Lattice-Based Identity-Based Encryption: Foundations, Constructions and Implementation

Abstract

Traditional public key encryption (PKE) is widely used over the internet and overcomes the key distribution problem. However, accessing the correct public keys of users still remain as a challenge. The Public Key Infrastructure (PKI) addresses this problem by managing the creation, distribution, secure storage of public keys, and their verification through trusted Certificate Authorities (CA). Moreover, Certificate Authorities can be corrupted and fake certificates can be issued. Identity-Based Encryption (IBE) solves this problem by generating secret keys from user identities, enabling any string — such as an email address, phone number, or other identifier to serve as a valid public key for a user. Additionally, it encompasses several advantages over traditional public key encryption, offering easier key revocation and flexibility for delegation of keys. Hence, this study focuses on examining the underlying mathematical foundations of Identity-Based Encryption (IBE) schemes and analyzing their structural properties. On the other hand, the recent developments in quantum computing pose a significant threat against contemporary cryptographic constructions, including PKE and IBE. This trend brings the necessity of developing quantum-resistant schemes, and Lattice-based cryptography has gained significant attention from researchers, as there is no known polynomial time algorithm to break its security. Additionally, operations on lattices are highly parallelizable and efficient, and more importantly, they offer strong worst-case security guarantees. Furthermore, our work focuses on the foundational principles of lattice-based cryptography and its application to Identity-Based Encryption (IBE) schemes. To understand the basic building blocks of lattice-based IBE schemes, we study two notions of trapdoor sampling - a critical step in lattice IBE construction. We implement two variants of lattice-based trapdoor sampling and experimentally evaluate their performances.