71 - x^72 - x^73 + x^76 - 2x^77 + x^78 + 2x^79 + x^80 - 2x^81 - x^82 + x^84 - x^86 + x^88 + 2x^89 - 2x^90 - x^92 + 2x^93 + x^94 - x^95 - x^96 + x^97 - 2x^99 - x^101 + x^105 - x^106 + x^107 + x^109 + x^113 - x^114 + x^119 - 2x^120 - x^121 + x^122 + x^124 - x^126 + x^128 + x^129 - x^130 - x^132 - x^135 - 2x^137 + x^139 + x^140 + x^141 + x^142 + x^143 - x^145 + x^146 - x^147 - x^148 + x^149 + x^150 + x^152 - x^153 + x^155 + 2x^157 - x^158 - x^161 + 2x^163 + x^164 + x^165 + x^166 + x^167 - x^168 + x^172 + x^173 + 2x^174 + 2x^177 + 2x^178 + 2x^179 + x^181 + x^183 + x^185 - x^186 - x^190 - x^191 + x^193 - x^194 - x^195 + x^196 + x^198 + x^199 + x^200 - x^201 - x^202 + x^204 - x^205 - x^206 + x^208 + x^209 + x^210 + 2x^212 + x^213 - x^215 + x^217 - 2x^218 + x^219 - x^220 + x^221 - x^222 - x^225 - x^229 + x^230 + 2x^231 + x^232 + x^233 + x^235 - x^236 + 2x^237 - x^240 + x^242 + 2x^243 + x^247 + x^248 - x^249 - x^250 - x^251 - x^252 - x^253$

$r_{ 3 } = x + x^2 - x^3 - 2x^5 + x^7 + x^8 - x^9 + x^14 + x^15 + x^16 + x^17 + x^18 + x^20 - x^23 + x^26 + x^27 + x^29 - x^30 + x^31 - 2x^33 + x^34 + 2x^35 - 2x^38 - x^41 + x^42 + x^45 + x^47 + x^52 - x^53 - x^55 + x^56 + x^57 - x^58 + x^61 + x^64 + x^65 + x^68 - 2x^69 + x^71 + x^72 + x^73 - 2x^74 + 2x^77 + x^79 - x^80 - x^81 + x^83 - x^84 + x^86 - 2x^90 - x^92 - x^93 + 2x^95 - 2x^97 - x^98 - x^101 + x^105 - x^107 + x^108 - x^109 - x^110 - x^111 - x^113 - x^114 - x^116 - x^119 - x^121 - 2x^122 - x^125 + x^128 + x^129 + x^130 - x^132 + x^134 + x^135 + 2x^139 - x^141 + 2x^143 + x^144 + x^146 - x^148 - x^149 - x^150 + x^151 - x^154 - 2x^155 + 2x^160 - 2x^161 - 2x^162 - 2x^164 - 2x^165 - x^166 - 2x^167 - 2x^168 - 2x^169 + 2x^170 - x^171 + 2x^172 - x^178 - x^179 - x^180 + x^181 - x^182 + x^183 + x^184 - 2x^185 + x^186 + x^188 + 2x^189 + x^191 - x^192 + x^194 - x^195 + 2x^196 + x^198 + x^199 + 2x^201 + x^202 - x^203 - x^205 + 2x^208 + x^209 - 2x^211 - x^213 + x^214 - 2x^216 - x^218 - 2x^219 - x^221 + x^222 + 2x^225 - x^226 - 2x^228 - x^229 - x^230 + x^231 - x^235 + 2x^236 + x^238 - x^242 + x^245 - x^246 - x^247 + x^248 - x^249 - x^250 + x^251 - x^252 - x^254$

Error Vector $e_1 \in CBD_2^3$:

$e_{1, 1 } = -1 + x - x^5 + x^6 - x^7 + x^8 - 2x^9 - x^10 + 2x^11 - x^13 + x^14 - x^15 + 2x^16 - x^17 + x^18 - x^19 - 2x^20 - x^21 + x^22 - 2x^24 + x^27 - x^28 + x^30 + 2x^31 + x^33 - x^34 - 2x^35 + x^36 - x^38 - x^39 + x^40 + x^41 - x^42 + x^44 + x^45 + x^46 - x^47 + x^49 + 2x^50 - 2x^51 + x^52 + x^53 - 2x^54 + 2x^57 - x^59 - x^60 - 2x^61 - x^63 + 2x^64 - 2x^66 - x^70 + x^71 + 2x^72 + x^73 - 2x^74 + x^77 + x^78 - x^79 + 2x^81 - 2x^82 + 2x^85 + x^86 - x^87 - 2x^88 + 2x^89 + x^91 + x^94 + x^95 + x^96 - x^97 + 2x^99 + x^100 + x^101 - x^102 + x^106 - x^107 + x^108 + 2x^109 - 2x^111 + x^113 - 2x^115 - x^117 + 2x^120 + x^121 - x^122 + x^123 - 2x^124 + x^125 - x^127 - x^128 - x^129 + 2x^133 + 2x^134 + x^135 - x^136 - x^137 - x^138 + x^139 - 2x^141 - x^146 - x^148 + 2x^150 + x^151 - 2x^152 + x^156 + x^158 - x^159 + x^160 - x^161 + x^162 - x^163 + x^164 - x^165 - x^166 + x^167 + x^169 - x^172 + 2x^173 - x^174 + x^175 + 2x^176 - 2x^178 + x^181 - x^185 + x^188 - x^189 + x^191 - x^193 - x^196 - x^198 - x^199 + x^200 + x^201 + x^202 + x^203 - 2x^204 - x^205 - x^208 + x^209 - x^211 - x^212 - x^213 - x^214 - 2x^215 - x^216 - x^217 - x^219 - x^220 - 2x^221 + x^222 - x^223 - x^224 - x^225 + x^228 - x^232 - x^233 - x^235 + x^236 + x^237 + x^238 + x^239 + 2x^241 + x^242 - x^243 + x^245 - 2x^246 - 2x^247 + x^248 + 2x^249 - x^250 + x^251 + 2x^252 - 2x^255$

$e_{1, 2 } = -1 - x + x^5 - 2x^7 - x^8 - x^9 - x^10 - x^11 + x^12 - x^13 - x^17 + x^18 + x^22 - 2x^25 - x^26 - x^28 - x^29 + x^34 + x^35 + x^36 + x^37 + 2x^38 + x^39 - x^41 + x^44 + x^46 + x^48 + x^49 - x^51 + 2x^52 - x^53 + x^54 + x^56 + x^57 + x^58 - x^59 + x^60 + 2x^61 + x^64 - x^65 + x^66 + x^67 - x^68 + 2x^69 + x^70 - x^71 + x^72 + 2x^74 + x^75 + x^77 + x^80 - x^81 - 2x^82 - 2x^84 - 2x^85 + 2x^86 + x^87 + 2x^88 - x^91 + x^93 - x^94 + x^95 - x^97 + x^101 - x^102 - x^103 - x^104 + x^107 + 2x^108 - x^110 - x^111 - x^112 + x^115 - x^116 - x^117 + x^118 - 2x^121 + x^122 - x^123 + x^124 - x^125 - x^126 - x^127 - x^128 - x^129 + x^130 + 2x^133 - 2x^134 + x^135 + x^136 - x^137 - x^138 + x^139 + x^140 + x^141 + x^142 + x^144 + x^145 - x^146 - x^147 + x^149 + x^150 + x^153 - x^154 + x^156 + 2x^159 - x^160 + x^161 + 2x^164 - x^165 - x^167 - x^168 - x^169 - x^170 - x^171 - x^172 - x^173 - 2x^174 - x^178 - x^180 + x^181 + x^183 - x^184 + x^186 - x^188 - 2x^189 - x^190 + x^192 - 2x^193 - 2x^196 + x^198 + x^199 + x^200 - x^202 + x^205 + x^206 - x^207 + x^209 - x^212 + x^213 + x^215 - x^216 + x^218 + x^219 + x^220 + x^221 + x^223 + x^224 + 2x^226 + x^227 - x^228 + x^229 - x^230 - x^233 + x^234 - x^236 - x^237 - 2x^238 - x^241 + x^242 - x^245 - x^246 + x^247 - x^248 + x^249 - x^250 + x^254 + x^255$

