Post-Quantum Pseudorandom Functions from Mersenne Primes
Pseudorandom functions (PRFs) serve as a fundamental cryptographic primitive that is essential for encryption, identification and authentication. The concept of PRFs first formalized by Goldreich, Goldwasser, and Micali (JACM 1986), and their construction is based on length-doubling pseudorandom generators (PRGs) by using the tree-extention technique. Subsequently, Naor and Reingold proposed a construction based on synthesizers (JACM 2004) which can be instantiated from factoring and the Diffie-Hellman assumption. Recently, some efficient constructions were proposed in the post-quantum background. Banerjee, Peikert, and Rosen (Eurocrypt 2012) constructed relatively more efficient PRFs based on “learning with error” (LWE). Soon afterwards, Yu and Steinberger (Eurocrypt 2016) proposed two efficient constructions of randomized PRFs (with public coin as a parameter) from “learning parity with noise” (LPN). In this paper, we construct standard and randomized PRFs via Mersenne prime assumptions which were proposed by Aggarwal et al. (Crypto 2018) as new post-quantum candidate hardness assumptions. In contrast with Yu and Steinberger’s constructions, our first construction could have the same parameters to their second construction but not needs extra public coin and our second construction has a smaller public coin and key size comparing with their first construction.
KeywordsMersenne prime problem Pseudorandom functions Pseudorandom generators
The authors would like to thank the anonymous reviewers for their valuable comments and suggestions. This work was partially supported by the National Natural Science Foundation of China (Grant No. 61632013).
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