Proving tight security for Rabin-Williams signatures”. URL httpcr.yp.topapers.html#rwtight.pdfVIP

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Proving tight security for Rabin-Williams signatures”. URL httpcr.yp.topapers.html#rwtight.pdf

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Proving tight security for Rabin-Williams signatures”. URL httpcr.yp.topapers.html#rwtight

Proving tight security for Rabin/Williams signatures Daniel J. Bernstein Department of Mathematics, Statistics, and Computer Science (M/C 249) The University of Illinois at Chicago, Chicago, IL 60607–7045 djb@cr.yp.to Date of this document: 2007.10.07. Permanent ID of this document: c30057d690a8fb42af6a5172b5da9006. Abstract. This paper proves “tight security in the random-oracle model relative to factorization” for the lowest-cost signature systems available today: every hash-generic signature-forging attack can be converted, with negligible loss of efficiency and effectiveness, into an algorithm to factor the public key. The most surprising system is the “fixed unstructured B = 0 Rabin/Williams” system, which has a tight security proof despite hashing unrandomized messages. At a lower level, the three main accomplishments of the paper are (1) a “B ≥ 1” proof that handles some of the lowest-cost signature systems by pushing an idea of Katz and Wang beyond the “claw-free permutation pair” context; (2) a new expository structure, elaborating upon an idea of Koblitz and Menezes; and (3) a proof that uses a new idea and that breaks through the “B ≥ 1” barrier. B, number of bits of hash randomization large B B = 1 B = 0: no random bits in hash input Variable unstructured Rabin/Williams tight security (1996 Bellare/Rogaway) no security (easy attack) no security (easy attack) Variable principal Rabin/Williams tight security (this paper) loose security loose security? Variable RSA tight security (1996 Bellare/Rogaway) loose security (1993 Bellare/Rogaway) loose security (1993 Bellare/Rogaway) Fixed RSA tight security (1996 Bellare/Rogaway) tight security (2003 Katz/Wang) loose security (1993 Bellare/Rogaway) Fixed principal Rabin/Williams tight security (this paper) tight security (this paper) loose security? Fixed unstructured Rabin/Williams tight security (1996 Bellare/Rogaway) tight security (this paper) tight security (this paper) Table 1. Proven lower bounds on “secur