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GI
2007
Springer
13 years 11 months ago
On Factoring Arbitrary Integers with Known Bits
: We study the factoring with known bits problem, where we are given a composite integer N = p1p2 . . . pr and oracle access to the bits of the prime factors pi, i = 1, . . . , r. ...
Mathias Herrmann, Alexander May
EUROCRYPT
1999
Springer
13 years 10 months ago
Proving in Zero-Knowledge that a Number Is the Product of Two Safe Primes
Abstract. We present the first efficient statistical zero-knowledge protocols to prove statements such as: – A committed number is a prime. – A committed (or revealed) number ...
Jan Camenisch, Markus Michels
MOC
2010
13 years 12 days ago
The number field sieve for integers of low weight
We define the weight of an integer N to be the smallest w such that N can be represented as w i=1 i2ci , with 1,..., w{1,-1}. Since arithmetic modulo a prime of low weight is parti...
Oliver Schirokauer
ANTS
1998
Springer
139views Algorithms» more  ANTS 1998»
13 years 10 months ago
Generating Arithmetically Equivalent Number Fields with Elliptic Curves
In this note we address the question whether for a given prime number p, the zeta-function of a number field always determines the p-part of its class number. The answer is known t...
Bart de Smit
ACNS
2007
Springer
172views Cryptology» more  ACNS 2007»
13 years 11 months ago
Estimating the Prime-Factors of an RSA Modulus and an Extension of the Wiener Attack
In the RSA system, balanced modulus N denotes a product of two large prime numbers p and q, where q < p < 2q. Since IntegerFactorization is difficult, p and q are simply esti...
Hung-Min Sun, Mu-En Wu, Yao-Hsin Chen