Thirty years after RSA was first publicized, it remains an active research area. Although
several good surveys exist, they are either slightly outdated or only focus on one type of …

It is sometimes argued that finding meaningful hash collisions might prove difficult. We show
that for several common public key systems it is easy to construct pairs of meaningful and …

We propose a key generation method for RSA moduli which allows the cost of the public
operations (encryption/verifying) and the private operations (decryption/signing) to be …

Multi-prime RSA is a variant of RSA in which the modulus is the product of more than two
distinct primes. In this work we collect the strongest known algebraic attacks on multi-prime …

The RSA cryptosystem, named after its inventors, Rivest, Shamir and Adleman, is the most
widely known and widely used public-key cryptosystem in the world today. Compared to …

In this work, we give a partial overview of lattice attacks in cryptography. While different kinds
of attacks are considered, the emphasis of this work is given to attacks that are based on …

Thus far, partial key exposure attacks on RSA have been intensively studied using lattice
based Coppersmith's methods. In the context, attackers are given partial information of a …

In 1999, Boneh and Durfee introduced the small inverse problem, which solves the bivariate
modular equation x (N+y)≡ 1 (mod e. Absolute values of solutions for x and y are bounded …

In this paper, I present some of the variants of RSA and analyse the cryptanalytic attacks
against these variants. The first variant I present is called the Efficient RSA, where the …

We show that the attack of de Weger on RSA using continued fractions extends to Multi-
Prime RSA. Let (n, e) be a Multi-Prime RSA public-key with private key d, where n= p 1 p 2⋯ …