# 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. ]