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Tate pairing

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RĂĽck, Hans-Georg; Frey, Gerhard (1994), "A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves",
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Proceedings of the International Congress of Mathematicians (Stockholm, 1962)
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applied the Tate pairing over finite fields to cryptography.
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For the related pairing on the Tate–Shafarevich group, see
222:"Duality theorems in Galois cohomology over number fields" 96:(1969), "Duality theorems for curves over p-adic fields", 228:, Djursholm: Inst. Mittag-Leffler, pp. 288–295, 299: 282: 92: 64: 289: 275: 149: 68: 257:This cryptography-related article is a 300: 245: 216: 195: 60: 56: 27:is any of several closely related 13: 14: 334: 249: 1: 86: 261:. You can help Knowledge by 202:WC-groups over p-adic fields 7: 313:Elliptic curve cryptography 74: 10: 339: 308:Pairing-based cryptography 244: 153:Mathematics of Computation 15: 99:Inventiones Mathematicae 51:pairings introduced by 69:RĂĽck & Frey (1994) 94:Lichtenbaum, Stephen 18:Cassels–Tate pairing 112:1969InMat...7..120L 323:Cryptography stubs 120:10.1007/BF01389795 65:Lichtenbaum (1969) 63:) and extended by 270: 269: 37:abelian varieties 29:bilinear pairings 23:In mathematics, 330: 291: 284: 277: 253: 246: 241: 236:, archived from 213: 192: 160:(206): 865–874, 146: 338: 337: 333: 332: 331: 329: 328: 327: 318:Elliptic curves 298: 297: 296: 295: 166:10.2307/2153546 89: 77: 47:, based on the 39:, usually over 33:elliptic curves 21: 12: 11: 5: 336: 326: 325: 320: 315: 310: 294: 293: 286: 279: 271: 268: 267: 254: 243: 242: 214: 193: 147: 106:(2): 120–136, 88: 85: 84: 83: 76: 73: 9: 6: 4: 3: 2: 335: 324: 321: 319: 316: 314: 311: 309: 306: 305: 303: 292: 287: 285: 280: 278: 273: 272: 266: 264: 260: 255: 252: 248: 247: 240:on 2011-07-17 239: 235: 231: 227: 223: 219: 215: 212: 208: 204: 203: 198: 194: 191: 187: 183: 179: 175: 171: 167: 163: 159: 155: 154: 148: 145: 141: 137: 133: 129: 125: 121: 117: 113: 109: 105: 101: 100: 95: 91: 90: 82: 79: 78: 72: 70: 66: 62: 58: 54: 50: 46: 45:finite fields 42: 38: 34: 30: 26: 19: 263:expanding it 256: 238:the original 225: 201: 157: 151: 103: 97: 81:Weil pairing 49:Tate duality 25:Tate pairing 24: 22: 302:Categories 218:Tate, John 197:Tate, John 87:References 31:involving 174:0025-5718 144:122239828 128:0020-9910 220:(1963), 199:(1958), 75:See also 234:0175892 211:0105420 190:1218343 182:2153546 136:0242831 108:Bibcode 55: ( 232:  209:  188:  180:  172:  142:  134:  126:  178:JSTOR 140:S2CID 41:local 259:stub 170:ISSN 124:ISSN 61:1963 57:1958 53:Tate 162:doi 116:doi 43:or 35:or 304:: 230:MR 224:, 207:MR 186:MR 184:, 176:, 168:, 158:62 156:, 138:, 132:MR 130:, 122:, 114:, 102:, 67:. 59:, 290:e 283:t 276:v 265:. 164:: 118:: 110:: 104:7 20:.

Index

Cassels–Tate pairing
bilinear pairings
elliptic curves
abelian varieties
local
finite fields
Tate duality
Tate
1958
1963
Lichtenbaum (1969)
RĂĽck & Frey (1994)
Weil pairing
Lichtenbaum, Stephen
Inventiones Mathematicae
Bibcode
1969InMat...7..120L
doi
10.1007/BF01389795
ISSN
0020-9910
MR
0242831
S2CID
122239828
Mathematics of Computation
doi
10.2307/2153546
ISSN
0025-5718

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