Public-Key Cryptography Based on Modular Lattices

TL;DR

This paper explores extending identity-based encryption schemes to finite modular lattices and vector spaces over finite fields, aiming to broaden cryptographic applications within algebraic structures.

Contribution

It introduces a novel approach to generalize practical identity-based encryption to modular lattices and vector spaces, expanding the algebraic frameworks used in cryptography.

Findings

Protocol can be adapted to finite modular lattices

Security proof does not yet hold in the generalized setting

Work in progress to establish security in new structures

Abstract

We present an approach to generalization of practical Identity-Based Encryption scheme of Boneh and Franklin. In particular we show how the protocol could be used on finite modular lattices and as a special case on vector spaces over finite field. The original proof of security for this protocol does not hold in this general algebraic structure, thus this is still a work in progress.