... less than M, then Alice learnsrAand Bob learns rB, where rAand rBare random integers, called shares,between 0 and M − 1 such that rA+ rBmod M = A · B. Therefore, togetherAlice and ... encryption depends onnew random values being used for each encryption. In the frequency miningprotocol, the xl, yl, pl, and qlare random values, and associated X and Y ,cannot be reused in ... Paillier cryptosystem [50] and then improvedby Damgard and Jurik [12].2.2.4. Variant ElGamal CryptosystemOur protocols in Chapter 3 and 4 are based on the standard variant ofthe ElGamal encryption...