We put forth a new mathematical framework called Isogenous Pairing Groups (IPG) and new intractable assumptions in the framework, the Isogenous DBDH (Isog-DBDH) assumption and its variants. Three operations, i.e., exponentiation, pairing and isogeny on elliptic curves are treated under a unified notion of trapdoor homomorphisms, and combinations of the operations have potential new cryptographi...

This paper presents an improved Plantard’s modular arithmetic (Plantard arithmetic) tailored for Lattice-Based Cryptography (LBC). Based on the Plantard arithmetic, we present faster implementations of two LBC schemes, Kyber and NTTRU, running Cortex-M4. The intrinsic advantage is that one multiplication can be saved from a constant. However, original not very practical in schemes because limit...

Cryptography is the technique of changing data or information into unreadable for unauthorized persons. In cryptography process information transfer from sender to receiver in a manner that prevents from unauthorized third person. There are so many cryptography methods are available which based on number theory. The cryptography based on number system has some disadvantages such as large comput...