The most popular public key cryptosystems are based on the problem of factorization of large integers and discrete logarithm problem in finite groups, in particular in the multiplicative group of finite field and the group of points on elliptic curve over finite field. Elliptic curves are of special interest since they at present alow much shorter keys, for the same level of security, compared ...

This paper presents three methods for strengthening pub lic key cryptosystems in such a way that they become secure against adaptively chosen ciphertext attacks In an adaptively chosen ciphertext attack an attacker can query the deciphering algorithm with any cipher texts except for the exact object ciphertext to be cryptanalyzed The rst strengthening method is based on the use of one way hash ...

In this paper, we propose a new method for designing public key cryptosystems based on general non-commutative rings. The key idea of our proposal is that for a given non-commutative ring, we can define polynomials and take them as the underlying work structure. By doing so, it is easy to implement Diffie-Helman-like key exchange protocol. And consequently, ElGamal-like cryptosystems can be der...

The Naccache-Stern (ns) knapsack cryptosystem is an original yet little-known public-key encryption scheme. In this scheme, the ciphertext is obtained by multiplying public-keys indexed by the message bits modulo a prime p. The cleartext is recovered by factoring the ciphertext raised to a secret power modulo p. ns encryption requires a multiplication per two plaintext bits on the average. Decr...

Trusted parties are fundamental for the establishment of secure communication among users. Such is the case, for example, when establishing a trusted relationship between users and certain public information in a public-key infrastructure for public-key encryption and signature schemes or when storing high-entropy secret keys in a cryptographic device. Clearly, if the trusted party misbehaves i...