Contemporary Cryptology by Dario Catalano, Ronald Cramer, Ivan Damgard, Giovanni Di

By Dario Catalano, Ronald Cramer, Ivan Damgard, Giovanni Di Crescenzo, David Pointcheval, Tsuyoshi Takagi

The goal of this article is to regard chosen subject matters of the topic of latest cryptology, established in 5 fairly autonomous yet comparable topics: effective allotted computation modulo a shared mystery, multiparty computation, glossy cryptography, provable safety for public key schemes, and effective and safe public-key cryptosystems.

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Robust Efficient Distributed RSA-Key Generation. 663–672. [28] M. Franklin ans S. Haber. Joint Encryption and Message Efficient Secure Computation. 9, pp. 217-232, 1996. [29] E. Fujisaki and T. Okamoto. Statistical Zero-Knowledge Protocols to Prove Modular Polynomial Relations. In Advances in Cryptology – Crypto ’97, LNCS vol. 1294, Springer, 1997, pages 16-30. [30] P. Gemmell. An Introduction to Threshold Cryptography. 3, Winter 1997. [31] R. Gennaro, S. Halevi and T. Rabin. Secure Hash-and-Sign Signatures without the Random Oracle.

Obviously d = i di . Note that the only information leaked by the protocol is the integer γ = λφ + Re. However it is possible to prove (and we do that for the general protocol in the next section) that the distribution of γ is (almost) independent of φ. More precisely, it can be shown that, when λ and R follow the probability distribution described above, then the distributions {γ = λφ + Re} and {γ = λN + Re} are statistically close. The above protocol, however, is not secure when it is used more than once with the same λ and different e’s.

Practical Threshold RSA Signatures without a trusted dealer. In Advances in Cryptology–Eurocrypt ’01, Lecture Notes in Computer Science Vol. 2045, pp. 152–165, Springer-Verlag, 2001. [16] A. De Santis, Y. Desmedt, Y. Frankel and M. Yung. How to share a function securely. In Proc. 522– 533, ACM Press, 1994. [17] Y. Desmedt. Society and group oriented cryptography: A new concept. In Carl Pomerance, editor, Advances in Cryptology–CRYPTO’87, Lecture Notes in Computer Science Vol. 293, pp. 120–127, Springer-Verlag, 1988.

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