Homomorphic Encryption via Geometric Algebra Multivectors
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Solution Overview
Problem
Current encryption methods for secure data transfer over the internet lack the ability to perform computations on encrypted data without decryption, especially in cloud computing environments, where providing access to encryption keys increases security risks.
Innovation Solution
The use of Geometric Algebra multivectors with Hensel encoding for homomorphic encryption, allowing computations to be performed on encrypted data without decryption, using Geometric Algebra geometric product operations and Hensel encoding to secure and decrypt numeric message data across multiple dimensions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If encryption keys are provided to cloud computing environments for data processing, then data processing capability is improved, but security risk increases
Solution Approach 1:
The patent introduces homomorphic encryption as an intermediary mechanism that allows cloud servers to process encrypted data without accessing the decryption keys. The encryption scheme acts as a mediator between the need for data processing and the requirement for security, enabling computations on ciphertext while keeping plaintext and keys isolated from the processing environment.
Solution Approach 2:
The patent replaces the traditional mechanical key-based encryption system with a homomorphic encryption system based on geometric algebra and Hensel codes. This substitution eliminates the need for key exchange and management mechanisms, allowing direct computation on encrypted data through algebraic operations that preserve encryption structure.
2Reliability
If data is encrypted before cloud storage, then security is improved, but computation on encrypted data becomes impossible
Solution Approach 1:
The patent changes the mathematical parameters of the encryption system by using geometric algebra multivectors with Hensel code encoding instead of traditional encryption schemes. This parameter change enables the encryption structure to support algebraic operations, transforming the encryption from a computation-blocking format to one that preserves computational functionality through homomorphic properties.
Solution Approach 2:
The patent creates a composite encryption structure combining geometric algebra multivectors with Hensel codes. This composite approach merges two mathematical frameworks to produce an encryption system that simultaneously provides security through encryption and computation capability through the homomorphic properties of geometric algebra operations.
3Ease of manufacture
If traditional encryption methods are used, then implementation simplicity is maintained, but ability to perform computations on encrypted data is lost
Solution Approach 1:
The patent creates a universal encryption framework based on geometric algebra that serves multiple functions simultaneously: it provides security through encryption, enables computation through homomorphic properties, and supports various algebraic operations (addition, multiplication, etc.). This multi-functional system replaces traditional single-purpose encryption with a versatile platform that handles both security and computation needs.
Data Source
AI summary
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. The additional Hensel encoding of the coefficients of the multivectors does not impede the homomorphic aspects of the Geometric Algebra encryption operations. Operations for security key updates and exchanges are also provided.