Non-interactive generation of shared pseudorandom sequences
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We address the following problem: given a random seed secretly shared among a group of individuals, non-interactively generate pieces corresponding to a much longer shared pseudorandom sequence. Shared randomness is an essential resource in distributed computing and non-interactive ways of generating it can be useful in applications such as Byzantine Agreement, common coin flipping or secure computation protocols.
Our first result is negative: well known cryptographically strong pseudorandom number generators cannot be evaluated without interaction and, in particular, it is shown that constructions that recursively apply a one-way function to a random seed and output at each iteration the simultaneously hard bits in the input of the one-way function are actually incompatible with a homomorphic evaluation.
On the other hand, we show that pseudorandom generators that can be both proven cryptographically strong and sharedly evaluated without interaction do exist. A concrete implementation, under the RSA assumption, is described.
- S. Akl and P. Taylor. “Cryptographic solution to a problem of access control in a hierarchy.” ACM TOCS, 1, 1983, pp. 239–248.
- W. Alexi, B. Chor, O. Goldreich and C.P. Schnorr. “RSA and Rabin Functions: Certain Parts are as Hard as the Whole.” SIAM Journal on Computing, vol. 17, no. 2, April 1988, pp. 194–209.
- M. Ben-Or, S. Goldwasser and A. Wigderson. “Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation.” Proc. 20th STOC, ACM, 1988, pp. 1–10.
- D. Beaver. “Foundations of Secure Interactive Computing.” Proc. Crypto '91, Springer-Verlag, LNCS vol. 576, pp. 377–391.
- J.C. Benaloh. “Secret Sharing Homomorphisms: Keeping Shares of a Secret Secret.” Proc. Crypto '86. Springer-Verlag, LNCS vol. 293, 1987.
- M. Blum and S. Micali. “How to Generate Cryptographically Strong Sequences Of Pseudo-Random Bits.” Proc. 22nd FOCS, IEEE, 1982, pp. 112–117.
- D. Beaver, S. Micali and P. Rogaway. “The Round Complexity of Secure Protocols.” Proc. 22nd STOC, ACM, 1990, pp. 503–513.
- J. Carter and M. Wegman. “Universal Classes of Hash Functions.” Journal of Computer and System Sciences, 1979, vol. 18, pp. 143–154.
- B. Chor and C. Dwork. “Randomization in Byzantine Agreement.” Advances in Computing Research, vol. 5, JAI Press, 1989, pp. 443–497.
- B. Chor, S. Goldwasser, S. Micali and B. Awerbuch. “Verifiable Secret Sharing and Achieving Simultaneity in the Presence of Faults.” Proc. 26th FOCS, IEEE, 1985, pp. 383–395.
- J.-H. Evertse and E. van Heyst. “Which New RSA-Signatures Can Be Computed from Certain Given RSA-Signatures?” Journal of Cryptology, vol. 5, no. 1, 1992, pp. 41–52.
- P. Feldman. “A Practical Scheme for Non-Interactive Verifiable Secret Sharing.” Proc. 28th FOCS, IEEE, 1987, pp. 427–437.
- Y. Frankel and Y. Desmedt. “Classification of ideal homomorphic threshold schemes over finite Abelian groups.” Proc. Eurocrypt '92. To appear in Springer-Verlag, LNCS.
- P. Feldman and S. Micali. “Optimal Algorithms for Byzantine Agreement.” Proc. 20th STOC, ACM, 1988, pp. 148–161.
- Y. Frankel, Y. Desmedt and M. Burmester. “Non-existence of homomorphic general sharing schemes for some key spaces.” Proc. Crypto '92. To appear in Springer-Verlag, LNCS.
- O. Goldreich, S. Micali and A. Wigderson. “How to Play Any Mental Game.” Proc. 19th STOC, ACM, 1987, pp. 218–229.
- S. Goldwasser, S. Micali and C. Rackoff. The Knowledge Complexity of Interactive Proof Systems. SIAM Journal on Computing, vol. 18, no. 1, Feb. 1989, pp. 186–208.
- J. Håstad. “Pseudo-Random Generators under Uniform Assumptions.” Proc. 22nd STOC, ACM, 1990, pp. 395–404.
- R. Impagliazzo, L.A. Levin and M. Luby. “Pseudo-Random Generation from Oneway Functions.” Proc. 21st STOC, ACM, 1989, pp. 12–24.
- R. Impagliazzo, M. Naor. “Efficient Cryptographic Schemes Provably as Secure as Subset Sum.” Proc. 30th FOCS, IEEE, 1989, pp. 236–241.
- S. Micali and T. Rabin. “Collective Coin Tossing without Assumptions nor Broadcasting.” Proc. Crypto '90, Springer-Verlag, LNCS vol. 537, 1991.
- S. Micali and P. Rogaway. Secure Computation. Proc. Crypto '91, Springer-Verlag, LNCS vol. 576, pp. 392–404.
- T.P. Pedersen. “Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing.” Proc. Crypto '91, Springer-Verlag, LNCS vol. 576, 1992, pp. 129–140.
- T. Rabin and M. Ben-Or. “Verifiable Secret Sharing and Multi-Party Protocols with Honest Majority.” Proc. 21st STOC, ACM, 1989, pp. 73–85.
- A. Shamir. “On the Generation of Cryptographically Strong Pseudorandom Sequences.” ACM Trans. on Computer Systems, vol. 1, no. 1, Feb. 1983, pp. 38–44.
- A.C. Yao. “Theory and Applications of Trapdoor Functions.” Proc. 23rd FOCS, IEEE, 1982, pp. 80–91.
- Non-interactive generation of shared pseudorandom sequences
- Book Title
- Advances in Cryptology — AUSCRYPT '92
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- Workshop on the Theory and Application of Cryptographic Techniques Gold Coast, Queensland, Australia, December 13–16, 1992 Proceedings
- pp 385-396
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- Lecture Notes in Computer Science
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- Springer Berlin Heidelberg
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- Author Affiliations
- 1. Division of Electrical and Computer Engineering, Yokohama National University, 156 Tokiwadai, Hodogaya, 240, Yokohama, Japan
- 2. Institute of Industrial Science, University of Tokyo, 7-22-1 Roppongi, Minato-ku, 106, Tokyo, Japan
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