Guaranteeing the Diversity of Number Generators |
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Authors: | Adi Shamir Boaz Tsaban |
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Affiliation: | Department of Applied Mathematics, The Weizmann Institute of Science, Rehovot, 76100, Israelf1;Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900, Israel, http://www.cs.biu.ac.il/˜tsaban, f2 |
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Abstract: | A major problem in using iterative number generators of the form xi=f(xi−1) is that they can enter unexpectedly short cycles. This is hard to analyze when the generator is designed, hard to detect in real time when the generator is used, and can have devastating cryptanalytic implications. In this paper we define a measure of security, called sequence diversity, which generalizes the notion of cycle-length for noniterative generators. We then introduce the class of counter-assisted generators and show how to turn any iterative generator (even a bad one designed or seeded by an adversary) into a counter-assisted generator with a provably high diversity, without reducing the quality of generators which are already cryptographically strong. |
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Keywords: | Abbreviations: pseudorandomnessAbbreviations: cycle lengthAbbreviations: cryptography |
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