Cryptology ePrint Archive: Report 2020/289

The security of Groups of Unknown Order based on Jacobians of Hyperelliptic Curves

Jonathan Lee

Abstract: Recent work using groups of unknown order to construct verifiable delay functions, polynomial commitment schemes and non interactive zero knowledge proofs have provoked fresh interest in the construction of efficient cryptographic groups of unknown order. It has been suggested that the Jacobian of hyperelliptic curves of genus 3 could be suitable for this purpose. Regrettably, efficient algorithms to compute the order of the Jacobian of a hyperelliptic curve are known. Concretely, it is unclear whether these groups are competitive with RSA groups or class groups at or above the 128 bit security level.

Category / Keywords: cryptographic protocols / hyperelliptic curves, accumulators, unknown order groups, verifiable delay function, zksnark

Date: received 4 Mar 2020

Contact author: jonatlee at microsoft com

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Version: 20200306:085051 (All versions of this report)

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