The RSA and Rabin encryption function are respectively defined as E N (z) = ze mod N and E N (E) = z2 mod N , where N is a product of two large random primes p , q and e is relatively prime to (p (N). We present a much simpler and stronger proof of the result of ALEXI, CHOR, GOLDREICH and SCHNORR [ACGS88] that the following problems are equivalent by probabilistic polynomial time reductions: (1) given E N (z) find x; (2) given E N (z) predict the least-significant bit of J with success probability i + h, where N has n bits. The new proof consists of a more efficient algorithm for i n v e r h g the RSA/Rabinfunction with the help of an oracle that predicts the least-significant bit of Z. It yields provable security guarantees for RSA-message bits and for the RSA-random number generator for moduli N of practical size.
Abstract. We present efficient non-malleable commitment schemes based on standard assumptions such as RSA and Discrete-Log, and under the condition that the network provides publicly available RSA or Discrete-Log parameters generated by a trusted party. Our protocols require only three rounds and a few modular exponentiations. We also discuss the difference between the notion of non-malleable commitment schemes used by Dolev, Dwork and Naor [DDN00] and the one given by Di Crescenzo, Ishai and Ostrovsky [DIO98].
We review the representation problem based on factoring and show that this problem gives rise to alternative solutions to a lot of cryptographic protocols in the literature. And, while the solutions so far usually either rely on the RSA problem or the intractability of factoring integers of a special form (e.g., Blum integers), the solutions here work with the most general factoring assumption. Protocols we discuss include identification schemes secure against parallel attacks, secure signatures, blind signatures and (non-malleable) commitments.
We propose two trapdoors for the Closest-Vector-Problem in lattices (CVP) related to the lattice tensor product. Using these trapdoors we set up a lattice-based cryptosystem which resembles to the McEliece scheme. 1
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.