## Cryptology ePrint Archive: Report 2006/206

On the Provable Security of an Efficient RSA-Based Pseudorandom Generator

Ron Steinfeld and Josef Pieprzyk and Huaxiong Wang

Abstract: Pseudorandom Generators (PRGs) based on the RSA inversion (one-wayness) problem have been extensively studied in the literature over the last 25 years. These generators have the attractive feature of provable pseudorandomness security assuming the hardness of the RSA inversion problem. However, despite extensive study, the most efficient provably secure RSA-based generators output asymptotically only at most \$O(\log n)\$ bits per multiply modulo an RSA modulus of bitlength \$n\$, and hence are too slow to be used in many practical applications.

To bring theory closer to practice, we present a simple modification to the proof of security by Fischlin and Schnorr of an RSA-based PRG, which shows that one can obtain an RSA-based PRG which outputs \$\Omega(n)\$ bits per multiply and has provable pseudorandomness security assuming the hardness of a well-studied variant of the RSA inversion problem, where a constant fraction of the plaintext bits are given. Our result gives a positive answer to an open question posed by Gennaro (J. of Cryptology, 2005) regarding finding a PRG beating the rate \$O(\log n)\$ bits per multiply at the cost of a reasonable assumption on RSA inversion.

Category / Keywords: Pseudorandom generator, RSA, provable security, lattice attack

Publication Info: To appear at Asiacrypt 2006.

Date: received 20 Jun 2006, last revised 21 Sep 2006

Contact author: rons at ics mq edu au

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

Note: Several small corrections and additions have been made.

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