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Public-Key Generation with Verifiable Randomness

Abstract : We revisit the problem of proving that a user algorithm se-lected and correctly used a truly random seed in the generation of hercryptographic key. A first approach was proposed in 2002 by Juels andGuajardo for the validation of RSA secret keys. We present a new secu-rity model and general tools to efficiently prove that a private key wasgenerated at random according to a prescribed process, without revealingany further information about the private key.We give a generic protocol for all key-generation algorithms based onprobabilistic circuits and prove its security. We also propose a new pro-tocol for factoring-based cryptography that we prove secure in the afore-mentioned model. This latter relies on a new efficient zero-knowledgeargument for the double discrete logarithm problem that achieves an ex-ponential improvement in communication complexity compared to thestate of the art, and is of independent interest.
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https://hal.archives-ouvertes.fr/hal-02929843
Contributor : Damien Vergnaud <>
Submitted on : Thursday, September 3, 2020 - 8:46:06 PM
Last modification on : Tuesday, March 23, 2021 - 9:28:03 AM

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Olivier Blazy, Patrick Towa, Damien Vergnaud. Public-Key Generation with Verifiable Randomness. Asiacrypt 2020 - 26th Annual International Conference on the Theory and Application of Cryptology and Information Security, Dec 2020, Daejeon / Virtual, South Korea. pp.97-127, ⟨10.1007/978-3-030-64837-4_4⟩. ⟨hal-02929843⟩

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