Publications related to On the Use of the Negation Map in the Pollard Rho Method

Elliptic and Hyperelliptic Curves: A Practical Security Analysis

Motivated by the advantages of using elliptic curves for discrete logarithm-based public-key cryptography, there is an active research area investigating the potential of using hyperelliptic curves of genus 2. For both types of curves, the best known algor ...

Springer Berlin Heidelberg2014

Solving a $6120$-bit DLP on a Desktop Computer

Robert Granger, Jens Markus Zumbrägel

In this paper we show how some recent ideas regarding the discrete logarithm problem (DLP) in finite fields of small characteristic may be applied to compute logarithms in some very large fields extremely efficiently. By combining the polynomial time relat ...

Springer Berlin Heidelberg2013

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}_{2^{1971}}$ and $\mathbb{F}_{2^{3164}}$

Robert Granger, Jens Markus Zumbrägel

In this paper we propose a binary field variant of the Joux-Lercier medium-sized Function Field Sieve, which results not only in complexities as low as

L_{q^n}(1/3,(4/9)1/3)

for computing arbitrary logarithms, but also in an heuristic polynomial time alg ...

Springer Berlin Heidelberg2013

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

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

Hardness of Computing Individual Bits for One-way Functions on Elliptic Curves

Dimitar Petkov Jetchev, Alexandre Raphaël Duc

We prove that if one can predict any of the bits of the input to an elliptic curve based one-way function over a finite field, then we can invert the function. In particular, our result implies that if one can predict any of the bits of the input to a clas ...

Springer2012

Some remarks on the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication

Jeanine Marie Van Order

We establish several results towards the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication over imaginary quadratic fields, namely (i) the existence of an appropriate p-adic L-function, building on works of H ...

2012

On isogeny classes of Edwards curves over finite fields

Robert Granger

We count the number of isogeny classes of Edwards curves over finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class contains a {\em complete} Edwards curve, and that an Edwards curve is isogeno ...

Elsevier2012

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

On the Static Diffie-Hellman Problem on Elliptic Curves over Extension Fields

Robert Granger

Recent work by Koblitz and Menezes has highlighted the existence, in some cases, of apparent separations between the hardness of breaking discrete logarithms in a particular group, and the hardness of solving in that group problems to which the security of ...

2010

On the Use of the Negation Map in the Pollard Rho Method

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Elliptic and Hyperelliptic Curves: A Practical Security Analysis

Solving a $6120$-bit DLP on a Desktop Computer

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}_{2^{1971}}$ and $\mathbb{F}_{2^{3164}}$

On the Cryptanalysis of Public-Key Cryptography

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

Hardness of Computing Individual Bits for One-way Functions on Elliptic Curves

Some remarks on the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication

On isogeny classes of Edwards curves over finite fields

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

On the Static Diffie-Hellman Problem on Elliptic Curves over Extension Fields

On the Cryptanalysis of Public-Key Cryptography

Some remarks on the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication

Elliptic and Hyperelliptic Curves: A Practical Security Analysis

Solving a $6120$-bit DLP on a Desktop Computer

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}_{2^{1971}}$ and $\mathbb{F}_{2^{3164}}$

Hardness of Computing Individual Bits for One-way Functions on Elliptic Curves

On the Static Diffie-Hellman Problem on Elliptic Curves over Extension Fields

On isogeny classes of Edwards curves over finite fields

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

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