Methods and systems for somewhat homomorphic encryption and key updates based on geometric algebra for distributed ledger/blockchain technology

A distributed ledger/blockchain system that performs somewhat homomorphic operations on encrypted data without decrypting said encrypted data and where data resulting from said somewhat homomorphic operations remains encrypted, the distributed ledger/blockchain system comprising:

• a data owner node device, wherein said data owner node device further comprises:
• a key generation subsystem that generates, off-chain, a secret/private key sk and a public evaluation key pk, wherein said secret/private key skis comprised of a first key multivector (K1), a second key multivector (K2), and an integer g, and wherein said public evaluation key pk is comprised of a prime number q;
• an encryption subsystem that encrypts, off-chain, an integer message m as a function of at least one Geometric Algebra geometric product operation of said first key multivector (K1), said second key multivector (K2), and a message multivector (M), and a scalar multiplication operation with integer g to obtain message ciphertext multivector (C), wherein said message multivector (M) is a representation of said integer message m;
• a ciphertext submission subsystem that submits, on-chain, said message ciphertext multivector (C) as a transaction for said distributed ledger/blockchain system;
• and
• a decryption subsystem that decrypts, off-chain, a result ciphertext multivector (CR) as a function of at least one Geometric Algebra geometric product operation of an inverse of said first key multivector (K1−1), an inverse of said second key multivector (K2−1), said result ciphertext multivector (CR), and a scalar division operation with integer g to obtain a result multivector (R), wherein said result multivector (R) is a representation of a numeric result r;
• and,
• a calculation node device, wherein said calculation node device further comprises:
• a somewhat homomorphic operation calculation subsystem that performs, on-chain, at least one somewhat homomorphic operation with said message ciphertext multivector (C) to calculate a result ciphertext multivector (CR), wherein a smart contract for said distributed ledger/blockchain defines available somewhat homomorphic operations and wherein said calculation node device is part of said same distributed ledger/blockchain system as said owner node device.