Strong fully homomorphic white-box and method for using same

A method of computing an algorithm A(m, S) having i operations with input m and secret S, the method comprising:

• defining a white-box fully-homomorphic key generation function with a public key P and a private key p;
• defining a white-box fully-homomorphic encoding function Enc(P, m)=mrk+1(mod N) that generates a random integer r∈W, then performs an encoding of the input m∈B;
• defining a white-box fully-homomorphic decoding function Dec(p, c):=c(mod p) that decodes c by computing c modulo p;
• defining i transform key pairs (Ti, ti), at least on part from P and p, wherein Ti is the ith transform public key and ti is the ith transform private key;
• accepting an encoded input c0, where c0=Enc(P, m);
• and
• generating an encoded output c′ by performing, for each of the i operations, the steps of:
• accepting an encoded transform public key Ti=Enc(Ti, S);
• performing the ith operation on the encoded input ci-1 and the encoded transform public key in modulo Ni to obtain an encoded output ci;
• and
• reencoding ci with transform Ti without any interim decoding operation;
• decoding the encoded output c′ with the private key p to recover an output m′ according to m′=Dec(p, c′), such that m′=A(m, S).