$e_{1, 3 } = 1 + x - x^2 + x^3 + x^4 - x^5 + x^7 - x^8 - x^12 - x^13 + x^14 - 2x^15 + x^16 + x^17 - 2x^21 + x^22 + x^23 + 2x^24 + x^25 + x^29 + x^31 + x^32 - x^34 - x^36 - x^37 - x^38 + x^39 - x^41 + x^44 - x^45 - x^46 - x^50 + x^51 - x^52 + x^53 + x^54 + x^56 - x^57 + x^59 - x^61 - x^62 - x^65 + x^67 + x^73 + x^74 - x^75 - 2x^77 - x^78 - x^79 + x^80 + x^81 + x^82 + x^84 - x^85 + x^86 - x^90 - 2x^91 + 2x^92 - x^93 - x^96 - x^97 - x^98 - 2x^100 + x^102 + x^103 + x^104 + 2x^105 - x^106 + 2x^107 + x^108 - x^109 - x^111 - x^114 - x^115 + x^116 + 2x^119 - x^120 - x^122 + x^123 + x^125 - 2x^127 - x^128 + 2x^129 - x^132 + x^134 + x^135 - x^138 + x^141 + x^142 + x^143 - 2x^144 + x^145 + 2x^146 + x^148 + x^151 + x^154 + x^156 - 2x^157 + x^159 - x^166 - x^172 + x^173 + x^174 + 2x^175 - 2x^176 - x^179 - x^181 + x^182 - x^183 - x^184 + 2x^188 + 2x^189 - 2x^190 - x^191 + x^192 + 2x^194 + x^195 + x^196 - 2x^197 - x^200 + x^201 - 2x^202 - x^204 - x^206 + x^207 + 2x^209 - 2x^210 - x^212 - x^213 - x^214 + x^217 - x^219 - x^220 - x^221 + x^223 + x^224 - x^226 + x^227 + x^229 - x^230 - x^231 - x^232 - x^233 + x^234 + x^235 - x^237 + x^238 - x^239 - x^240 + x^243 - x^246 - x^247 + x^248 - x^249 - x^250 + x^252 - x^253 + x^254$

۲. بخش اول متن رمز شده: بردار $u = A^T r + e_1 \pmod{3329}$

$$ u = A^T \cdot r + e_1 \pmod{3329} $$

$u_{ 1 } = -1622 - 162x + 298x^2 + 452x^3 + 1414x^4 + 1331x^5 + 305x^6 + 1085x^7 + 393x^8 - 763x^9 - 1072x^10 - 646x^11 + 1085x^12 - 965x^13 - 427x^14 + 771x^15 - 1393x^16 - 1368x^17 - 602x^18 - 1010x^19 + 1581x^20 - 856x^21 + 469x^22 - 615x^23 + 196x^24 + 83x^25 + 318x^26 + 585x^27 + 1337x^28 - 165x^29 - 314x^30 + 767x^31 - 900x^32 - 689x^33 - 1019x^34 - 1273x^35 - 1647x^36 + 217x^37 - 542x^38 - 1422x^39 + 609x^40 - 652x^41 - 515x^42 + 1564x^43 - 105x^44 - 563x^45 - 1354x^46 + 78x^47 - 1599x^48 - 13x^49 + 1564x^50 + 777x^51 - 1546x^52 - 708x^53 + 48x^54 - 953x^55 - 723x^56 - 320x^57 + 1656x^58 + 616x^59 + 1353x^60 - 534x^61 + 1482x^62 - 1601x^63 - 830x^64 + 186x^65 - 673x^66 - 135x^67 + 61x^68 + 1022x^70 + 1017x^71 - 994x^72 - 1419x^73 + 1066x^74 + 1146x^75 + 461x^76 + 224x^77 + 770x^78 + 1092x^79 - 1627x^80 + 1506x^81 + 1022x^82 + 1144x^83 - 334x^84 + 779x^85 - 1170x^86 - 1647x^87 - 873x^88 + 204x^89 + 929x^90 + 278x^91 - 24x^92 + 516x^93 - 565x^94 - 242x^95 - 221x^96 - 783x^97 + 554x^98 + 402x^99 - 1057x^100 + 1543x^101 + 196x^102 + 451x^103 - 478x^104 - 1484x^105 - 1339x^106 + 1551x^107 - 224x^108 + 519x^109 - 172x^110 + 797x^111 + 1521x^112 + 139x^113 - 506x^114 + 581x^115 - 852x^116 - 949x^117 + 1129x^118 - 569x^119 - 20x^120 - 54x^121 + 782x^122 + 383x^123 - 1329x^124 - 377x^125 + 965x^126 + 714x^127 - 679x^128 + 1392x^129 - 1362x^130 - 747x^131 - 1617x^132 - 654x^133 - 303x^134 - 647x^135 - 1621x^136 + 1341x^137 - 233x^138 - 1635x^139 - 332x^140 + 259x^141 - 1340x^142 - 886x^143 + 836x^144 + 1470x^145 + 273x^146 - 529x^147 + 687x^148 - 36x^149 + 256x^150 + 587x^151 - 516x^152 - 1149x^153 + 222x^154 - 1618x^155 - 307x^156 - 827x^157 - 814x^158 + 1526x^159 - 194x^160 - 1348x^161 - 1388x^162 + 568x^163 - 159x^164 + 1338x^165 - 1664x^166 - 921x^167 - 127x^168 + 1451x^169 - 225x^170 + 232x^171 - 1189x^172 - 887x^173 + 851x^174 - 438x^175 - 1663x^176 - 911x^177 - 591x^178 + 1377x^179 - 558x^180 + 528x^181 + 1034x^182 + 806x^183 + 401x^184 - 1072x^185 + 1615x^186 - 742x^187 - 1538x^188 + 618x^189 - 663x^190 + 222x^191 + 1196x^192 - 784x^193 + 1234x^194 - 1494x^195 - 995x^196 + 1142x^197 + 1335x^198 - 651x^199 + 1623x^200 - 254x^201 - 196x^202 - 15x^203 - 460x^204 - 169x^205 - 962x^206 - 244x^207 + 532x^208 - 1541x^209 + 1411x^210 - 702x^211 - 1458x^212 - 117x^213 + 266x^214 + 1193x^215 + 1332x^216 - 845x^217 + 205x^218 - 1489x^219 - 1025x^220 - 1132x^221 - 236x^222 - 81x^223 - 160x^224 + 249x^225 + 286x^226 - 1329x^227 + 797x^228 + 1419x^229 + 1484x^230 + 391x^231 - 964x^232 + 1404x^233 - 1262x^234 - 1146x^235 + 1209x^236 + 957x^237 - 1197x^238 + 198x^239 + 90x^240 + 985x^241 + 530x^242 - 276x^243 - 1071x^244 + 711x^245 - 1358x^246 + 1051x^247 - 1506x^248 + 1416x^249 - 1138x^250 - 173x^251 - 1386x^252 - 1520x^253 - 1106x^254 - 482x^255$

