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Let x be a curve in positive characteristic. A Hasse–Witt matrix for x is a matrix that
represents the action of the Frobenius operator on the cohomology group H1 (x, OX) with …

Computing discrete logarithms in finite fields is a main concern in cryptography. The best
algorithms in large and medium characteristic fields (eg, $\rm {GF}(p^ 2) $, $\rm {GF}(p^{12}) …

In this paper we present a complete Magma implementation for solving the discrete
logarithm problem (DLP) on a binary GLS curve defined over the field F _ 2^ 62 F 2 62. For …

Computing discrete logarithms in finite fields is a main concern in cryptography. The best
algorithms known are the Number Field Sieve and its variants in large and medium …

In this chapter, the author shall see to what extent physical attacks have been successful so
far in attacking implementations of pairing calculations. Both side-channel and fault attacks …

The security of modern cryptography is based on the impossibility of breaking the
implemented algorithms in practice. In order to reach such a goal, the algorithms are built in …

The security of elliptic curve cryptography, which is based on the computational hardness of
ECDLP, has been extensively studied for decades. Index calculus algorithm has been paid …

The main approach to solve hyperelliptic curve DLP is index calculus algorithm. One of the
most important steps is to obtain relations among the factor basis elements. Although Nagao …

Desde el inicio de la criptografıa de llave pública, los campos finitos de caracterıstica chica
han sido propuestos como estructuras matemáticas en implementación de protocolos de …