Abstract: Disclosed are methods and systems to encrypt data with SomeWhat Homomorphic Encryption (SWHE) properties for submission to a distributed ledger/blockchain that allows further open operations retained in the distributed ledger/blockchain on the encrypted data that will be properly reflected when the encrypted result is decrypted by the data owner. The somewhat homomorphic properties include addition and scalar division. Also disclosed is an ability to update a secret key applied for a ciphertext such that a single piece of data may be provided on the distributed ledger/blockchain by a data owner to a new data owner without also exposing other data encrypted with the original secret key of the original data owner.

Abstract: Disclosed are methods and systems to encrypt/decrypt a data message using Geometric Algebra and Hensel encoding (i.e., finite p-adic arithmetic). The security key(s), message data, and ciphertext are all represented as Geometric Algebra multivectors where a sum of the coefficients of an individual multivector is equal to the numeric value of the corresponding message or security key. Various Geometric Algebra operations with the message and security key multivectors act to encrypt/decrypt the message data. Each coefficient of the security key and message multivectors is further Hensel encoded to provide additional confusion/diffusion for the encrypted values. The Geometric Algebra operations permit homomorphic operations for adding, subtracting, multiplication and division of ciphertext multivectors such that the resulting ciphertext, when decrypted, is equal to corresponding mathematical operations using the unencrypted values.

Abstract: Disclosed are methods and systems to encrypt data with SomeWhat Homomorphic Encryption (SWHE) properties for submission to a distributed ledger/blockchain that allows further open operations retained in the distributed ledger/blockchain on the encrypted data that will be properly reflected when the encrypted result is decrypted by the data owner. The somewhat homomorphic properties include addition and scalar division. Also disclosed is an ability to update a secret key applied for a ciphertext such that a single piece of data may be provided on the distributed ledger/blockchain by a data owner to a new data owner without also exposing other data encrypted with the original secret key of the original data owner.

Abstract: Disclosed are methods and systems to encrypt/decrypt a data message using Geometric Algebra and Hensel encoding (i.e., finite p-adic arithmetic). The security key(s), message data, and ciphertext are all represented as Geometric Algebra multivectors where a sum of the coefficients of an individual multivector is equal to the numeric value of the corresponding message or security key. Various Geometric Algebra operations with the message and security key multivectors act to encrypt/decrypt the message data. Each coefficient of the security key and message multivectors is further Hensel encoded to provide additional confusion/diffusion for the encrypted values. The Geometric Algebra operations permit homomorphic operations for adding, subtracting, multiplication and division of ciphertext multivectors such that the resulting ciphertext, when decrypted, is equal to corresponding mathematical operations using the unencrypted values.