CPC H04L 9/008 (2013.01) [H04L 9/30 (2013.01); H04L 9/3033 (2013.01); H04L 9/3249 (2013.01)] | 6 Claims |
1. A method for distributing an arithmetic computation o across a number t computational units of a private-key Fully Homomorphic Encryption (FHE) system, where t is at least 2, the method comprising:
generating by a source device a secret key sk comprised of prime numbers p1 . . . p2t and public evaluation key pk equal to g of a g-adic number system;
choosing by said source device random numbers sa2 . . . sat for a message ma;
computing by said source device rational number αa as a g-adic number inverse Hg−1 with said prime numbers p1 . . . pt and Hensel codes ha1 . . . hat where said Hensel codes ha1 . . . hat are said message ma and said random numbers sa2 . . . sat;
computing by said source device Hensel codes hat+1 . . . ha2t as g-adic Hensel codes Hg from said prime numbers pt+1 . . . p2t and said rational number αa such that said Hensel codes hat+1 . . . ha2t are message ma ciphertexts ca1 . . . cat;
choosing by said source device random numbers sb2 . . . sbt for a message mb;
computing by said source device rational number αb as a g-adic number inverse Hg−1 with said prime numbers p1 . . . pt and Hensel codes hb1 . . . hbt where said Hensel codes hb1 . . . hbt are said message mb and said random numbers sb2 . . . sbt;
computing by said source device Hensel codes hbt+1 . . . hb2t as g-adic Hensel codes Hg from said prime numbers pt+1 . . . p2t and said rational number αb such that said Hensel codes hbt+1 . . . hb2t are message mb ciphertexts cb1 . . . cbt;
sending by said source device each Hensel digit of said ciphertexts ca1 . . . cat and each Hensel digit of said ciphertexts cb1 . . . cbt to corresponding computational units 1 . . . t, respectively;
performing at each computational unit i of said computational units 1 . . . t arithmetic function cai o cbi to obtain encrypted result cri corresponding to said computational unit i;
sending by each of said computational units 1 . . . t said corresponding encrypted result cri to a destination device;
computing by said destination device a result rational number αr as a g-adic number inverse Hg−1 with said prime numbers pt+1 . . . p2t and said encrypted results cr1 . . . crt as Hensel codes for said g-adic number inverse Hg−1; and
computing by said destination device a result message mr as Hensel Code Generation H with said prime p1 and said result rational number αr such that result message mr is equal to arithmetic function message ma o message mb.
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