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, San 56-1 Shinrim-dong, Kwanak-gu, Seoul 151-747, Republic of Korea;National Security Research Institute, 161 Gajeong-dong, Yuseong-gu, Daejeon 305-350, Republic of Korea;ISaC and Department of Mathematical Sciences, Seoul National University, San 56-1 Shinrim-dong, Kwanak-gu, Seoul 151-747, 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 E:Z"n-(Z"pxZ"q)^d where n=pq. We show that the scheme can be broken by (d+1) known plaintexts in O(d^3log^2n) time. Even when the modulus n is kept secret, it can be broken by 2(d+1) known plaintexts in O(d^4logdn+d^3log^2n+@?(m)) time with overwhelming probability.