A Digital Signature Scheme for Long-Term Security

In this paper we propose a signature scheme based on two intractable problems, namely the integer factorization problem and the discrete logarithm problem for elliptic curves. It is suitable for applications requiring long-term security and provides a more efficient solution than the existing ones

Characterizing algebraic curves with infinitely many integral points

A classical theorem of Siegel asserts that the set of S-integral points of an algebraic curve C over a number field is finite unless C has genus 0 and at most two points at infinity. In this paper we give necessary and sufficient conditions for C to have infinitely many S-integral points.Comment: Int. J. Number Th. 5 (2009), 585-59

An Attack on Small Private Keys of RSA Based on Euclidean Algorithm

In this paper, we describe an attack on RSA cryptosystem which is based on Euclid\u27s algorithm. Given a public key $(n,e)$ with corresponding private key $d$ such that $e$ has the same order of magnitude as $n$ and one of the integers $k = (ed-1)/\phi(n)$ and $e-k$ has at most one-quarter as many bits as $e$, it computes the factorization of $n$ in deterministic time $O((\log n)^2)$ bit operations

Some Lattices Attacks on DSA and ECDSA

In this paper, using the LLL reduction method and computing the integral points of two classes of conics, we develop attacks on DSA and ECDSA in case where the secret and the ephemeral key and their modular inverse are quite small or quite large

New Lattice Attacks on DSA Schemes

We prove that a system of linear congruences of a particular form has at most a unique solution below a certain bound which can be computed efficiently. Using this result we develop attacks against the DSA schemes which, under some assumptions, can provide the secret key in the case where one or several signed messages are available