$u_{ 2 } = -711 + 1161x - 1096x^2 - 335x^3 - 891x^4 - 1370x^5 - 1088x^6 + 1376x^7 + 1406x^8 + 1374x^9 - 568x^10 - 1466x^11 - 1618x^12 - 1001x^13 - 302x^14 - 445x^15 + 1491x^16 - 324x^17 - 1612x^18 - 696x^19 - 932x^20 - 1287x^21 - 255x^22 - 1532x^23 + 1340x^24 + 231x^25 - 1217x^26 + 1290x^27 + 322x^28 - 1137x^29 - 494x^30 + 124x^31 + 136x^32 - 112x^33 + 1562x^34 + 2x^35 - 509x^36 + 821x^37 - 133x^38 - 1557x^39 + 972x^40 + 1430x^41 + 1346x^42 - 768x^43 - 84x^44 + 950x^45 - 364x^46 - 170x^47 + 230x^48 - 167x^49 + 413x^50 + 1564x^51 - 1618x^52 + 438x^53 + 40x^54 + 116x^55 + 1305x^56 + 729x^57 + 1355x^58 + 1418x^59 - 930x^60 - 1298x^61 - 1399x^62 + 970x^63 + 1187x^64 - 1608x^65 + 581x^66 + 1190x^67 - 816x^68 + 13x^69 + 793x^70 + 495x^71 - 493x^72 + 1362x^73 - 337x^74 + 873x^75 + 1421x^76 - 1349x^77 - 815x^78 - 1416x^79 - 958x^80 + 948x^81 - 353x^82 + 783x^83 - 229x^84 + 1227x^85 + 1583x^86 + 1024x^87 + 1059x^88 + 347x^89 - 1463x^90 - 46x^91 + 140x^92 + 845x^93 - 528x^94 - 1460x^95 + 486x^96 - 1036x^97 + 218x^98 - 1050x^99 - 939x^100 + 1092x^101 + 1291x^102 + 1011x^103 + 1146x^104 + 761x^105 - 1200x^106 - 786x^107 + 1173x^108 - 1497x^109 + 1195x^110 - 40x^111 + 408x^112 - 77x^113 + 362x^114 - 284x^115 - 1652x^116 - 792x^117 + 1131x^118 - 859x^119 - 597x^120 + 177x^121 - 716x^122 - 285x^123 + 1310x^124 - 1353x^125 - 811x^126 - 965x^127 + 1648x^128 + 283x^129 - 602x^130 - 890x^131 + 382x^132 + 1629x^133 - 1612x^134 - 1540x^135 - 310x^136 + 1629x^137 - 799x^138 + 655x^139 + 1266x^140 + 152x^141 + 1520x^142 - 531x^143 + 1046x^144 + 1611x^145 - 1543x^146 - 569x^147 - 1602x^148 - 1050x^149 + 23x^150 - x^151 + 182x^152 - 781x^153 + 90x^154 + 703x^155 - 308x^156 - 109x^157 - 795x^158 + 1431x^159 + 245x^160 - 419x^161 + 918x^162 + 1154x^163 + 870x^164 - 543x^165 - 1361x^166 + 532x^167 - 917x^168 - 387x^169 + 133x^170 + 1645x^171 - 1016x^172 - 609x^173 + 319x^174 - 517x^175 + 61x^176 - 499x^177 - 951x^178 - 827x^179 + 1091x^180 + 1375x^181 + 1250x^182 - 259x^183 - 47x^184 - 392x^185 + 235x^186 - 1487x^187 - 1560x^188 + 1046x^189 + 813x^190 - 810x^191 + 260x^192 + 721x^193 + 1077x^194 - 144x^195 + 32x^196 + 821x^197 - 431x^198 + 834x^199 + 1157x^200 + 1322x^201 - 1074x^202 - 1521x^203 - 1571x^204 + 1269x^205 + 1526x^206 + 1395x^207 + 453x^208 + 764x^209 - 1091x^210 - 173x^211 + 1246x^212 + 894x^213 + 215x^214 - 1000x^215 - 680x^216 + 910x^217 + 678x^218 - 1075x^219 + 320x^220 + 955x^221 + 1357x^222 - 974x^223 + 1315x^224 + 444x^225 + 942x^226 - 653x^227 + 993x^228 - 584x^229 - 996x^230 - 695x^231 - 1479x^232 - 177x^233 + 1372x^234 + 364x^235 + 750x^236 + 330x^237 + 156x^238 - 1257x^239 + 188x^240 + 733x^241 - 134x^242 - 1170x^243 - 1319x^244 - 1160x^245 - 698x^246 + 761x^247 - 974x^248 - 1478x^249 + 5x^250 + 890x^251 + 686x^252 - 200x^253 + 144x^254 + 1013x^255$

$u_{ 3 } = -326 + 1190x + 790x^2 + 704x^3 - 618x^4 + 240x^5 - 417x^6 - 1484x^7 + 808x^8 + 1497x^9 + 757x^10 - 1211x^11 - 788x^12 + 23x^13 + 582x^14 - 767x^15 - 257x^16 - 254x^17 - 1455x^18 - 1430x^19 + 1423x^20 - 1377x^21 - 1165x^22 + 539x^23 - 1190x^24 - 127x^25 - 1344x^26 + 1634x^27 - 463x^28 + 598x^29 - 1553x^30 - 1320x^31 + 851x^32 - 771x^33 + 862x^34 - 715x^35 + 576x^36 + 1664x^37 - 1468x^38 - 1345x^39 + 895x^40 + 549x^41 - 276x^42 - 36x^43 + 1256x^44 + 685x^45 + 221x^46 - 1173x^47 - 945x^48 + 260x^49 + 700x^50 + 915x^51 + 810x^52 - 75x^53 - 983x^54 - 1567x^55 + 222x^56 - 81x^57 - 1195x^58 + 268x^59 - 312x^60 - 968x^61 + 840x^62 + 528x^63 + 172x^64 + 710x^65 - 584x^66 - 170x^67 - 61x^68 + 802x^69 - 63x^70 + 916x^71 + 771x^72 + 775x^73 + 445x^74 - 1081x^75 + 637x^76 + 907x^77 + 177x^78 - 1155x^79 - 48x^80 - 1305x^81 + 1353x^82 + 1660x^83 - 442x^84 - 1166x^85 - 1282x^86 + 1147x^87 + 139x^88 - 1351x^89 - 1047x^90 + 1586x^91 + 1458x^92 - 575x^93 - 958x^94 + 378x^95 - 825x^96 + 1574x^97 - 824x^98 - 1520x^99 + 1151x^100 - 21x^101 - 670x^102 - 679x^103 - 1089x^104 + 1402x^105 + 680x^106 + 1160x^107 - 707x^108 - 819x^109 + 141x^110 - 585x^111 + 323x^112 - 1015x^113 - 167x^114 + 469x^115 - 230x^116 - 1644x^117 + 771x^118 + 563x^119 + 837x^120 - 1488x^121 - 941x^122 - 608x^123 + 1131x^124 - 641x^125 + 53x^126 + 489x^127 + 1415x^128 - 1603x^129 + 537x^130 + 554x^131 - 649x^132 - 1115x^133 + 406x^134 - 1274x^135 - 722x^136 + 522x^137 + 1568x^138 + 946x^139 - 43x^140 - 1225x^141 + 1393x^142 + 1126x^143 + 1539x^144 - 1126x^145 + 1016x^146 + 1298x^147 + 1078x^148 - 1482x^149 + 1153x^150 + 214x^151 - 496x^152 + 1242x^153 - 1488x^154 - 1647x^155 - 703x^156 - 1015x^157 - 285x^158 - 334x^159 - 932x^160 + 1402x^161 - 273x^162 - 486x^163 + 1131x^164 - 426x^165 - 406x^166 + 779x^167 + 348x^168 + 429x^169 - 190x^170 - 332x^171 + 1488x^172 + 53x^173 - 336x^174 + 382x^175 + 1617x^176 + 894x^177 - 1652x^178 - 1382x^179 - 942x^180 - 319x^181 - 1015x^182 - 570x^183 + 1190x^184 + 1273x^185 - 1420x^186 + 520x^187 + 1260x^188 - 921x^189 - 1258x^190 - 747x^191 + 722x^192 - 336x^193 + 642x^194 + 693x^195 - 1009x^196 + 1283x^197 - 1456x^198 - 1653x^199 + 1467x^200 + 1008x^201 - 1375x^202 + 808x^203 - 727x^204 + 148x^205 + 1254x^206 - 315x^207 + 400x^208 + 1199x^209 - 827x^210 + 1216x^211 + 1101x^212 + 358x^213 - 1373x^214 + 590x^215 + 301x^216 - 408x^217 + 1176x^218 + 137x^219 + 912x^220 + 403x^221 + 813x^222 - 1461x^223 + 485x^224 + 1587x^225 + 1494x^226 - 1338x^227 + 1151x^228 + 887x^229 + 1039x^230 - 1525x^231 - 148x^232 + 1613x^233 - 382x^234 + 1589x^235 - 212x^236 - 1511x^237 + 1418x^238 - 882x^239 + 651x^240 - 500x^241 - 210x^242 + 1080x^243 - 243x^244 - 866x^245 - 252x^246 - 1555x^247 - 1569x^248 - 732x^249 + 1414x^250 + 398x^251 - 829x^252 - 608x^253 + 1247x^254 + 1146x^255$

۳. بخش دوم متن رمز شده: چندجمله‌ای $v = t^T r + e_2 + 1665 \cdot m \pmod{3329}$

$$ v = t^T \cdot r + e_2 + \left\lceil \frac{3329}{2} \right\rceil \cdot m(x) \pmod{3329} $$

بلوک 1 پیام (تا ۲۵۶ بیت):

چندجمله‌ای پیام $m(x)$:

$m(x) = x + x^7 + x^9 + x^10 + x^13 + x^17 + x^18 + x^19 + x^21 + x^22 + x^25 + x^26 + x^31 + x^33 + x^34 + x^36 + x^37 + x^38 + x^41 + x^42 + x^46 + x^47 + x^49 + x^50 + x^53 + x^55 + x^57 + x^58 + x^61 + x^66 + x^73 + x^78 + x^79 + x^81 + x^82 + x^83 + x^86 + x^89 + x^90 + x^91 + x^92 + x^95 + x^97 + x^98 + x^99 + x^105 + x^106 + x^107 + x^109 + x^113 + x^114 + x^116 + x^117 + x^118 + x^119 + x^121 + x^122 + x^125 + x^126 + x^127 + x^129 + x^130 + x^131 + x^134 + x^137 + x^138 + x^143 + x^145 + x^146 + x^147 + x^153 + x^154 + x^156 + x^161 + x^162 + x^163 + x^164 + x^167 + x^170 + x^177 + x^182 + x^183 + x^185 + x^186 + x^188 + x^189 + x^193 + x^194 + x^199 + x^201 + x^202 + x^203 + x^206 + x^207 + x^209 + x^210 + x^211 + x^214 + x^215 + x^218 + x^220 + x^221 + x^226 + x^233 + x^237 + x^241 + x^242 + x^243 + x^246 + x^250 + x^252 + x^253 + x^254$

پیام مقیاس شده $1665 \cdot m(x)$:

$\bar{m}(x) = 1665x + 1665x^7 + 1665x^9 + 1665x^10 + 1665x^13 + 1665x^17 + 1665x^18 + 1665x^19 + 1665x^21 + 1665x^22 + 1665x^25 + 1665x^26 + 1665x^31 + 1665x^33 + 1665x^34 + 1665x^36 + 1665x^37 + 1665x^38 + 1665x^41 + 1665x^42 + 1665x^46 + 1665x^47 + 1665x^49 + 1665x^50 + 1665x^53 + 1665x^55 + 1665x^57 + 1665x^58 + 1665x^61 + 1665x^66 + 1665x^73 + 1665x^78 + 1665x^79 + 1665x^81 + 1665x^82 + 1665x^83 + 1665x^86 + 1665x^89 + 1665x^90 + 1665x^91 + 1665x^92 + 1665x^95 + 1665x^97 + 1665x^98 + 1665x^99 + 1665x^105 + 1665x^106 + 1665x^107 + 1665x^109 + 1665x^113 + 1665x^114 + 1665x^116 + 1665x^117 + 1665x^118 + 1665x^119 + 1665x^121 + 1665x^122 + 1665x^125 + 1665x^126 + 1665x^127 + 1665x^129 + 1665x^130 + 1665x^131 + 1665x^134 + 1665x^137 + 1665x^138 + 1665x^143 + 1665x^145 + 1665x^146 + 1665x^147 + 1665x^153 + 1665x^154 + 1665x^156 + 1665x^161 + 1665x^162 + 1665x^163 + 1665x^164 + 1665x^167 + 1665x^170 + 1665x^177 + 1665x^182 + 1665x^183 + 1665x^185 + 1665x^186 + 1665x^188 + 1665x^189 + 1665x^193 + 1665x^194 + 1665x^199 + 1665x^201 + 1665x^202 + 1665x^203 + 1665x^206 + 1665x^207 + 1665x^209 + 1665x^210 + 1665x^211 + 1665x^214 + 1665x^215 + 1665x^218 + 1665x^220 + 1665x^221 + 1665x^226 + 1665x^233 + 1665x^237 + 1665x^241 + 1665x^242 + 1665x^243 + 1665x^246 + 1665x^250 + 1665x^252 + 1665x^253 + 1665x^254$

خطای تصادفی $e_2 \in CBD_2$:

$e_2 = 1 - x - x^3 - x^4 + x^6 - x^9 + x^10 + x^11 + x^13 - x^14 - x^17 + 2x^18 + x^19 - x^20 + x^21 - x^24 + x^28 + x^29 + x^30 + x^32 - x^33 + x^34 - x^36 - x^37 + x^40 - x^41 + x^42 + x^43 + x^45 + x^47 - x^51 + 2x^53 - x^55 - x^56 + 2x^57 - x^58 + x^59 + 2x^60 - x^61 + x^62 - 2x^64 + x^65 - x^66 + x^67 + x^71 + x^72 - x^73 - x^74 + x^75 - x^77 - 2x^78 - x^79 + x^80 - x^81 + 2x^83 - x^84 - x^86 - x^87 - x^89 - 2x^90 - x^91 - 2x^92 + x^93 - 2x^94 - x^95 - x^97 - x^98 + x^99 + x^100 + x^101 - x^102 - x^103 - 2x^105 - x^106 + x^107 - x^109 + x^110 - x^112 - 2x^114 - x^119 + x^120 - x^121 + 2x^122 - x^124 - x^125 - 2x^126 + x^127 + x^128 - x^129 - x^130 + 2x^133 + x^135 - x^137 - x^139 + x^140 + x^141 - x^142 - x^143 + x^144 - x^146 - x^147 - x^148 - x^149 + x^150 - x^151 + x^156 - x^159 - x^160 + x^163 + x^164 - 2x^165 + 2x^167 + 2x^169 + x^173 + x^175 - x^176 - x^177 - x^178 + x^179 + 2x^180 - x^181 - x^182 - 2x^183 + x^185 - x^188 + 2x^189 + x^190 - 2x^191 + 2x^193 + x^197 + x^198 - 2x^200 + x^201 - x^202 - x^203 + 2x^204 - x^205 - x^206 - 2x^210 + x^211 - x^212 - x^213 - x^214 + x^215 + x^216 + x^217 - x^218 - x^219 + x^221 + x^222 + x^224 - x^225 - 2x^228 + x^231 - x^235 - x^236 - x^237 - x^238 - x^242 - x^244 + x^245 + x^247 - x^248 + 2x^249 - 2x^251 + 2x^253 + x^254$

