Concept

Modulo (opération)

Publications associées (14)

Endo-trivial modules: a reduction to p'-central extensions

We examine how, in prime characteristic p, the group of endotrivial modules of a finite group G and the group of endotrivial modules of a quotient of G modulo a normal subgroup of order prime to p are related. There is always an inflation map, but examples ...

2017

Experimental observations and modelling of intrinsic rotation reversals in tokamaks

Basil Duval, Yann Camenen, Emiliano Fable, Alessandro Bortolon

The progress made in understanding spontaneous toroidal rotation reversals in tokamaks is reviewed and current ideas to solve this ten-year-old puzzle are explored. The paper includes a summarial synthesis of the experimental observations in AUG, C-Mod, KS ...

Iop Publishing Ltd2017

Note on the relation between profile scalelengths and lambda's

Olivier Sauter

The calculation of the inverse scalelengths

R/L_T

R/L_n

may depend on the choice of the radial variable, depending on the definition of the scalelength. The value of

\lambda_T

and

\lambda_n

, as defined in [O. Sauter {\it et al}, Phys. Plasmas {\bf ...

SPC-EPFL2016

The algebra of essential relations on a finite set

Jacques Thévenaz, Serge Bouc

Let X be a finite set and let k be a commutative ring. We consider the k-algebra of the monoid of all relations on X, modulo the ideal generated by the relations factorizing through a set of cardinality strictly smaller than Card(X), called inessential rel ...

Walter de Gruyter2016

Faster ECC over $\mathbb{F}_{2^{521}-1}$

Robert Granger

In this paper we present a new multiplication algorithm for residues modulo the Mersenne prime

2^{521}−1

. Using this approach, on an Intel Haswell Core i7-4770, constant-time variable-base scalar multiplication on NIST’s (and SECG’s) curve P-521 requires ...

Springer Berlin Heidelberg2015

Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions

Philippe Michel

We show that, in a restricted range, the divisor function of integers in residue classes modulo a prime follows a Gaussian distribution, and a similar result for Hecke eigenvalues of classical holomorphic cusp forms. Furthermore, we obtain the joint distri ...

European Mathematical Soc2014

Generalised Mersenne Numbers Revisited

Robert Granger

Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus making them an attrac ...

2013

The valuation criterion for normal basis generators

If L/K is a finite Galois extension of local fields, then we say that the valuation criterion VC(L/K) holds if there is an integer d such that every element x is an element of L with valuation d generates a normal basis for L/K. Answering a question of Byo ...

2012

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

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 implementa ...

IEEE2011

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Faster ECC over $\mathbb{F}_{2^{521}-1}$

Robert Granger

In this paper we present a new multiplication algorithm for residues modulo the Mersenne prime

2^{521}−1

. Using this approach, on an Intel Haswell Core i7-4770, constant-time variable-base scalar multiplication on NIST’s (and SECG’s) curve P-521 requires ...

Springer Berlin Heidelberg2015

Note on the relation between profile scalelengths and lambda's

Olivier Sauter

The calculation of the inverse scalelengths

R/L_T

R/L_n

may depend on the choice of the radial variable, depending on the definition of the scalelength. The value of

\lambda_T

and

\lambda_n

, as defined in [O. Sauter {\it et al}, Phys. Plasmas {\bf ...

SPC-EPFL2016