At Eurocrypt ’99, Paillier showed a cryptographic application of the group [Formula: see text], the multiplicative group modulo [Formula: see text] where [Formula: see text] is some RSA modulus. In this paper, we have present a new public key cryptosystem over [Formula: see text] where [Formula: see text] is a product of two safe primes, which is based on two intractable problems namely, integer factorization and partial discrete logarithm problem over [Formula: see text], the group of quadratic residues modulo [Formula: see text]. This scheme is a combination of BCP (Bresson–Catalano–Pointcheval) cryptosystem, proposed by Bresson et al. at Asiacrypt ’03 and the Rabin–Paillier scheme proposed by Galindo et al. at PKC 2003. We will show that the one-wayness of this new scheme equally depends on the Computational Diffie–Hellman assumption and factoring assumption. We will also prove that the proposed scheme is more secure than the BCP cryptosystem and the Rabin–Paillier cryptosystem.
Undirected Complete Graph to Design New Public Key Cryptosystem
