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Analysis of Bernstein's factorization circuit

Related publications (42)

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A heterogeneous computing environment to solve the 768-bit RSA challenge

Arjen Lenstra, Pénélope Leyland, Pascal Jermini, Joppe Willem Bos, Thorsten Kleinjung, Dag Arne Osvik, Michela Thiémard, Heinz Stockinger

In December 2009 the 768-bit, 232-digit number RSA-768 was factored using the number field sieve. Overall, the computational challenge would take more than 1700 years on a single, standard core. In the article we present the heterogeneous computing approac ...

Springer Verlag2012

Efficient SIMD Arithmetic Modulo a Mersenne Number

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung

This paper describes carry-less arithmetic operations modulo an integer 2^M-1 in the thousand-bit range, targeted at single instruction multiple data platforms and applications where overall throughput is the main performance criterion. Using an implementa ...

IEEE2011

Efficient SIMD arithmetic modulo a Mersenne number

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung

This paper describes carry-less arithmetic operations modulo an integer 2^M − 1 in the thousand-bit range, targeted at single instruction multiple data platforms and applications where overall throughput is the main performance criterion. Using an implemen ...

IEEE Computer Soc Press2011

Factorization of a 768-Bit RSA Modulus

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung, Dag Arne Osvik, Patric Zimmermann

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. ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2010

Polar Codes: Characterization of Exponent, Bounds, and Constructions

Rüdiger Urbanke, Satish Babu Korada, Eren Sasoglu

Polarization codes were recently introduced by Ar\i kan. They are explicit code constructions which achieve the capacity of arbitrary symmetric binary-input discrete memoryless channels (and even extensions thereof) under a low complexity successive decodi ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009

Efficient multiplication using type $2$ optimal normal bases

Mohammad Amin Shokrollahi

In this paper we propose a new structure for multiplication using optimal normal bases of type

2

. The multiplier uses an efficient linear transformation to convert the normal basis representations of elements of

F_{q^{n}}

to suitable polynomials of deg ...

2007

, ,

We describe how we reached a new factoring milestone by completing the first special number field sieve factorization of a number having more than 1024 bits, namely the Mersenne number 21039 -1. Although this factorization is orders of magnitude ...

2007

We introduce VSH, very smooth hash, a new S-bit hash function that is provably collision-resistant assuming the hardness of finding nontrivial modular square roots of very smooth numbers modulo an S-bit composite. By very smooth, we mean that the smoothnes ...

Springer Verlag2006

Optimal Interpolation of Fractional Brownian Motion Given Its Noisy Samples

Michaël Unser, Thierry Blu

We consider the problem of estimating a fractional Brownian motion known only from its noisy samples at the integers. We show that the optimal estimator can be expressed using a digital Wiener-like filter followed by a simple time-variant correction accoun ...

IEEE2006

The project consists in the study, implementation and comparison of binary matrix multiplication algorithms in C++. We consider Strassen’s algorithm (which is known to perform well over the real numbers) the Four Russians algorithm (which is designed for b ...

2005

Efficient multiplication using type $2$ optimal normal bases

Mohammad Amin Shokrollahi

In this paper we propose a new structure for multiplication using optimal normal bases of type

2

. The multiplier uses an efficient linear transformation to convert the normal basis representations of elements of

F_{q^{n}}

to suitable polynomials of deg ...

2007