Abstract
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.
Supported by Japanese Ministry of Education, Science and Culture Scholarship, No. 890864.
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Cerecedo, M., Matsumoto, T., Imai, H. (1993). Non-interactive generation of shared pseudorandom sequences. In: Seberry, J., Zheng, Y. (eds) Advances in Cryptology — AUSCRYPT '92. AUSCRYPT 1992. Lecture Notes in Computer Science, vol 718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57220-1_77
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DOI: https://doi.org/10.1007/3-540-57220-1_77
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