Verifiable Rotation of Homomorphic Encryptions

Similar to verifiable shuffling (or, mixing), we consider the problem of verifiable rotating (and random re-encrypting) a given list of homomorphic encryptions. The offset by which the list is rotated (cyclic shift) should remain hidden. Basically, we will present zeroknowledge proofs of knowledge for the existence of a rotation offset and re-encryption exponents, which define how the input list is transformed into the output list. We also briefly address various applications of verifiable rotators, ranging from `fragile mixing' as introduced by Reiter and Wang at CCS'04 to applications in protocols for secure multiparty computation and voting. We present two new, efficient protocols. Our first protocol is quite elegant and involves the use of the Discrete Fourier Transform (and also the FFT algorithm), and works under some reasonable conditions. We believe that this is the first time that Fourier Transforms are used to construct an efficient zero-knowledge proof of knowledge...

• Type: Conference
• Year: 2009
• Where: PKC
• Authors: Sebastiaan de Hoogh, Berry Schoenmakers, Boris Skoric, José Villegas
• Keywords: Cryptography, PKC 2009, Verifiable Rotating, Verifiable Rotators, Verifiable Shuffling