مقدار نهایی $v$ برای این بلوک:

$v_{ 1 } = -25 + 1372x + 731x^2 + 54x^3 + 697x^4 + 1283x^5 - 488x^6 - 1064x^7 + 205x^8 - 1607x^9 - 995x^10 - 668x^11 - 684x^12 + 498x^13 - 1503x^14 + 1228x^15 - 948x^16 - 572x^17 - 413x^18 + 111x^19 - 1141x^20 + 1118x^21 + 1396x^22 + 819x^23 - 58x^24 - 851x^25 + 1549x^26 - 644x^27 + 409x^28 + 1461x^29 + 1494x^30 + 524x^31 + 143x^32 - 1229x^33 - 678x^34 - 1464x^35 - 1292x^36 + 1102x^37 + 246x^38 - 1194x^39 + 1471x^40 + 1299x^41 - 189x^42 - 112x^43 - 650x^44 - 1277x^45 + 536x^46 - 1527x^47 + 920x^48 + 396x^49 - 498x^50 - 1420x^51 - 60x^52 - 572x^53 - 243x^54 + 7x^55 + 843x^56 - 1232x^57 - 581x^58 + 194x^59 - 48x^60 - 1196x^61 + 1233x^62 + 464x^63 - 692x^64 + 1232x^65 - 1273x^66 + 1033x^67 - 1173x^68 + 1236x^69 + 629x^70 - 674x^71 + 579x^72 + 942x^73 - 623x^74 - 1373x^75 + 1027x^76 - 662x^77 - 1312x^78 - 118x^79 + 570x^80 - 1462x^81 - 608x^82 + 1615x^83 - 152x^84 + 487x^85 - 1119x^86 + 1311x^87 + 1016x^88 + 1608x^89 - 209x^90 + 48x^91 - 587x^92 - 405x^93 - 225x^94 + 715x^95 - 1347x^96 + 1037x^97 + 852x^98 + 250x^99 + 256x^100 - 1090x^101 + 36x^102 - 378x^103 - 448x^104 + 592x^105 - 1423x^106 + 1326x^107 + 545x^108 - 152x^109 - 771x^110 - 890x^111 - 766x^112 - 1254x^113 + 206x^114 - 1253x^115 - 1375x^116 + 1458x^117 - 15x^118 + 98x^119 - 1417x^120 + 766x^121 - 287x^122 - 1459x^123 - 42x^124 - 452x^125 - 1290x^126 + 1066x^127 + 1104x^128 - 42x^129 - 946x^130 - 922x^131 - 1108x^132 - 705x^133 - 728x^134 - 858x^135 - 1403x^136 - 584x^138 - 148x^139 - 298x^140 - 732x^141 + 1137x^142 + 603x^143 - 1141x^144 + 788x^145 - 571x^146 + 1442x^147 + 1335x^148 - 1112x^149 - 1624x^150 - 738x^151 - 716x^152 - 447x^153 - 1613x^154 - 1216x^155 - 1398x^156 + 1066x^157 - 276x^158 - 224x^159 - 1249x^160 + 1567x^161 - 959x^162 - 318x^163 + 1307x^164 + 1229x^165 - 879x^166 + 1477x^167 + 1436x^168 - 1242x^169 + 1407x^170 + 861x^171 - 1112x^172 + 1322x^173 + 321x^174 + 248x^175 - 1361x^176 - 1215x^177 - 776x^178 - 771x^179 + 880x^180 - 744x^181 + 1131x^182 - 1296x^183 + 380x^184 - 342x^185 - 469x^186 - 1460x^187 - 1026x^188 - 782x^189 + 1514x^190 - 886x^191 + 685x^192 + 241x^193 + 767x^194 + 796x^195 + 1011x^196 - 258x^197 + 458x^198 - 34x^199 + 1227x^200 - 867x^201 - 1623x^202 - 1521x^203 + 359x^204 + 1413x^205 - 316x^206 - 1512x^207 - 330x^208 - 252x^209 - 842x^210 - 1393x^211 - 144x^212 + 262x^213 + 220x^214 - 720x^215 - 1020x^216 + 206x^217 + 10x^218 + 400x^219 + 631x^220 - 51x^221 + 319x^222 - 855x^223 + 691x^224 + 1381x^225 + 849x^226 + 373x^227 + 740x^228 + 1155x^229 - 616x^230 - 1165x^231 + 131x^232 - 1230x^233 + 1488x^234 + 478x^235 + 330x^236 - 504x^237 - 726x^238 + 244x^239 + 1276x^240 - 260x^241 - 1180x^242 - 1455x^243 + 1028x^244 - 337x^245 - 1080x^246 + 1658x^247 + 306x^248 + 172x^249 + 1431x^250 + 1326x^251 - 946x^252 - 1563x^253 + 1087x^254 + 1058x^255$

بلوک 2 پیام (تا ۲۵۶ بیت):

چندجمله‌ای پیام $m(x)$:

$m(x) = x^2 + x^9 + x^12 + x^13 + x^14 + x^17 + x^18 + x^23 + x^25 + x^26 + x^28 + x^30 + x^33 + x^34 + x^39 + x^41 + x^42 + x^45 + x^46 + x^49 + x^50 + x^52 + x^55$

پیام مقیاس شده $1665 \cdot m(x)$:

$\bar{m}(x) = 1665x^2 + 1665x^9 + 1665x^12 + 1665x^13 + 1665x^14 + 1665x^17 + 1665x^18 + 1665x^23 + 1665x^25 + 1665x^26 + 1665x^28 + 1665x^30 + 1665x^33 + 1665x^34 + 1665x^39 + 1665x^41 + 1665x^42 + 1665x^45 + 1665x^46 + 1665x^49 + 1665x^50 + 1665x^52 + 1665x^55$

خطای تصادفی $e_2 \in CBD_2$:

$e_2 = -x^2 + x^4 - x^5 + x^6 - x^7 - x^9 + x^10 - x^11 + x^12 - x^13 + x^15 - x^16 + x^19 + x^21 + 2x^23 + x^24 - x^26 + x^27 + x^28 - 2x^29 + x^31 + x^32 - x^33 - x^34 - x^37 + x^38 - x^39 + x^40 + x^43 - x^45 - x^46 - x^48 - 2x^51 - x^52 - x^53 + x^54 + x^55 + x^59 - x^61 - x^62 + x^63 - x^64 - x^65 - x^67 - x^68 - x^72 - x^73 + x^74 - x^75 + x^77 - x^78 + 2x^80 + x^84 - x^86 - x^88 - x^91 - x^93 + x^95 + x^97 - 2x^98 - 2x^100 - x^102 - x^103 + x^104 + x^105 - x^106 + x^107 - x^110 + 2x^111 - x^113 + x^115 + x^117 - x^118 - x^120 - x^121 + x^124 - x^126 + x^128 + x^131 - x^133 - x^136 - x^139 + x^140 + 2x^143 - x^144 + x^145 - x^146 - x^147 + 2x^148 - x^150 - x^151 - 2x^154 - 2x^155 - 2x^157 + x^158 + x^159 + 2x^161 - x^165 - 2x^166 + x^167 + x^168 - x^170 + x^172 - x^174 - x^175 + 2x^177 - 2x^178 - x^182 + x^183 + x^184 + x^185 - x^186 - x^191 + x^193 - 2x^194 - x^195 + x^196 - x^197 + x^199 - x^200 - x^202 - x^203 - x^205 + x^207 + x^208 + x^213 + 2x^214 - x^215 + x^216 - x^217 + x^218 - x^219 + 2x^220 + x^221 + x^222 - x^223 - x^224 - x^227 - x^228 + x^229 - 2x^230 + x^232 + 2x^233 + 2x^234 + x^235 + x^237 + x^239 + x^241 + x^243 - x^244 - x^245 - x^247 + x^249 - x^251 + x^252$

