Computer Analysis of Number Sequences by Henry Ibstedt

By Henry Ibstedt

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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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