Secure distributed key generation for multiparty homomorphic encryption

A system for collaborative multiparty homomorphic encryption, comprising:

• one or more microprocessors configured to:
• receive a linear common public key that is collaboratively generated by a plurality of parties each contributing a linear public key share associated with the party, which in combination with linear public key shares associated with each of the other parties, generates the linear common public key that is a sum of the linear public key shares associated with the respective plurality of parties, encrypt each of two ciphertexts with the linear common public key, combine the two ciphertexts by a non-linear computation to generate a result ciphertext encrypted by a higher order non-linear public key, re-encrypt the result ciphertext with a re-linearization key to swap encryption keys from the non-linear public key to a linear public key, wherein the re-linearization key represents encryptions of 2irs2 under the linear common public key associated with a linear common secret key s, and distribute the re-encrypted result ciphertext to the plurality of parties to each partially decrypt the re-encrypted result ciphertext by a linear secret key share associated with the party, which in combination with partial decryptions of the re-encrypted result ciphertext by each of the other parties, fully decrypts the result by the linear common secret key that is a sum of the secret key shares of the respective plurality of parties.

A non-transitory computer readable storage medium for collaborative homomorphic encryption by a plurality of parties, the computer readable storage medium having instructions stored thereon, which when executed by one or more processors, cause the processors to:

• receive a linear common public key that is collaboratively generated by the plurality of parties each party of the plurality of parties contributing a linear public key share associated with the party, which in combination with linear public key shares associated with each of the other parties, generates the linear common public key that is a sum of the linear public key shares associated with the respective plurality of parties;
• encrypt each of two ciphertexts with the linear common public key;
• combine the two ciphertexts by a non-linear computation to generate a result ciphertext encrypted by a higher order non-linear public key;
• re-encrypt the result ciphertext with a re-linearization key to swap encryption keys from the non-linear public key to a linear public key, wherein the re-linearization key represents encryptions of 2irs2 under the linear common public key associated with a linear common secret keys;
• and
• distribute the re-encrypted result ciphertext to each of the plurality of parties to each partially decrypt the re-encrypted result ciphertext by the linear secret key share associated with the party, which in combination with partial decryptions of the re-encrypted result ciphertext by each of the other parties, fully decrypts the result by the linear common secret key that is a sum of the secret key shares of the respective plurality of parties.