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

Some consequences of Masser's counting theorem on elliptic curves

We use Masser's counting theorem to prove a lower bound for the canonical height in powers of elliptic curves. We also prove the Galois case of the elliptic Lehmer problem, combining Kummer theory and Masser's result with bounds on the rank and torsion of ...

Springer Heidelberg2017

Computational Aspects of Jacobians of Hyperelliptic Curves

Alina Dudeanu

Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest ...

EPFL2016

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

Height of rational points on quadratic twists of a given elliptic curve

Pierre Francis André Le Boudec

We formulate a conjecture about the distribution of the canonical height of the lowest non-torsion rational point on a quadratic twist of a given elliptic curve, as the twist varies. This conjecture seems to be very deep and we can prove only partial resul ...

Oxford Univ Press2016

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption

Robert Granger, Philipp Svetolik Jovanovic

A popular approach to tweakable blockcipher design is via masking, where a certain primitive (a blockcipher or a permutation) is preceded and followed by an easy-to-compute tweak-dependent mask. In this work, we revisit the principle of masking. We do so a ...

Springer Int Publishing Ag2016

On The Number Of Ordinary Conics

Frank de Zeeuw, Adrian Claudiu Valculescu

We prove a lower bound on the number of ordinary conics determined by a finite point set in R-2. An ordinary conic for S subset of R-2 is a conic that is determined by five points of S and contains no other points of S. Wiseman and Wilson proved the Sylves ...

Siam Publications2016

On the Analysis of Public-Key Cryptologic Algorithms

Andrea Miele

The RSA cryptosystem introduced in 1977 by Ron Rivest, Adi Shamir and Len Adleman is the most commonly deployed public-key cryptosystem. Elliptic curve cryptography (ECC) introduced in the mid 80's by Neal Koblitz and Victor Miller is becoming an increasin ...

EPFL2015

A Tale of Two Quasi-Polynomial Algorithms

Robert Granger

In 2013 the Discrete Logarithm Problem in finite fields of small characteristic enjoyed a rapid series of developments, starting with the heuristic polynomial-time relation generation method due to Gologlu, Granger, McGuire and Zumbragel, and culminating w ...

2015

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

\mathbb{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 log ...

2015

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption

Robert Granger, Philipp Svetolik Jovanovic

A popular approach to tweakable blockcipher design is via masking, where a certain primitive (a blockcipher or a permutation) is preceded and followed by an easy-to-compute tweak-dependent mask. In this work, we revisit the principle of masking. We do so a ...

2015

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

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Some consequences of Masser's counting theorem on elliptic curves

Computational Aspects of Jacobians of Hyperelliptic Curves

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Height of rational points on quadratic twists of a given elliptic curve

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption

On The Number Of Ordinary Conics

On the Analysis of Public-Key Cryptologic Algorithms

A Tale of Two Quasi-Polynomial Algorithms

On the discrete logarithm problem in finite fields of fixed characteristic

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption

Computational Aspects of Jacobians of Hyperelliptic Curves

Some consequences of Masser's counting theorem on elliptic curves

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Height of rational points on quadratic twists of a given elliptic curve

On the Analysis of Public-Key Cryptologic Algorithms

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption

On The Number Of Ordinary Conics

On the discrete logarithm problem in finite fields of fixed characteristic

A Tale of Two Quasi-Polynomial Algorithms

Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption