Subexponential Crypto Computation, B. Dodson

Primes and Factorization

News:

  • December 2005: New Mersenne prime, nears 10-million digit EFF Challenge. See also Intro. and Largest 10 primes,

    • 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
  • 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. Also with same subexp runtime: Diffie-Hellman, Discrete Log mod p.
  • Certicom (ECC)
  • 108-bit challenge solved EC Discrete Log

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

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

    • [ Index. Ref2. ]