By Dario Catalano, Ronald Cramer, Ivan Damgard, Giovanni Di Crescenzo, David Pointcheval, Tsuyoshi Takagi
The purpose of this article is to regard chosen issues of the topic of up to date cryptology, established in 5 fairly autonomous yet similar issues: effective disbursed computation modulo a shared mystery, multiparty computation, glossy cryptography, provable safeguard for public key schemes, and effective and safe public-key cryptosystems.
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Extra resources for Contemporary Cryptology (Advanced Courses in Mathematics - CRM Barcelona)
403, Springer, 1990, pages 232-243.  H. Ong and C. Schnorr. Fast Signature Generation with a Fiat-Shamir-like Scheme. In Advances in Cryptology – Eurocrypt ’90, LNCS vol. 473, Springer, 1991, pages 432-440.  T. Pedersen. A threshold cryptosystem without a trusted party. 547, Springer-Verlag, 1991.  T. Pedersen. Non-interactive and information-theoretic secure veriﬁable secret sharing. 576, SpringerVerlag, 1992.  M. O. Rabin. Probabilist Algorithms for testing primality. Journal of Number Theory, 12 (1980), 128-138.
Another remark is that although the general protocol constructions we give are phrased as solutions to the basic MPC problem, they can in fact also handle the more general type of problem. A key tool for secure MPC, interesting in its own right, is veriﬁable secret sharing (VSS): a dealer distributes a secret value s among the players, where the dealer and/or some of the players may be cheating. It is guaranteed that if the dealer is honest, then the cheaters obtain no information about s, and all honest players are later able to reconstruct s, even against the actions of cheating players.
In Proc. 17th ACM Symposium on Principle of Distributed Computing, 1998.  N. Gilboa. Two party RSA key Generation. In Advances in Cryptology – Crypto ’99, LNCS vol. 1666, Springer, 1999, pages 116-129. Eﬃcient Distributed Computation Modulo a Shared Secret 39  O. Goldreich, S. Micali, and A. Wigderson. Proofs that Yield Nothing but the Validity of the Assertion, and a Methodology of Cryptographic Protocol Design. 174–187. IEEE Computer Society Press, 1986.  O. Goldreich, S. Micali, and A.