Tightly-Secure Pseudorandom Functions via Work Factor Partitioning

We introduce a new technique for tight security proofs called work factor partitioning. Using this technique in a modified version of the framework of D¨ottling and Schr¨oder (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(log2 λ), where λ 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 Θ(λ)), 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.

• Type: Journal
• Year: 2016
• Where: IACR
• Authors: Tibor Jager
• Keywords: Biometrics, IACR 2016