# Subexponential Crypto Computation, B. Dodson

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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.
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Factoring News, Elliptic Curve Method (ECM) hits 66-digit Record.

Index.