A method for processing a generalized Goldwasser-Micali ciphertext, said ciphertext being obtained through a use of a public key associated to a private key p, p being a prime number, said method being executed on an electronic device and being characterized in that it comprises: determining at least one bit of a binary representation m j of a plaintext m associated with said ciphertext, said at least one bit m j corresponding to a bit positioned at j -th position of said binary representation of said plaintext, j being an integer greater or equal to one, and position zero of said binary representation corresponding to the least significant bit of said binary representation, said determining at least one bit comprising: determining said at least one bit m j based on the relationship c y m mod 2 j λ j + 1 = − 1 m j mod p, where c corresponds to said ciphertext, mod is a modular reduction, and y corresponds to an element comprised in said public key; wherein that said binary representation of said plaintext is a k -bit string, k being an integer greater or equal to two, and λ j +1 = 2 k -( j +1) p', where p' is an odd integer linked to said private key p by the following equation: p = 2 k p' + 1, and wherein p = 1 mod 2 k and p ≠ 1 mod 2 k +1, and wherein the generalized Goldwasser-Micali ciphertext c is equal to y m x 2 k mod N, where N = pq, with q being a prime number such that q = 1 mod 2 k and q ≠ 1 mod 2 k +1, and wherein x is a random element of Z N *. determining at least one bit of a binary representation m j of a plaintext m associated with said ciphertext, said at least one bit m j corresponding to a bit positioned at j -th position of said binary representation of said plaintext, j being an integer greater or equal to one, and position zero of said binary representation corresponding to the least significant bit of said binary representation, said determining at least one bit comprising: determining said at least one bit m j based on the relationship c y m mod 2 j λ j + 1 = − 1 m j mod p, where c corresponds to said ciphertext, mod is a modular reduction, and y corresponds to an element comprised in said public key; wherein that said binary representation of said plaintext is a k -bit string, k being an integer greater or equal to two, and λ j +1 = 2 k -( j +1) p', where p' is an odd integer linked to said private key p by the following equation: p = 2 k p' + 1, and wherein p = 1 mod 2 k and p ≠ 1 mod 2 k +1, and wherein the generalized Goldwasser-Micali ciphertext c is equal to y m x 2 k mod N, where N = pq, with q being a prime number such that q = 1 mod 2 k and q ≠ 1 mod 2 k +1, and wherein x is a random element of Z N *. determining said at least one bit m j based on the relationship c y m mod 2 j λ j + 1 = − 1 m j mod p, where c corresponds to said ciphertext, mod is a modular reduction, and y corresponds to an element comprised in said public key; wherein that said binary representation of said plaintext is a k -bit string, k being an integer greater or equal to two, and λ j +1 = 2 k -( j +1) p', where p' is an odd integer linked to said private key p by the following equation: p = 2 k p' + 1, and wherein p = 1 mod 2 k and p ≠ 1 mod 2 k +1, and wherein the generalized Goldwasser-Micali ciphertext c is equal to y m x 2 k mod N, where N = pq, with q being a prime number such that q = 1 mod 2 k and q ≠ 1 mod 2 k +1, and wherein x is a random element of Z N *.