مقدار نهایی $v$ برای این بلوک:

$v_{ 2 } = -26 - 292x - 934x^2 + 55x^3 + 699x^4 + 1282x^5 - 488x^6 + 599x^7 + 205x^8 - 1607x^9 + 669x^10 - 670x^11 + 982x^12 + 496x^13 + 163x^14 + 1229x^15 - 949x^16 - 571x^17 - 415x^18 - 1554x^19 - 1140x^20 - 547x^21 - 269x^22 - 843x^23 - 56x^24 - 851x^25 + 1548x^26 - 643x^27 - 1255x^28 + 1458x^29 - 171x^30 - 1140x^31 + 143x^32 - 1229x^33 - 680x^34 - 1464x^35 + 373x^36 - 563x^37 - 1418x^38 + 470x^39 + 1471x^40 + 1300x^41 - 190x^42 - 112x^43 - 650x^44 + 386x^45 + 535x^46 + 136x^47 + 919x^48 + 396x^49 - 498x^50 - 1421x^51 + 1604x^52 + 1089x^53 - 242x^54 + 9x^55 + 844x^56 + 430x^57 + 1084x^58 + 194x^59 - 50x^60 + 468x^61 + 1231x^62 + 465x^63 - 691x^64 + 1230x^65 + 392x^66 + 1031x^67 - 1174x^68 + 1236x^69 + 629x^70 - 675x^71 + 577x^72 - 723x^73 - 621x^74 - 1375x^75 + 1027x^76 - 660x^77 + 353x^78 + 1547x^79 + 571x^80 + 203x^81 + 1056x^82 - 52x^83 - 150x^84 + 487x^85 + 545x^86 + 1312x^87 + 1015x^88 - 56x^89 + 1457x^90 - 1617x^91 + 1079x^92 - 407x^93 - 223x^94 - 948x^95 - 1347x^96 - 626x^97 - 814x^98 - 1416x^99 + 253x^100 - 1091x^101 + 36x^102 - 378x^103 - 447x^104 - 1070x^105 + 241x^106 - 339x^107 + 545x^108 + 1513x^109 - 773x^110 - 888x^111 - 765x^112 + 409x^113 - 1457x^114 - 1252x^115 + 289x^116 - 206x^117 + 1648x^118 - 1566x^119 - 1419x^120 - 899x^121 + 1375x^122 - 1459x^123 - 40x^124 + 1213x^125 + 375x^126 - 600x^127 + 1104x^128 + 1623x^129 + 719x^130 + 743x^131 - 1108x^132 - 708x^133 + 936x^134 - 859x^135 - 1404x^136 - 1664x^137 + 1080x^138 - 148x^139 - 298x^140 - 733x^141 + 1138x^142 - 1059x^143 - 1143x^144 - 876x^145 + 1093x^146 - 223x^147 + 1338x^148 - 1111x^149 - 1626x^150 - 738x^151 - 716x^152 + 1217x^153 + 49x^154 - 1218x^155 + 265x^156 + 1064x^157 - 275x^158 - 222x^159 - 1248x^160 - 96x^161 + 705x^162 + 1345x^163 - 359x^164 + 1230x^165 - 881x^166 - 189x^167 + 1437x^168 - 1244x^169 - 259x^170 + 861x^171 - 1111x^172 + 1321x^173 + 320x^174 + 246x^175 - 1360x^176 + 452x^177 - 777x^178 - 772x^179 + 878x^180 - 743x^181 - 534x^182 + 371x^183 + 381x^184 + 1322x^185 + 1194x^186 - 1460x^187 + 639x^188 + 880x^189 + 1513x^190 - 885x^191 + 685x^192 - 1425x^193 - 900x^194 + 795x^195 + 1012x^196 - 260x^197 + 457x^198 + 1631x^199 + 1228x^200 + 796x^201 + 41x^202 + 143x^203 + 357x^204 + 1413x^205 + 1349x^206 + 153x^207 - 329x^208 + 1412x^209 + 824x^210 + 270x^211 - 143x^212 + 264x^213 - 1442x^214 + 942x^215 - 1020x^216 + 204x^217 - 1653x^218 + 400x^219 - 1032x^220 + 1613x^221 + 319x^222 - 856x^223 + 689x^224 + 1382x^225 - 816x^226 + 372x^227 + 741x^228 + 1156x^229 - 618x^230 - 1166x^231 + 132x^232 + 436x^233 + 1490x^234 + 480x^235 + 331x^236 + 1162x^237 - 725x^238 + 245x^239 + 1276x^240 + 1405x^241 + 485x^242 + 210x^243 + 1028x^244 - 339x^245 + 584x^246 + 1656x^247 + 307x^248 + 171x^249 - 234x^250 + 1327x^251 + 719x^252 + 99x^253 - 579x^254 + 1058x^255$

خروجی کامل متن رمزنگاری شده Kyber-768 ($c = (u, v)$)

جفت خروجی متن رمزنگاری شده $$c = (u, v)$$ شامل بردار چندجمله‌ای $u \in R_q^3$ و چندجمله‌ای‌های $v \in R_q$ به صورت خوانا آماده ارسال برای آلیس می‌باشد.

$$ Ciphertext \quad c = \left( u_{3 \times 1}, v \right) $$

مرحله سوم - رمزگشایی (Decryption)

$m' = \text{Round}_q(v - s^T u)$

در این مرحله، آلیس متن رمز شده $$c=(u, v)$$ را دریافت نموده و با استفاده از کلید خصوصی خود ( $s \in R_q^3$ ) چندجمله‌ای پیام اولیه را بازیابی می‌کند.

یادآوری کلید خصوصی آلیس (

s \in R_q^3

$$ m = \text{Round}_q \left( v - s^T \cdot u \right) $$

مراحل محاسباتی بازیابی پیام برای هر بلوک:

بلوک 1: تطابق دقیق با پیام اولیه

محاسبه ضرب داخلی $s^T u \pmod q$:

