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On Improving Integer Factorization and Discrete Logarithm Computation using Partial Triangulation
RSA factoring discrete logarithm problem
2017/8/8
The number field sieve is the best-known algorithm for factoring integers and solving the discrete logarithm problem in prime fields. In this paper, we present some new improvements to various steps o...
A Simple and Improved Algorithm for Integer Factorization with Implicit Hints
public-key cryptography / factoring
2016/1/6
Given two integers N1=p1q1 and N2=p2q2 with α-bit primes q1,q2, suppose that the t least significant bits of p1 and p2 are equal. May and Ritzenhofen (PKC 2009) developed a factoring algorithm for N1,...
On the Complexity of Integer Factorization
Integer Factorization irreducible polynomials integer factorization algorithm
2009/6/12
This note presents a deterministic integer factorization algorithm based on a system of polynomials
equations. This technique exploits a new idea in the construction of irreducible polynomials with p...
On Black-Box Ring Extraction and Integer Factorization
Black-Box Ring Extraction Integer Factorization Diffie-Hellman problem
2009/6/3
The black-box extraction problem over rings has (at least) two important interpretations in
cryptography: An efficient algorithm for this problem implies (i) the equivalence of computing discrete
lo...
Achieving a log(n) Speed Up for Boolean Matrix Operations and Calculating the Complexity of the Dense Linear Algebra step of Algebraic Stream Cipher Attacks and of Integer Factorization Methods
Matrix Inversion Matrix Multiplication Boolean Matrices
2008/11/20
The purpose of this paper is to calculate the running time of dense boolean matrix operations,
as used in stream cipher cryptanalysis and integer factorization. Several variations of Gaussian
Elimin...