Publications related to Digital Signature Schemes with Domain Parameters

An efficient deterministic test for Kloosterman sum zeros

We propose a simple deterministic test for deciding whether or not a non-zero element

a \in \mathbb{F}_{2^n}

or

\mathbb{F}_{3^n}

is a zero of the corresponding Kloosterman sum over these fields, and analyse its complexity. The test seems to have been o ...

American Mathematical Society2014

Prime Power Terms In Elliptic Divisibility Sequences

Valéry Aurélien Mahé

We study a problem on specializations of multiples of rational points on elliptic curves analogous to the Mersenne problem. We solve this problem when descent via isogeny is possible by giving explicit bounds on the indices of prime power terms in elliptic ...

American Mathematical Society2014

Primeless Factoring-Based Cryptography

Serge Vaudenay, Sonia Mihaela Bogos

Factoring-based public-key cryptosystems have an overall complexity which is dominated by the key-production algorithm, which requires the generation of prime numbers. This is most inconvenient in settings where the key-generation is not an one-off process ...

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

Primeless Modular Cryptography (Extended Abstract)

Serge Vaudenay, Sonia Mihaela Bogos

Most of the known public-key cryptosystems have an overall complexity which is dominated by the key-production algorithm, which requires the generation of prime numbers. This is most inconvenient in settings where the key-generation is not an one-off proce ...

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

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

OREN: Optimal Revocations in Ephemeral Networks

Jean-Pierre Hubaux, Maxime Raya, Igor Bilogrevic

Public-key certificates allow a multitude of entities to securely exchange and verify the authenticity of data. However, the ability to effectively revoke compromised or untrustworthy certificates is of great importance when coping with misbehavior. In thi ...

2011

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

Digital Signature Schemes with Domain Parameters

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An efficient deterministic test for Kloosterman sum zeros

Prime Power Terms In Elliptic Divisibility Sequences

Primeless Factoring-Based Cryptography

On the Cryptanalysis of Public-Key Cryptography

Primeless Modular Cryptography (Extended Abstract)

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

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

OREN: Optimal Revocations in Ephemeral Networks

Efficient SIMD arithmetic modulo a Mersenne number

An efficient deterministic test for Kloosterman sum zeros

Prime Power Terms In Elliptic Divisibility Sequences

Primeless Modular Cryptography (Extended Abstract)

Primeless Factoring-Based Cryptography

On the Cryptanalysis of Public-Key Cryptography

OREN: Optimal Revocations in Ephemeral Networks

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

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

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

Efficient SIMD arithmetic modulo a Mersenne number