Method for fully homomorphic encryption using multivariate cryptography

A method of performing fully homomorphic encryption on a data set, comprising:

• providing a public multivariate encryption polynomial to encrypt the data set and produce an encrypted data set;
• providing a private multivariate decryption polynomial to decrypt the encrypted data set;
• providing a vectorial multivariate function polynomial that represents an operation to be performed on the encrypted data set;
• and
• distributing the multivariate function polynomial to a user publicly, wherein the fully homomorphic encryption is performed based on orthogonal embeddings and based on a nondeterministic polynomial time complete (NP-complete) problem, and wherein the multivariate function polynomial and the multivariate encryption polynomial are algebraic equations and the multivariate function polynomial represents a Boolean circuit.

A method of performing fully homomorphic encryption on a data set, comprising:

• providing a public multivariate encryption polynomial to encrypt the data set and produce an encrypted data set;
• providing a private multivariate decryption polynomial to decrypt the encrypted data set;
• and
• providing multiple vectorial function polynomials that represent a functionally complete set of operations to be performed on the encrypted data set;
• and
• distributing the multiple vectorial function polynomials to a user publicly, wherein the fully homomorphic encryption is performed based on orthogonal embeddings and based on a nondeterministic polynomial time complete (NP-complete) problem, and wherein the public multivariate encryption polynomial and the private multivariate decryption polynomial are algebraic equations and the multiple vectorial multivariate function polynomials represent a functionally complete set of operators that are chained together to create a Boolean circuit.