Publications related to On Small Degree Extension Fields in Cryptology

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Short Stickelberger Class Relations and Application to Ideal-SVP

Benjamin Pierre Charles Wesolowski

The worst-case hardness of finding short vectors in ideals of cyclotomic number fields (Ideal-SVP) is a central matter in lattice based cryptography. Assuming the worst-case hardness of Ideal-SVP allows to prove the Ring-LWE and Ring-SIS assumptions, and t ...

Springer International Publishing Ag2017

Isogeny graphs of ordinary abelian varieties

Dimitar Petkov Jetchev, Benjamin Pierre Charles Wesolowski, Ernest Hunter Brooks

Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse gr ...

Springer Heidelberg2017

A Szemeredi-Trotter type theorem, sum-product estimates in finite quasifields, and related results

Van Thang Pham

We prove a Szemeredi-Trotter type theorem and a sum product estimate in the setting of finite quasifields. These estimates generalize results of the fourth author, of Garaev, and of Vu. We generalize results of Gyarmati and Sarkozy on the solvability of th ...

Academic Press Inc Elsevier Science2017

Universal p'-central extensions

Jacques Thévenaz, Caroline Lassueur

It is well-known that a finite group possesses a universal central extension if and only if it is a perfect group. Similarly, given a prime number p, we show that a finite group possesses a universal p′-central extension if and only if the p′-part of its a ...

Elsevier2017

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

For~

q

a prime power, the discrete logarithm problem (DLP) in~

\F_{q}

consists in finding, for any

g \in \mathbb{F}_{q}^{\times}

and

h \in \langle g \rangle

, an integer~

x

such that

g^x = h

. We present an algorithm for computing discrete logarithm ...

2016

Efficient Public-Key Distance Bounding Protocol

Serge Vaudenay, Handan Kilinç Alper

Distance bounding protocols become more and more important because they are the most accurate solution to defeat relay attacks. They consist of two parties: a verifier and a prover. The prover shows that (s)he is close enough to the verifier. In some appli ...

Springer-Verlag Berlin2016

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Robert Granger

For any positive integers

n\geq 3, r\geq 1

we present formulae for the number of irreducible polynomials of degree

n

over the finite field

\mathbb{F}_{2^r}

where the coefficients of

x^{n-1}

x^{n-2}

and

x^{n-3}

are zero. Our proofs involve coun ...

Elsevier2016

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Robert Granger

For any positive integers

n\geq 3, r\geq 1

we present formulae for the number of irreducible polynomials of degree

n

over the finite field

\mathbb{F}_{2^r}

where the coefficients of

x^{n-1}

x^{n-2}

and

x^{n-3}

are zero. Our proofs involve coun ...

Elsevier2016

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

For~

q

a prime power, the discrete logarithm problem (DLP) in~

\F_{q}

consists in finding, for any

g \in \mathbb{F}_{q}^{\times}

and

h \in \langle g \rangle

, an integer~

x

such that

g^x = h

. We present an algorithm for computing discrete logarithm ...

2016

On Small Degree Extension Fields in Cryptology

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LPN in Cryptography

Indiscreet discrete logarithms

Short Stickelberger Class Relations and Application to Ideal-SVP

Isogeny graphs of ordinary abelian varieties

A Szemeredi-Trotter type theorem, sum-product estimates in finite quasifields, and related results

Universal p'-central extensions

Computational Aspects of Jacobians of Hyperelliptic Curves

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Efficient Public-Key Distance Bounding Protocol

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

A Szemeredi-Trotter type theorem, sum-product estimates in finite quasifields, and related results

Computational Aspects of Jacobians of Hyperelliptic Curves

Isogeny graphs of ordinary abelian varieties

Efficient Public-Key Distance Bounding Protocol

Short Stickelberger Class Relations and Application to Ideal-SVP

LPN in Cryptography

Indiscreet discrete logarithms

Universal p'-central extensions

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC