The article redefines the foundations of asymmetric cryptography’s homomorphic cryptosystems through the application of the Yoneda Lemma. The Yoneda Encryption Scheme is proposed as a unifying framework for various homomorphic encryption systems such as ElGamal, RSA, Benaloh, Regev’s LWE, and NTRUEncrypt. The paper introduces a fully homomorphic encryption scheme capable of processing arbitrary finite sequences of encrypted multiplications and additions without additional tweaking techniques. This not only underscores the practical implications of the proposed theoretical advancements but also introduces new possibilities for leveraging model theory and forcing techniques in cryptography to facilitate the design of fully homomorphic encryption schemes.
Publication date: 24 Jan 2024
Project Page: https://arxiv.org/abs/2401.13255v1
Paper: https://arxiv.org/pdf/2401.13255
