US 12,587,357 B2 · Methods and systems for p-adic encoding and decoding of rational data for FHE systems

Abstract

Disclosed are methods and systems to provide homomorphic compatible, p-adic arithmetic based encoding and decoding of rational numbers to integers and back to rational numbers for use with existing Fully Homomorphic Encryption (FHE) systems. Embodiments support both Approximate Greatest Common Devisor (AGCD) systems such as those with an Integer—Dijk, Gentry, Halevi, and Vaikuntanathan (IDGHV) scheme, and Ring Learning With Error (RLWE) systems such as a Fan and Vercauteren (FV) scheme modified for encrypting integers (ModFV). Encoded integers are provided to an FHE system on a source device that may optionally deliver the encrypted ciphertext to an intermediary device for performance of homomorphic algebra operations, and, the resultant and/or original ciphertext is delivered to a destination device for decryption of the ciphertext, and decoding of the decrypted integer back to a rational number.

Claims22

Dependent claims

A method for Homomorphic Encryption (HE) compatible encoding and decoding of rational data for encrypted data transmission with a Fully Homomorphic Encryption (FHE) system between a source computing device and a destination computing device, the method comprising:

encoding by said source computing device at least one rational number x/y into at least one integer corresponding to said at least one rational number x/y as a function of p-adic arithmetic performed on each of said at least one rational number x/y such that said at least one integer retains homomorphic properties;
encrypting by said source computing device said at least one integer into at least one ciphertext with said FHE system operating on said source computing device;
sending by said source computing device said at least one ciphertext to said destination computing device;
decrypting by said destination computing device said at least one ciphertext into said at least one integer with said FHE system operating on said destination computing device;
and
decoding by said destination computing device said at least one integer into said at least one rational number x/y corresponding to said at least one integer as a function of inverse p-adic arithmetic performed on each of said at least one integer.

3 more elements

A PIE (p-adic encoding) system that encodes and decodes rational data with Homomorphic Encryption (HE) compatibility for encrypted data transmission with a Fully Homomorphic Encryption (FHE) system between a source computing device and a destination computing device, the PIE system comprising:

said source computing device, wherein said source device further comprises:
a PIE encode subsystem that encodes at least one rational number x/y into at least one integer corresponding to said at least one rational number x/y as a function of p-adic arithmetic performed on each of said at least one rational number x/y such that said at least one integer has homomorphic properties and is HE compatible;
said FHE system operating on said source computing device that encrypts said at least one integer into at least one ciphertext;
a ciphertext send subsystem that sends said at least one ciphertext to said destination computing device;
said destination computing device, wherein said destination computing device further comprises:
said FHE system operating on said destination computing device that decrypts said at least one ciphertext into said at least one integer;
and
a PIE decode subsystem that decodes said at least one integer into said at least one rational number x/y corresponding to said at least one integer as a function of inverse p-adic arithmetic performed on each of said at least one integer.

5 more elements

Dependencies are inferred from the claim text.

Methods and systems for p-adic encoding and decoding of rational data for FHE systems

Life of this patent

Methods and systems for p-adic encoding and decoding of rational data for FHE systems

Life of this patent

Abstract

Claims22