The increasing importance of security in computers and communication systems introduces the need for several public-key cryptosystems. The modular division and multiplication arithmetic operations in GF (p) and GF (2 n ) are extensively used in many public key cryptosystems, such as El-Gamal cryptosystem, Elliptic Curve Cryptography (ECC), and the Elliptic Curve Digital Signature Algorithm (ECD...

Modular exponentiation is one of the most important operations in public-key cryptosystems. A modular exponentiation is composed of repetition of modular multiplications. Again, the modular multiplication consists of a multi-precision multiplication and a modular reduction. Therefore, we can reduce the execution time of the modular exponentiation by two methods. One is to reduce the number of m...

This note describes an improvement to the rst two of the three public key cryptosystems proposed by Zheng and Seberry, which are provably secure against chosen ciphertext attacks. The improvement removes a shortcoming with the original cryptosystems, which occurs when they are used for both con dentiality and sender authentication purposes.

This paper describes a hardware implementation of an arithmetic processor which is efficient for elliptic curve (EC) cryptosystems, which are becoming increasingly popular as an alternative for public key cryptosystems based on factoring. The modular multiplication is implemented using a Montgomery modular multiplication in a systolic array architecture, which has the advantage that the clock f...

Most common public key cryptosystems and public key exchange protocols presently in use, such as the RSA algorithm, Diffie-Hellman, and elliptic curve methods are number theory based and hence depend on the structure of abelian groups. The strength of computing machinery has made these techniques theoretically susceptible to attack and hence recently there has been an active line of research to...

Public Key Cryptosystems have been in use for more than three decades. A number of schemes based on integer factorization problem, discrete log problem, residuosity problem, digital signature methods, Lucas sequence, Lattice problems, error-correcting codes, braid groups etc. have been designed. Recently, Multivariate Quadratic (MQ) Polynomials could be efficiently used for design of a number o...

New results in cryptanalysis are constantly being presented in the academic community, and this process poses no problems. Paradoxically, the discovery of a method that would allow breaking for example an RSA key in the same time as it takes to encrypt a message with it, would have serious and disturbing impacts on sectors such as finance and defence, and would in fact be impossible to publish ...

At Crypto’99, Fujisaki and Okamoto [8] presented a nice generic transformation from weak asymmetric and symmetric schemes into an IND-CCA hybrid encryption scheme in the Random Oracle Model. Two specific candidates for standardization were designed from this transformation: PSEC-2 [14] and EPOC-2 [7], based on El Gamal and OkamotoUchiyama primitives, respectively. Since then, several cryptanaly...

In this paper we introduce two notions of security: multiuser indistinguishability and multiuser non-malleability. We believe that they encompass the correct requirements for public key encryp-tion schemes in the context of multicast communications. A precise and non-trivial analysis prove that they are equivalent to the former single-user notions, provided the number of participants is polynom...

We analyze the security of the simplified Paillier (S-Paillier) cryptosystem, which was proposed by Catalano et al. We prove that the one-wayness of the S-Paillier scheme is as intractable as the standard RSA problem. We also prove that an adversary, which breaks the semantic security, can compute the least significant bits of the nonce. This observation is interesting, because the least signif...