Homomorphic Data Concealment Powered by Clifford Geometric Algebra
- D. W. H. A. D. SilvaMarcelo A. XavierPhilip N. BrownC. E. ChowCarlos Paz de Araujo
- 20 October 2020
Computer Science, Mathematics
This work proposes general-purpose methods for data representation and data concealment via multivector decompositions and a small subset of functions in the three dimensional Clifford geometric algebra and implements these mechanisms in the Ruby programming language.
Experiments with Clifford Geometric Algebra Applied to Cryptography
- D. W. H. A. D. SilvaMarcelo A. XavierC. E. ChowCarlos Paz de Araujo
- 5 December 2020
Computer Science, Mathematics
2020 Joint 11th International Conference on Soft…
This work introduces preliminary experiments of cryptographic solutions based on Clifford geometric algebra, including a key exchange protocol, a hash algorithm, and a private-key encryption scheme, with the hope of providing appealing pieces of evidence that this powerful mathematical resource is worth investigating as a strong candidate for broad adoption in cryptography.
PIE: p-adic Encoding for High-Precision Arithmetic in Homomorphic Encryption
- Luke HarmonGaetan DelavignetteArnab RoyD. W. H. A. D. Silva
- 2023
Computer Science, Mathematics
This work identifies mathematical techniques (supported by p -adic number theory) as appropriate tools to construct a generic rational encoder which is compatible with HE and proposes a new encoding scheme PIE that can be easily combined with both AGCD-based and RLWE-based HE to perform high precision arithmetic.
Homomorphic Image Processing Over Geometric Product Spaces and Finite P-Adic Arithmetic
- D. W. H. A. D. SilvaHanes Barbosa Marques de OliveiraC. E. ChowBryan Sosa BarillasCarlos Paz de Araujo
- 1 December 2019
Computer Science, Mathematics
2019 IEEE International Conference on Cloud…
This work introduces a homomorphic image encryption framework with which images can be processed while encrypted, and demonstrates the practicability of the construction by implementing a set of pixel transformations that are only performed over encrypted images.
An Efficient Homomorphic Data Encoding with Multiple Secret Hensel Codes
- D. W. H. A. D. SilvaCarlos Paz de AraujoEdward Chow
- 1 March 2020
Computer Science, Mathematics
This work introduces a probabilistic fully homomorphic encoding scheme that is practical as a stand-alone entry-level solution to data privacy or as an added component of existing encryption schemes, especially those that are deterministic.
Threshold Secret Sharing with Geometric Algebra
- D. W. H. A. D. SilvaLuke HarmonGaetan Delavignette
- 7 February 2022
Mathematics, Computer Science
Any application in GA dealing with multivectors can immediately add threshold security using the variant of a well-known threshold secret sharing scheme introduced by Adi Shamir in 1979, a cryptographic solution that allows a secret input to be divided into multiple random shares which are then sent to distinct parties.
Leveled Fully Homomorphic Encryption Schemes with Hensel Codes
- D. W. H. A. D. SilvaLuke HarmonGaetan DelavignetteCarlos Paz de Araujo
- 2021
Computer Science, Mathematics
Experimental results indicate the Hensel codes scheme is practical for a large variety of applications and can be seen as a natural unification of error-free computation (computation free of rounding errors over rational numbers) and homomorphic encryption.