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Using cyclotomic polynomials to construct efficient discrete logarithm cryptosystems over finite fields

Related publications (39)

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Forgery-Resilience for Digital Signature Schemes

Khaled Ouafi, Atefeh Mashatan

We introduce the notion of forgery-resilience for digital signature schemes, a new paradigm for digital signature schemes exhibiting desirable legislative properties. It evolves around the idea that, for any message, there can only be a unique valid signat ...

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 Fail-Stop Signatures from the Factoring Assumption

Khaled Ouafi, Atefeh Mashatan

In this paper, we revisit the construction of fail-stop signatures from the factoring assumption. These signatures were originally proposed to provide information-theoretic-based security against forgeries. In contrast to classical signature schemes, in wh ...

Springer2011

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

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

Faster Squaring in the Cyclotomic Subgroup of Sixth Degree Extensions

Robert Granger

This paper describes an extremely efficient squaring operation in the so-called ‘cyclotomic subgroup’ of

\mathbb{F}_{q^6}

, for

q \equiv 1 \bmod{6}

. Our result arises from considering the Weil restriction of scalars of this group from

\mathbb{F}_{q^6}

...

Springer Berlin Heidelberg2010

On Small Degree Extension Fields in Cryptology

Robert Granger

This thesis studies the implications of using public key cryptographic primitives that are based in, or map to, the multiplicative group of finite fields with small extension degree. A central observation is that the multiplicative group of extension field ...

PhD dissertation, University of Bristol, UK, February 20062006

Discrete logarithm variants of VSH

Arjen Lenstra, Martijn Stam

Recent attacks on standardised hash functions such as SHA1 have reawakened interest in design strategies based on techniques common in provable security. In presenting the VSH hash function, a design based on RSA-like modular exponentiation, the authors in ...

2006

On Small Characteristic Algebraic Tori in Pairing-Based Cryptography

Robert Granger, Martijn Stam

The value of the Tate pairing on an elliptic curve over a finite field may be viewed as an element of an algebraic torus. Using this simple observation, we transfer techniques recently developed for torus-based cryptography to pairing-based cryptography, r ...

2006

Upper bounds for Euclidean minima of algebraic number fields

Eva Bayer Fluckiger

The aim of this paper is to give new upper bounds for Euclidean minima of algebraic number fields. In particular, to show that Minkowski's conjecture holds for the maximal totally real subfields of cyclotomic fields of prime power conductor. ...

2006

Faster Squaring in the Cyclotomic Subgroup of Sixth Degree Extensions

Robert Granger

This paper describes an extremely efficient squaring operation in the so-called ‘cyclotomic subgroup’ of

\mathbb{F}_{q^6}

, for

q \equiv 1 \bmod{6}

. Our result arises from considering the Weil restriction of scalars of this group from

\mathbb{F}_{q^6}

...

Springer Berlin Heidelberg2010