$s^T u = -55 - 352x + 708x^2 + 55x^3 + 738x^4 + 1276x^5 - 463x^6 + 551x^7 + 152x^8 + 69x^9 + 661x^10 - 644x^11 - 717x^12 - 1203x^13 - 1520x^14 + 1209x^15 - 1005x^16 + 1085x^17 + 1267x^18 - 1540x^19 - 1079x^20 - 612x^21 - 297x^22 + 836x^23 - 35x^24 + 795x^25 - 125x^26 - 691x^27 + 421x^28 + 1453x^29 + 1509x^30 - 1136x^31 + 207x^32 + 475x^33 + 977x^34 - 1418x^35 + 338x^36 - 469x^37 - 1389x^38 - 1210x^39 + 1507x^40 - 368x^41 + 1512x^42 - 39x^43 - 649x^44 - 1253x^45 - 1089x^46 + 71x^47 + 870x^48 - 1262x^49 + 1124x^50 - 1421x^51 - 38x^52 + 1060x^53 - 235x^54 - 1658x^55 + 866x^56 + 409x^57 + 1095x^58 + 196x^59 - 24x^60 + 420x^61 + 1214x^62 + 398x^63 - 692x^64 + 1261x^65 + 376x^66 + 1048x^67 - 1129x^68 + 1223x^69 + 566x^70 - 722x^71 + 600x^72 - 692x^73 - 585x^74 - 1351x^75 + 996x^76 - 666x^77 + 416x^78 + 1468x^79 + 506x^80 + 167x^81 + 1077x^82 - 82x^83 - 174x^84 + 463x^85 + 602x^86 + 1345x^87 + 969x^88 + 62x^89 + 1467x^90 - 1588x^91 + 1040x^92 - 363x^93 - 279x^94 - 989x^95 - 1308x^96 - 618x^97 - 802x^98 - 1447x^99 + 194x^100 - 1117x^101 + 5x^102 - 378x^103 - 473x^104 - 1091x^105 + 250x^106 - 316x^107 + 625x^108 + 1518x^109 - 768x^110 - 977x^111 - 782x^112 + 408x^113 - 1451x^114 - 1230x^115 + 245x^116 - 200x^117 - 1587x^118 - 1530x^119 - 1407x^120 - 827x^121 + 1369x^122 - 1400x^123 - 3x^124 + 1278x^125 + 327x^126 - 579x^127 + 1103x^128 + 1555x^129 + 689x^130 + 737x^131 - 1121x^132 - 734x^133 + 920x^134 - 917x^135 - 1359x^136 - 1652x^137 + 1098x^138 - 97x^139 - 319x^140 - 700x^141 + 1200x^142 - 1118x^143 - 1102x^144 - 863x^145 + 1117x^146 - 177x^147 + 1266x^148 - 1073x^149 - 1664x^150 - 715x^151 - 731x^152 + 1272x^153 + 88x^154 - 1221x^155 + 255x^156 + 1106x^157 - 227x^158 - 196x^159 - 1189x^160 - 204x^161 + 688x^162 + 1354x^163 - 351x^164 + 1234x^165 - 887x^166 - 252x^167 + 1445x^168 - 1218x^169 - 158x^170 + 812x^171 - 1110x^172 + 1301x^173 + 252x^174 + 206x^175 - 1353x^176 + 411x^177 - 753x^178 - 813x^179 + 869x^180 - 787x^181 - 603x^182 + 384x^183 + 370x^184 + 1256x^185 + 1102x^186 - 1463x^187 + 620x^188 + 887x^189 + 1473x^190 - 848x^191 + 710x^192 - 1469x^193 - 862x^194 + 705x^195 + 1034x^196 - 220x^197 + 457x^198 + 1608x^199 + 1281x^200 + 748x^201 + 84x^202 + 110x^203 + 336x^204 + 1491x^205 + 1393x^206 + 116x^207 - 222x^208 + 1450x^209 + 826x^210 + 329x^211 - 46x^212 + 305x^213 - 1396x^214 + 935x^215 - 1009x^216 + 210x^217 + 1581x^218 + 437x^219 - 1026x^220 + 1648x^221 + 325x^222 - 865x^223 + 731x^224 + 1346x^225 - 832x^226 + 408x^227 + 711x^228 + 1169x^229 - 631x^230 - 1156x^231 + 114x^232 + 442x^233 + 1524x^234 + 397x^235 + 338x^236 + 1151x^237 - 721x^238 + 248x^239 + 1249x^240 + 1405x^241 + 434x^242 + 273x^243 + 1031x^244 - 386x^245 + 551x^246 - 1664x^247 + 347x^248 + 75x^249 - 218x^250 + 1224x^251 + 711x^252 + 73x^253 - 611x^254 + 1032x^255$

تفریق $v - s^T u \pmod q$:

$v - s^T u = 30 - 1605x + 23x^2 - x^3 - 41x^4 + 7x^5 - 25x^6 - 1615x^7 + 53x^8 + 1653x^9 - 1656x^10 - 24x^11 + 33x^12 - 1628x^13 + 17x^14 + 19x^15 + 57x^16 - 1657x^17 + 1649x^18 + 1651x^19 - 62x^20 - 1599x^21 - 1636x^22 - 17x^23 - 23x^24 - 1646x^25 - 1655x^26 + 47x^27 - 12x^28 + 8x^29 - 15x^30 + 1660x^31 - 64x^32 + 1625x^33 - 1655x^34 - 46x^35 - 1630x^36 + 1571x^37 + 1635x^38 + 16x^39 - 36x^40 - 1662x^41 + 1628x^42 - 73x^43 - x^44 - 24x^45 + 1625x^46 - 1598x^47 + 50x^48 + 1658x^49 - 1622x^50 + x^51 - 22x^52 - 1632x^53 - 8x^54 - 1664x^55 - 23x^56 - 1641x^57 + 1653x^58 - 2x^59 - 24x^60 - 1616x^61 + 19x^62 + 66x^63 - 29x^65 - 1649x^66 - 15x^67 - 44x^68 + 13x^69 + 63x^70 + 48x^71 - 21x^72 + 1634x^73 - 38x^74 - 22x^75 + 31x^76 + 4x^77 + 1601x^78 - 1586x^79 + 64x^80 - 1629x^81 + 1644x^82 - 1632x^83 + 22x^84 + 24x^85 + 1608x^86 - 34x^87 + 47x^88 + 1546x^89 + 1653x^90 + 1636x^91 - 1627x^92 - 42x^93 + 54x^94 - 1625x^95 - 39x^96 + 1655x^97 + 1654x^98 - 1632x^99 + 62x^100 + 27x^101 + 31x^102 + 25x^104 - 1646x^105 + 1656x^106 + 1642x^107 - 80x^108 + 1659x^109 - 3x^110 + 87x^111 + 16x^112 - 1662x^113 + 1657x^114 - 23x^115 - 1620x^116 + 1658x^117 + 1572x^118 + 1628x^119 - 10x^120 + 1593x^121 - 1656x^122 - 59x^123 - 39x^124 + 1599x^125 - 1617x^126 + 1645x^127 + x^128 - 1597x^129 - 1635x^130 - 1659x^131 + 13x^132 + 29x^133 - 1648x^134 + 59x^135 - 44x^136 + 1652x^137 + 1647x^138 - 51x^139 + 21x^140 - 32x^141 - 63x^142 - 1608x^143 - 39x^144 + 1651x^145 + 1641x^146 + 1619x^147 + 69x^148 - 39x^149 + 40x^150 - 23x^151 + 15x^152 + 1610x^153 + 1628x^154 + 5x^155 - 1653x^156 - 40x^157 - 49x^158 - 28x^159 - 60x^160 - 1558x^161 - 1647x^162 + 1657x^163 + 1658x^164 - 5x^165 + 8x^166 - 1600x^167 - 9x^168 - 24x^169 + 1565x^170 + 49x^171 - 2x^172 + 21x^173 + 69x^174 + 42x^175 - 8x^176 - 1626x^177 - 23x^178 + 42x^179 + 11x^180 + 43x^181 - 1595x^182 + 1649x^183 + 10x^184 - 1598x^185 - 1571x^186 + 3x^187 - 1646x^188 + 1660x^189 + 41x^190 - 38x^191 - 25x^192 - 1619x^193 + 1629x^194 + 91x^195 - 23x^196 - 38x^197 + x^198 - 1642x^199 - 54x^200 - 1615x^201 + 1622x^202 - 1631x^203 + 23x^204 - 78x^205 + 1620x^206 - 1628x^207 - 108x^208 + 1627x^209 + 1661x^210 + 1607x^211 - 98x^212 - 43x^213 + 1616x^214 - 1655x^215 - 11x^216 - 4x^217 - 1571x^218 - 37x^219 + 1657x^220 + 1630x^221 - 6x^222 + 10x^223 - 40x^224 + 35x^225 - 1648x^226 - 35x^227 + 29x^228 - 14x^229 + 15x^230 - 9x^231 + 17x^232 + 1657x^233 - 36x^234 + 81x^235 - 8x^236 - 1655x^237 - 5x^238 - 4x^239 + 27x^240 + 1664x^241 - 1614x^242 + 1601x^243 - 3x^244 + 49x^245 - 1631x^246 - 7x^247 - 41x^248 + 97x^249 + 1649x^250 + 102x^251 - 1657x^252 - 1636x^253 - 1631x^254 + 26x^255$

