# 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
**
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 2^{1734} +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
x^{4}-2x^{3}+2x^{2}-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
x^{4}+x^{3}-4x^{2}-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.