Constructing a fully homomorphic encryption scheme with the Yoneda Lemma. (arXiv:2401.13255v1 [cs.CR])

This paper redefines the foundations of asymmetric cryptography's homomorphic
cryptosystems through the application of the Yoneda Lemma. It explicitly
illustrates that widely adopted systems, including ElGamal, RSA, Benaloh,
Regev's LWE, and NTRUEncrypt, directly derive from the principles of the Yoneda
Lemma. This synthesis gives rise to a holistic homomorphic encryption framework
named the Yoneda Encryption Scheme. Within this scheme, encryption is
elucidated through the bijective maps of the Yoneda Lemma Isomorphism, and
decryption seamlessly follows from the naturality of these …

application arxiv cryptography encryption foundations fully homomorphic encryption homomorphic encryption principles rsa systems