Known-plaintext cryptanalysis of the Domingo-Ferrer algebraic privacy homomorphism scheme

Authors:
Jung Hee Cheon;Woo-Hwan Kim;Hyun Soo Nam
Affiliations:
ISaC and Department of Mathematical Sciences, Seoul National University, Seoul, Republic of Korea;National Security Research Institute, Daejeon, Republic of Korea;ISaC and Department of Mathematical Sciences, Seoul National University, Seoul, Republic of Korea
Venue:
Information Processing Letters
Year:
2006

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Abstract

We propose cryptanalysis of the First Domingo-Ferrer's algebraic privacy homomorphism ε: Zn → (Zp × Zq)d where n = pq. We show that the scheme can be broken by (d + 1) known plaintexts in O(d3 log2 n) time. Even when the modulus n is kept secret, it can be broken by 2(d + 1) known plaintexts in O(d4 log dn + d3 log2 n + ε(m)) time with overwhelming probability.