Concept

Elliptic curve primality

Related publications (32)

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Dictionary learning over large distributed models via dual-ADMM strategies

Ali H. Sayed

We consider the problem of dictionary learning over large scale models, where the model parameters are distributed over a multi-agent network. We demonstrate that the dual optimization problem for inference is better conditioned than the primal problem and ...

IEEE2014

Generalised Mersenne Numbers Revisited

Robert Granger

Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus making them an attrac ...

2013

On the Cryptanalysis of Public-Key Cryptography

Joppe Willem Bos

Nowadays, the most popular public-key cryptosystems are based on either the integer factorization or the discrete logarithm problem. The feasibility of solving these mathematical problems in practice is studied and techniques are presented to speed-up the ...

EPFL2012

Algebraic Divisibility Sequences Over Function Fields

Valéry Aurélien Mahé

In this note we study the existence of primes and of primitive divisors in function field analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields define ...

Australian Mathematical Society2012

Solving 112-bit prime ECDLP on game consoles using sloppy reduction

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung, Marcelo Kaihara

We describe a cell processor implementation of Pollard’s rho method to solve discrete logarithms in groups of elliptic curves over prime fields. The implementation was used on a cluster of PlayStation 3 game consoles to set a new record. We present in deta ...

2012

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

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

Group Testing with Probabilistic Tests: Theory, Design and Application

Martin Vetterli, Amin Karbasi, Ali Hormati, Mahdi Cheraghchi Bashi Astaneh

Identification of defective members of large populations has been widely studied in the statistics community under the name of group testing. It involves grouping subsets of items into different pools and detecting defective members based on the set of tes ...

Institute of Electrical and Electronics Engineers2011

Efficient and side-channel-aware implementations of elliptic curve cryptosystems over prime fields

Yusuf Leblebici

Elliptic curve cryptosystems (ECCs) are utilised as an alternative to traditional public-key cryptosystems, and are more suitable for resource-limited environments because of smaller parameter size. In this study, the authors carry out a thorough investiga ...

2010

High-Performance Modular Multiplication on the Cell Processor

Joppe Willem Bos

This paper presents software implementation speed records for modular multiplication arithmetic on the synergistic processing elements of the Cell broadband engine (Cell) architecture. The focus is on moduli which are of special interest in elliptic curve ...

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