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Title:
Generically Speeding-Up Repeated Squaring is Equivalent to Factoring: Sharp Thresholds for All Generic-Ring Delay Functions
Authors: Lior Rotem, Gil Segev
Abstract:Despite the fundamental importance of delay functions, repeated squaring in RSA groups (Rivest, Shamir and Wagner '96) is the main candidate offering both a useful structure and a realistic level of practicality. Somewhat unsatisfyingly, its sequentiality is provided directly by assumption (i.e., the function is assumed to be a delay function). We prove sharp thresholds on the sequentiality of all generic-ring delay functions relative to an RSA modulus based on the hardness of factoring in the standard model. In particular, we show that generically speeding-up repeated squaring (even with a preprocessing stage and any polynomial number parallel processors) is equivalent to factoring. More generally, based on the (essential) hardness of factoring, we prove that any generic-ring function is in fact a delay function, admitting a sharp sequentiality threshold that is determined by our notion of sequentiality depth. Moreover, we show that generic-ring functions admit not only sharp sequentiality thresholds, but also sharp pseudorandomness thresholds.
ePrint: https://eprint.iacr.org/2020/812
Talk: https://www.youtube.com/watch?v=r6Mk0MgJf4E
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