EFFICIENT IMPLEMENTATION OF FULLY HOMOMORPHIC ENCRYPTION

In one exemplary embodiment of the invention, a method for homomorphic decryption, including: providing a ciphertext with element c, there exists a big set B having N elements zi so B={z1,z2, . . . , zN}, there exists a small set S having n elements sj so S={s1, s2, . . . , sn}, the small set is a subset of the big set, summing up the elements of the small set yields the private key, there exists a bit vector {right arrow over (σ)} having N bits σi so {right arrow over (σ)}=σ1, σ2, . . . , σN, σi=1 if zi ε S else σi=0, there exists an encrypted vector {right arrow over (d)} having N ciphertexts di so d=d1, d2, . . . , dN, di is an encryption of σi; post-processing c by multiplying it by all zi to obtain an intermediate vector {right arrow over (y)}=y1, y2, . . . , yN with yi computed yi=c×zi; homomorphically multiplying yi by di obtaining a ciphertext vector {right arrow over (x)} having N ciphertexts xi so {right arrow over (x)}=x1, x2, . . . , xN, where xi is an encryption of the product yi·σi; and homomorphically summing all xi to obtain a resulting ciphertext that is an encryption of the at least one bit, where the big set is partitioned into n parts with each part having a plurality of different elements from the big set, where the elements of the small set are one element from each part.