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Factorization of a 768-Bit RSA Modulus
This paper reports on the factorization of the 768-bit number RSA-768 by the number field sieve factoring method and discusses some implications for RSA.
Factorization of a 512-Bit RSA Modulus
This paper reports on the factorization of the 512-bit number RSA-155 by the Number Field Sieve factoring method (NFS) and discusses the implications for RSA.
Factorization of RSA-140 Using the Number Field Sieve
TLDR
It is concluded that 512-bit (= 155-digit) RSA moduli are easily and realistically within reach of factoring efforts similar to the one presented here.
Computations concerning the conjecture of Mertens.
A self-contained data acquisition device or probe capable of monitoring any physical function that can be translated into an analog or digital signal. The data acquisition probe is coupled to a
Iteration of number-theoretic functions
This is a concise survey of literature on sequences which arise when a number-theoretic function f : 1N • 1N is iteratively applied to a given starting number. Many of the functions f discussed are
Factorization of RSA-140 Using the Number Field Sieve
On February 2, 1999, we completed the factorization of the 140-digit number RSA-140 with the help of the Number Field Sieve factoring method (NFS). This is a new general factoring record. The
Algorithms and applications on vector and parallel computers
TLDR
The gigantic capacities of present-day supercomputers offer the possibility of tackling problems of a size and complexity which could not be handled before, and the efficient use of these machines often requires the design of new numerical algorithms, or the re-design of existing algorithms and data organization in order to meet the possibilities of the new architectures.
A Comparative Study of Algorithms for Computing Continued Fractions of Algebraic Numbers
The obvious way to compute the continued fraction of a real number α > 1 is to compute a very accurate numerical approximation of α, and then to iterate the well-known truncate-and-invert step which
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