5 research outputs found
Descent methods for studying integer points on
We study the integer points on superelliptic and hyperelliptic curves of the
form $n\ge 2, {\rm{deg}}{f}+{\rm{deg}}{g}\ge 4.
Attacking (EC)DSA scheme with ephemeral keys sharing specific bits
In this paper, we present a deterministic attack on (EC)DSA signature scheme,
providing that several signatures are known such that the corresponding
ephemeral keys share a certain amount of bits without knowing their value. By
eliminating the shared blocks of bits between the ephemeral keys, we get a
lattice of dimension equal to the number of signatures having a vector
containing the private key. We compute an upper bound for the distance of this
vector from a target vector, and next, using Kannan's enumeration algorithm, we
determine it and hence the secret key. The attack can be made highly efficient
by appropriately selecting the number of shared bits and the number of
signatures
Product Subset Problem : Applications to number theory and cryptography
We consider applications of Subset Product Problem (SPP) in number theory and
cryptography. We obtain a probabilistic algorithm that attack SPP and we
analyze it with respect time/space complexity and success probability. In fact
we provide an application to the problem of finding Carmichael numbers and an
attack to Naccache-Stern knapsack cryptosystem, where we update previous
results.Comment: 17 pages, 2 figures, LaTeX; references added, typos corrected, a new
figure was inserted, sections 2.1, 2.2 improve
Quantitative Chevalley-Weil theorem for curves
The classical Chevalley-Weil theorem asserts that for an \'etale covering of
projective varieties over a number field K, the discriminant of the field of
definition of the fiber over a K-rational point is uniformly bounded. We obtain
a fully explicit version of this theorem in dimension 1.Comment: version 4: minor inaccuracies in Lemma 3.4 and Proposition 5.2
correcte