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Computational indistinguishability

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447:, must decide based on a single sample from one of the distributions. One might conceive of a situation in which the algorithm trying to distinguish between two distributions, could access as many samples as it needed. Hence two ensembles that cannot be distinguished by polynomial-time algorithms looking at multiple samples are deemed 419:. Another interpretation of computational indistinguishability, is that polynomial-time algorithms actively trying to distinguish between the two ensembles cannot do so: that any such algorithm will only perform negligibly better than if one were to just guess. 326: 148: 98: 369: 417: 445: 189: 569: 455:
that generates samples for it, then indistinguishability by polynomial-time sampling is equivalent to computational indistinguishability.
535: 176: 103: 53: 161:(which usually refers to the length of the input); we say they are computationally indistinguishable if for any 162: 31: 334: 151: 470: 42:
if no efficient algorithm can tell the difference between them except with negligible probability.
396: 553: 155: 17: 542:, "Introduction to Modern Cryptography: Principles and Protocols," Chapman & Hall/CRC, 2007 532:. Foundations of Cryptography: Volume 2 – Basic Applications. Cambridge University Press, 2004. 451:. If the polynomial-time algorithm can generate samples in polynomial time, or has access to a 519: 513: 166: 503: 539: 529: 499: 484: 430: 516:, The Round Complexity of Secure Protocols (Extended Abstract), 1990, pp. 503–513 563: 523: 509: 452: 35: 321:{\displaystyle \delta (n)=\left|\Pr _{x\gets D_{n}}-\Pr _{x\gets E_{n}}\right|.} 487:(2003). Foundations of cryptography. Cambridge, UK: Cambridge University Press. 549: 548:
This article incorporates material from computationally indistinguishable on
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s behavior does not significantly change when given samples according to
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Lecture 4 - Computational Indistinguishability, Pseudorandom Generators
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In computer science, relationship between two families of distributions
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Implicit in the definition is the condition that the algorithm,
143:{\displaystyle \scriptstyle \{E_{n}\}_{n\in \mathbb {N} }} 93:{\displaystyle \scriptstyle \{D_{n}\}_{n\in \mathbb {N} }} 107: 57: 526:. Probabilistic Encryption. JCSS, 28(2):270–299, 1984 433: 399: 337: 192: 106: 56: 439: 411: 363: 320: 142: 92: 554:Creative Commons Attribution/Share-Alike License 264: 214: 449:indistinguishable by polynomial-time sampling 8: 371:. In other words, every efficient algorithm 122: 108: 72: 58: 480: 478: 432: 398: 355: 342: 336: 278: 267: 228: 217: 191: 133: 132: 125: 115: 105: 83: 82: 75: 65: 55: 463: 7: 38:, two families of distributions are 406: 364:{\displaystyle D_{n}\approx E_{n}} 25: 40:computationally indistinguishable 18:Computationally indistinguishable 570:Algorithmic information theory 552:, which is licensed under the 403: 307: 298: 292: 286: 271: 257: 248: 242: 236: 221: 202: 196: 175:, the following quantity is a 1: 504:Introduction to Cryptography 412:{\displaystyle n\to \infty } 586: 32:computational complexity 441: 413: 365: 322: 152:distribution ensembles 144: 94: 442: 414: 366: 323: 145: 95: 431: 397: 335: 190: 104: 54: 177:negligible function 508:Donald Beaver and 437: 409: 361: 318: 285: 235: 156:security parameter 140: 139: 90: 89: 440:{\displaystyle A} 263: 213: 46:Formal definition 16:(Redirected from 577: 520:Shafi Goldwasser 488: 482: 473: 468: 446: 444: 443: 438: 418: 416: 415: 410: 393:in the limit as 370: 368: 367: 362: 360: 359: 347: 346: 327: 325: 324: 319: 314: 310: 284: 283: 282: 234: 233: 232: 149: 147: 146: 141: 138: 137: 136: 120: 119: 99: 97: 96: 91: 88: 87: 86: 70: 69: 21: 585: 584: 580: 579: 578: 576: 575: 574: 560: 559: 546: 514:Phillip Rogaway 496: 491: 483: 476: 469: 465: 461: 429: 428: 425: 423:Related notions 395: 394: 392: 383: 351: 338: 333: 332: 274: 224: 212: 208: 188: 187: 167:polynomial time 121: 111: 102: 101: 71: 61: 52: 51: 48: 28: 23: 22: 15: 12: 11: 5: 583: 581: 573: 572: 562: 561: 544: 543: 540:Yehuda Lindell 533: 530:Oded Goldreich 527: 517: 506: 500:Yehuda Lindell 495: 494:External links 492: 490: 489: 474: 462: 460: 457: 436: 424: 421: 408: 405: 402: 388: 379: 358: 354: 350: 345: 341: 329: 328: 317: 313: 309: 306: 303: 300: 297: 294: 291: 288: 281: 277: 273: 270: 266: 262: 259: 256: 253: 250: 247: 244: 241: 238: 231: 227: 223: 220: 216: 211: 207: 204: 201: 198: 195: 165:probabilistic 135: 131: 128: 124: 118: 114: 110: 85: 81: 78: 74: 68: 64: 60: 47: 44: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 582: 571: 568: 567: 565: 558: 557: 555: 551: 541: 537: 536:Jonathan Katz 534: 531: 528: 525: 524:Silvio Micali 521: 518: 515: 511: 510:Silvio Micali 507: 505: 501: 498: 497: 493: 486: 485:Goldreich, O. 481: 479: 475: 472: 467: 464: 458: 456: 454: 453:random oracle 450: 434: 422: 420: 400: 391: 387: 382: 378: 374: 356: 352: 348: 343: 339: 315: 311: 304: 301: 295: 289: 279: 275: 268: 260: 254: 251: 245: 239: 229: 225: 218: 209: 205: 199: 193: 186: 185: 184: 182: 178: 174: 171: 168: 164: 160: 157: 154:indexed by a 153: 129: 126: 116: 112: 79: 76: 66: 62: 45: 43: 41: 37: 33: 19: 547: 545: 466: 448: 426: 389: 385: 380: 376: 372: 330: 180: 172: 158: 49: 39: 36:cryptography 29: 163:non-uniform 550:PlanetMath 459:References 407:∞ 404:→ 349:≈ 272:← 261:− 222:← 194:δ 170:algorithm 130:∈ 80:∈ 564:Category 331:denoted 150:be two 522:and 512:and 100:and 50:Let 34:and 384:or 179:in 30:In 566:: 538:, 502:. 477:^ 373:A' 265:Pr 215:Pr 183:: 556:. 435:A 401:n 390:n 386:E 381:n 377:D 357:n 353:E 344:n 340:D 316:. 312:| 308:] 305:1 302:= 299:) 296:x 293:( 290:A 287:[ 280:n 276:E 269:x 258:] 255:1 252:= 249:) 246:x 243:( 240:A 237:[ 230:n 226:D 219:x 210:| 206:= 203:) 200:n 197:( 181:n 173:A 159:n 134:N 127:n 123:} 117:n 113:E 109:{ 84:N 77:n 73:} 67:n 63:D 59:{ 20:)

Index

Computationally indistinguishable
computational complexity
cryptography
distribution ensembles
security parameter
non-uniform
polynomial time
algorithm
negligible function
random oracle
Lecture 4 - Computational Indistinguishability, Pseudorandom Generators


Goldreich, O.
Yehuda Lindell
Introduction to Cryptography
Silvio Micali
Phillip Rogaway
Shafi Goldwasser
Silvio Micali
Oded Goldreich
Jonathan Katz
Yehuda Lindell
PlanetMath
Creative Commons Attribution/Share-Alike License
Category
Algorithmic information theory

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