Cryptology ePrint Archive: Report 2016/121

Tightly-Secure Pseudorandom Functions via Work Factor Partitioning

Tibor Jager

Abstract: We introduce a new technique for tight security proofs called work factor partitioning. Using this technique in a modified version of the framework of Döttling and Schröder (CRYPTO 2015), we obtain the first generic construction of tightly-secure pseudorandom functions (PRFs) from PRFs with small domain.

By instantiating the small-domain PRFs with the Naor-Reingold function (FOCS 1997) or its generalization by Lewko and Waters (ACM CCS 2009), this yields the first fully-secure PRFs whose black-box security proof loses a factor of only O(log^2 \lambda), where \lambda is the security parameter.

Interestingly, our variant of the Naor-Reingold construction can be seen as a standard Naor-Reingold PRF (whose security proof has a loss of \Theta(\lambda)), where a special encoding is applied to the input before it is processed. The tightness gain comes almost for free: the encoding is very efficiently computable and increases the length of the input only by a constant factor smaller than 2.

Category / Keywords: foundations / Tight security, pseudorandom functions, provable security

Date: received 11 Feb 2016, withdrawn 3 Oct 2016

Contact author: tibor jager at rub de

Available format(s): (-- withdrawn --)

Version: 20161003:071807 (All versions of this report)

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