Cryptology ePrint Archive: Report 2020/734

Mirror Theory: A simple proof of the Pi+Pj Theorem with xi_max=2

Benoît Cogliati and Jacques Patarin

Abstract: We provide a simple and complete proof of the famous Pi⊕Pj Theorem in the particular case where ξmax=2. This Theorem gives a lower bound for the number of solutions of simple linear systems of equations in the case where all the variables have to be pairwise distinct. Such systems often occur in cryptographic proofs of security, and this particular Theorem can be used to prove that the function x↦P(0||x)⊕P(1||x) is an optimally secure pseudorandom function when P is a uniformly random permutation.

Category / Keywords: secret-key cryptography / Mirror Theory, security proofs, optimal security

Date: received 17 Jun 2020, last revised 17 Jun 2020

Contact author: benoitcogliati at hotmail fr

Available format(s): PDF | BibTeX Citation

Version: 20200618:154737 (All versions of this report)

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