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Elliptic and Hyperelliptic Curves: A Practical Security Analysis

Publications associées (38)

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Bounded Tamper Resilience: How to go beyond the Algebraic Barrier

Sebastian Faust

Related key attacks (RKAs) are powerful cryptanalytic attacks where an adversary can change the secret key and observe the effect of such changes at the output. The state of the art in RKA security protects against an a-priori unbounded number of certain a ...

2013

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

Low-Latency Elliptic Curve Scalar Multiplication

Joppe Willem Bos

This paper presents a low-latency algorithm designed for parallel computer architectures to compute the scalar multiplication of elliptic curve points based on approaches from cryptographic side-channel analysis. A graphics processing unit implementation u ...

Springer Verlag2012

Faster Software Cryptography

Dag Arne Osvik

This thesis presents work on the efficiency and security of cryptographic software. First it describes several efforts to construct very efficient implementations of cryptographic primitives. These include the Advanced Encryption Standard (AES) as well as ...

EPFL2012

Cryptographic Hash Functions in Groups and Provable Properties

Juraj Sarinay

We consider several "provably secure" hash functions that compute simple sums in a well chosen group (G,*). Security properties of such functions provably translate in a natural way to computational problems in G that are simple to define and possibly also ...

EPFL2011

Using the Cloud to Determine Key Strengths

Arjen Lenstra, Thorsten Kleinjung

We develop a new methodology to assess cryptographic key strength using cloud computing, by calculating the true economic cost of (symmetric- or private-) key retrieval for the most common cryptographic primitives. Although the present paper gives the curr ...

2011

A Mobile World of Security

Christine Neuberg

Security in mobile communications is a topic of increasing relevance in everyday life. We all use mobile devices for everyday communications, maybe even for exchanging confidential information with the work place. This requires security systems that are re ...

EPFL2011

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 Use of the Negation Map in the Pollard Rho Method

Arjen Lenstra, Joppe Willem Bos, Thorsten Kleinjung

The negation map can be used to speed up the Pollard rho method to compute discrete logarithms in groups of elliptic curves over finite fields. It is well known that the random walks used by Pollard rho when combined with the negation map get trapped in fr ...

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

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