چندجمله‌ای بازگشتی $m'(x) = \text{Round}_q(\cdot)$:

$m'(x) = x + x^7 + x^9 + x^10 + x^13 + x^17 + x^18 + x^19 + x^21 + x^22 + x^25 + x^26 + x^31 + x^33 + x^34 + x^36 + x^37 + x^38 + x^41 + x^42 + x^46 + x^47 + x^49 + x^50 + x^53 + x^55 + x^57 + x^58 + x^61 + x^66 + x^73 + x^78 + x^79 + x^81 + x^82 + x^83 + x^86 + x^89 + x^90 + x^91 + x^92 + x^95 + x^97 + x^98 + x^99 + x^105 + x^106 + x^107 + x^109 + x^113 + x^114 + x^116 + x^117 + x^118 + x^119 + x^121 + x^122 + x^125 + x^126 + x^127 + x^129 + x^130 + x^131 + x^134 + x^137 + x^138 + x^143 + x^145 + x^146 + x^147 + x^153 + x^154 + x^156 + x^161 + x^162 + x^163 + x^164 + x^167 + x^170 + x^177 + x^182 + x^183 + x^185 + x^186 + x^188 + x^189 + x^193 + x^194 + x^199 + x^201 + x^202 + x^203 + x^206 + x^207 + x^209 + x^210 + x^211 + x^214 + x^215 + x^218 + x^220 + x^221 + x^226 + x^233 + x^237 + x^241 + x^242 + x^243 + x^246 + x^250 + x^252 + x^253 + x^254$

بلوک 2: تطابق دقیق با پیام اولیه

محاسبه ضرب داخلی $s^T u \pmod q$:

تفریق $v - s^T u \pmod q$:

$v - s^T u = 29 + 60x - 1642x^2 - 39x^4 + 6x^5 - 25x^6 + 48x^7 + 53x^8 + 1653x^9 + 8x^10 - 26x^11 - 1630x^12 - 1630x^13 - 1646x^14 + 20x^15 + 56x^16 - 1656x^17 + 1647x^18 - 14x^19 - 61x^20 + 65x^21 + 28x^22 + 1650x^23 - 21x^24 - 1646x^25 - 1656x^26 + 48x^27 + 1653x^28 + 5x^29 + 1649x^30 - 4x^31 - 64x^32 + 1625x^33 - 1657x^34 - 46x^35 + 35x^36 - 94x^37 - 29x^38 - 1649x^39 - 36x^40 - 1661x^41 + 1627x^42 - 73x^43 - x^44 + 1639x^45 + 1624x^46 + 65x^47 + 49x^48 + 1658x^49 - 1622x^50 + 1642x^52 + 29x^53 - 7x^54 - 1662x^55 - 22x^56 + 21x^57 - 11x^58 - 2x^59 - 26x^60 + 48x^61 + 17x^62 + 67x^63 + x^64 - 31x^65 + 16x^66 - 17x^67 - 45x^68 + 13x^69 + 63x^70 + 47x^71 - 23x^72 - 31x^73 - 36x^74 - 24x^75 + 31x^76 + 6x^77 - 63x^78 + 79x^79 + 65x^80 + 36x^81 - 21x^82 + 30x^83 + 24x^84 + 24x^85 - 57x^86 - 33x^87 + 46x^88 - 118x^89 - 10x^90 - 29x^91 + 39x^92 - 44x^93 + 56x^94 + 41x^95 - 39x^96 - 8x^97 - 12x^98 + 31x^99 + 59x^100 + 26x^101 + 31x^102 + 26x^104 + 21x^105 - 9x^106 - 23x^107 - 80x^108 - 5x^109 - 5x^110 + 89x^111 + 17x^112 + x^113 - 6x^114 - 22x^115 + 44x^116 - 6x^117 - 94x^118 - 36x^119 - 12x^120 - 72x^121 + 6x^122 - 59x^123 - 37x^124 - 65x^125 + 48x^126 - 21x^127 + x^128 + 68x^129 + 30x^130 + 6x^131 + 13x^132 + 26x^133 + 16x^134 + 58x^135 - 45x^136 - 12x^137 - 18x^138 - 51x^139 + 21x^140 - 33x^141 - 62x^142 + 59x^143 - 41x^144 - 13x^145 - 24x^146 - 46x^147 + 72x^148 - 38x^149 + 38x^150 - 23x^151 + 15x^152 - 55x^153 - 39x^154 + 3x^155 + 10x^156 - 42x^157 - 48x^158 - 26x^159 - 59x^160 + 108x^161 + 17x^162 - 9x^163 - 8x^164 - 4x^165 + 6x^166 + 63x^167 - 8x^168 - 26x^169 - 101x^170 + 49x^171 - x^172 + 20x^173 + 68x^174 + 40x^175 - 7x^176 + 41x^177 - 24x^178 + 41x^179 + 9x^180 + 44x^181 + 69x^182 - 13x^183 + 11x^184 + 66x^185 + 92x^186 + 3x^187 + 19x^188 - 7x^189 + 40x^190 - 37x^191 - 25x^192 + 44x^193 - 38x^194 + 90x^195 - 22x^196 - 40x^197 + 23x^199 - 53x^200 + 48x^201 - 43x^202 + 33x^203 + 21x^204 - 78x^205 - 44x^206 + 37x^207 - 107x^208 - 38x^209 - 2x^210 - 59x^211 - 97x^212 - 41x^213 - 46x^214 + 7x^215 - 11x^216 - 6x^217 + 95x^218 - 37x^219 - 6x^220 - 35x^221 - 6x^222 + 9x^223 - 42x^224 + 36x^225 + 16x^226 - 36x^227 + 30x^228 - 13x^229 + 13x^230 - 10x^231 + 18x^232 - 6x^233 - 34x^234 + 83x^235 - 7x^236 + 11x^237 - 4x^238 - 3x^239 + 27x^240 + 51x^242 - 63x^243 - 3x^244 + 47x^245 + 33x^246 - 9x^247 - 40x^248 + 96x^249 - 16x^250 + 103x^251 + 8x^252 + 26x^253 + 32x^254 + 26x^255$

چندجمله‌ای بازگشتی $m'(x) = \text{Round}_q(\cdot)$:

$m'(x) = x^2 + x^9 + x^12 + x^13 + x^14 + x^17 + x^18 + x^23 + x^25 + x^26 + x^28 + x^30 + x^33 + x^34 + x^39 + x^41 + x^42 + x^45 + x^46 + x^49 + x^50 + x^52 + x^55$

متن بازگشایی شده نهایی (Decrypted Plaintext Output):

                "Advanced Cryptography Class, Dr. Najafi"
            

پیام رمزگشایی شده کاملاً یکسان و برابر با متن اولیه انتخاب شده است!

بخش تعاملی (Interactive Playground) - سیستم Kyber-768

Live Execution Engine

راهنمای عملکرد:

سیستم با مشخصات فیکس‌شده استاد ($q=3329, n=256, k=3, \eta_1=2, \eta_2=2$) اجرا می‌گردد. با ارسال فرم فوق، کلیدهای جدید و بردارهای تصادفی تولید شده و خروجی تمام مراحل ریاضی در زبانه‌های مربوطه بروزرسانی خواهد شد.