Lehigh Math Contest, B. Dodson

Lenstra, Jones Video (2 Journeys)

  • Lenstra photos treurfeest
    • [NFSNET] [Cunningham project] [ECMNET quick start] [Mersenne project]

    News!:

  • 18 February 2005: Probable new Mersenne prime, extracted from a report at mathworld

    • References ( Scott Contini's Factor World ; K. Fong's list):

    Sieving, 1928-2003:

  • E. Tromer [TWIRL]

    • Secret Key (Symmetric, Random-based) encryption: end of 64-bits

  • Goldberg and Wagner's 1995 break of Netscape's random number generator; and unix version, 1996 break of MIT's kerberos
  • EFF's DES Cracker Project and rc5-64bits broken by distributed.net ; brute force attack
  • M. Matsui, The First Experimental Cryptanalysis of the Data Encryption Standard
  • AES, Advanced Encryption Standard (128-bits) Nat'l Inst. Standards & Tech.

    • Public Key (Asymmetric, Math-based) encryption: end of 384-bits and 512-bits

  • RSA Security Inc. and RSA Laboratories
  • Certicom
  • 108-bit challenge solved

    • Future Computing(?): end of 4-bits

  • IBM's 2001 announcement of the successful factorization of 15 using a 7-qubit quantum computer

    • Lehigh Factoring News, Number Field Sieve (NFS):

  • 3 January 2005: The factorization of 21734 +1 was completed when the cofactor having 156 digits: 4368442810835521581268899924524957424706430603565561 4251997719921942938829565641342379754148199838850876 8685853687232087083919375105407415049294640427023681 was factored, with one prime factor having 71 digits: 113908630435024549328114941768055223 22333679313892091082261899485723141, the other prime factor having 86 digits: 3835041115104405393812608016929173891645880 0482405483935438018190740632202303569628941. The number field used was of degree 4 with non-cyclic Galois group of order 4, and polynomial x4-2x3+2x2-4x+4.
  • 29 January 2005: The factorization of 7 390 +1 was completed when the cofactor having 163 digits: 1778498287704816928742247829325498465684164715658046774 8769640920001774729733927003247267769378676604409530757 62555817233231067167579448693420525197723461573177601 was factored, with one prime factor having 59 digits: 83045488934614078783587315830746672662467594739668065636081, the other prime factor having 104 digits: 2141595299782169678394228420555707230215610015828713 7380707797733278925848073819451149244991100839387921. The number field used was of degree 4 with cyclic Galois group of order 4, and polynomial x4+x3-4x2-4x+1.
  • February 2005: Sieving to factor 5 320 +1 is currently in progress.

    • Factoring News, Elliptic Curve Method (ECM):

  • Lehigh ECMNET page ecmnet2004a; update ecmnet2004.