METHODS AND SYSTEMS FOR ENHANCED DATA-CENTRIC SCALAR MULTIPLICATIVE HOMOMORPHIC ENCRYPTION SYSTEMS USING GEOMETRIC ALGEBRA

摘要

Disclosed are methods and systems for encrypting a numeric message using Geometric Algebra on a source computing device, performing scalar-vector multiplication on the encrypted numeric message and an unencrypted scalar data value to get an encrypted scalar multiplicative result without decrypting the encrypted numeric message on an intermediary computing system that does not have knowledge of the encryption security keys, and decrypting using Geometric Algebra the encrypted scalar multiplicative result on a destination computing device such that the decrypted result is equal to multiplication of the unencrypted numeric message and the scalar data value. Encrypt operations use the geometric product (Clifford Product) of multivectors created from plain text/data of the numeric data message with one or more other multivectors that carry encryption keys. Decrypt operation decrypts the scalar multiplicative result by employing geometric algebra operations such as multivector inverse, Clifford conjugate and others along with the geometric product.