Knowledge

Eric Bach

Source đź“ť

368: 381: 374: 317: 211: 246: 457: 452: 418: 217:). This result shows that the generalized Riemann hypothesis implies tight bounds for the necessary run-time of the deterministic version of the 472: 467: 257: 164: 447: 477: 437: 411: 147: 47: 462: 139: 131: 100: 78: 218: 404: 158: 325: 124: 280: 222: 154: 442: 51: 225:
where previous work relied on heuristic estimates and empirical data. He is the namesake of
221:. Bach also did some of the first work on pinning down the actual expected run-time of the 8: 226: 299: 120: 339: 35: 392: 334: 289: 85: 68: 278:
Bach, Eric (1990), "Explicit bounds for primality testing and related problems",
388: 431: 367: 380: 104: 143: 90: 303: 251: 294: 146:. He is currently a professor at the Computer Science Department, 135: 373: 206:{\displaystyle \left(\mathbb {Z} /n\mathbb {Z} \right)^{*}} 213:
is generated by its elements smaller than 2(log 
167: 387:This article about an American mathematician is a 205: 153:Among other work, he gave explicit bounds for the 429: 130:Bach completed his undergraduate studies at the 254:Theoretical Computer Science genealogy database 412: 419: 405: 453:UC Berkeley College of Engineering alumni 338: 318:"Toward a theory of Pollard's rho method" 293: 188: 175: 229:for generating random factored numbers. 458:University of Wisconsin–Madison faculty 430: 157:, which imply that if one assumes the 361: 315: 277: 142:, in 1984 under the supervision of 48:University of California - Berkeley 13: 140:University of California, Berkeley 14: 489: 132:University of Michigan, Ann Arbor 79:University of Wisconsin - Madison 473:21st-century American scientists 468:20th-century American scientists 379: 372: 366: 148:University of Wisconsin–Madison 309: 271: 239: 159:generalized Riemann hypothesis 123:who has made contributions to 1: 448:University of Michigan alumni 232: 138:in computer science from the 478:American mathematician stubs 438:American computer scientists 391:. You can help Knowledge by 340:10.1016/0890-5401(91)90001-i 7: 326:Information and Computation 219:Miller–Rabin primality test 125:computational number theory 16:American computer scientist 10: 494: 360: 281:Mathematics of Computation 155:Chebotarev density theorem 463:American number theorists 110: 96: 84: 74: 64: 57: 43: 28: 21: 207: 52:University of Michigan 208: 260:on November 27, 2005 165: 316:Bach, Eric (1991). 223:Pollard rho method 203: 121:computer scientist 400: 399: 114: 113: 97:Doctoral students 59:Scientific career 36:Chicago, Illinois 485: 421: 414: 407: 383: 378: 377: 376: 370: 362: 352: 351: 349: 347: 342: 322: 313: 307: 306: 297: 288:(191): 355–380, 275: 269: 268: 266: 265: 256:. Archived from 243: 227:Bach's algorithm 212: 210: 209: 204: 202: 201: 196: 192: 191: 183: 178: 86:Doctoral advisor 69:Computer Science 19: 18: 493: 492: 488: 487: 486: 484: 483: 482: 428: 427: 426: 425: 371: 365: 358: 356: 355: 345: 343: 320: 314: 310: 295:10.2307/2008811 276: 272: 263: 261: 245: 244: 240: 235: 197: 187: 179: 174: 173: 169: 168: 166: 163: 162: 119:is an American 103: 50: 44:Alma mater 39: 33: 24: 17: 12: 11: 5: 491: 481: 480: 475: 470: 465: 460: 455: 450: 445: 440: 424: 423: 416: 409: 401: 398: 397: 384: 354: 353: 333:(2): 139–155. 308: 270: 237: 236: 234: 231: 200: 195: 190: 186: 182: 177: 172: 134:, and got his 112: 111: 108: 107: 98: 94: 93: 88: 82: 81: 76: 72: 71: 66: 62: 61: 55: 54: 45: 41: 40: 34: 30: 26: 25: 22: 15: 9: 6: 4: 3: 2: 490: 479: 476: 474: 471: 469: 466: 464: 461: 459: 456: 454: 451: 449: 446: 444: 443:Living people 441: 439: 436: 435: 433: 422: 417: 415: 410: 408: 403: 402: 396: 394: 390: 385: 382: 375: 369: 364: 363: 359: 341: 336: 332: 328: 327: 319: 312: 305: 301: 296: 291: 287: 283: 282: 274: 259: 255: 253: 248: 242: 238: 230: 228: 224: 220: 216: 198: 193: 184: 180: 170: 160: 156: 151: 149: 145: 141: 137: 133: 128: 126: 122: 118: 109: 106: 102: 99: 95: 92: 89: 87: 83: 80: 77: 73: 70: 67: 63: 60: 56: 53: 49: 46: 42: 37: 31: 27: 20: 393:expanding it 386: 357: 344:. Retrieved 330: 324: 311: 285: 279: 273: 262:. Retrieved 258:the original 250: 241: 214: 152: 129: 116: 115: 105:Victor Shoup 101:John Watrous 75:Institutions 58: 247:"Eric Bach" 144:Manuel Blum 91:Manuel Blum 432:Categories 264:2008-06-04 252:ACM SIGACT 233:References 199:∗ 117:Eric Bach 32:November, 23:Eric Bach 346:March 4, 304:2008811 302:  161:then 65:Fields 38:, U.S. 321:(PDF) 300:JSTOR 136:Ph.D. 389:stub 348:2015 29:Born 335:doi 290:doi 434:: 331:90 329:. 323:. 298:, 286:55 284:, 249:. 150:. 127:. 420:e 413:t 406:v 395:. 350:. 337:: 292:: 267:. 215:n 194:) 189:Z 185:n 181:/ 176:Z 171:(

Index

Chicago, Illinois
University of California - Berkeley
University of Michigan
Computer Science
University of Wisconsin - Madison
Doctoral advisor
Manuel Blum
John Watrous
Victor Shoup
computer scientist
computational number theory
University of Michigan, Ann Arbor
Ph.D.
University of California, Berkeley
Manuel Blum
University of Wisconsin–Madison
Chebotarev density theorem
generalized Riemann hypothesis
Miller–Rabin primality test
Pollard rho method
Bach's algorithm
"Eric Bach"
ACM SIGACT
the original
Mathematics of Computation
doi
10.2307/2008811
JSTOR
2008811
"Toward a theory of Pollard's rho method"

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

↑