H. Riele

Publications43
h-index10
Citations1,033
Highly Influential Citations32
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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…
Proceedings of the European Congress of Mathematics
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.
Factoring with the quadratic sieve on large vector computers
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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