Provably Secure Identity-Based Encryption and Signature over Cyclotomic Fields

Yang Wang,Jing Wang,Jingdan Zou,Mingqiang Wang,Jin Xu

doi:10.1155/2019/1742386

Abstract

Identity-based cryptography is a type of public key cryptography with simple key management procedures. To our knowledge, till now, the existing identity-based cryptography based on NTRU is all over power-of-2 cyclotomic rings. Whether there is provably secure identity-based cryptography over more general fields is still open. In this paper, with the help of the results of collision resistance preimage sampleable functions (CRPSF) over cyclotomic fields, we give concrete constructions of provably secure identity-based encryption schemes (IBE) and identity-based signature schemes (IBS) based on NTRU over any cyclotomic field. Our IBE schemes are provably secure under adaptive chosen-plaintext and adaptive chosen-identity attacks, meanwhile, our IBS schemes are existentially unforgeable against adaptively chosen message and adaptively chosen identity attacks for any probabilistic polynomial time (PPT) adversary in the random oracle model. The securities of both schemes are based on the worst-case approximate shortest independent vectors problem (SIVPγ) over corresponding ideal lattices. The secret key size of our IBE (IBS) scheme is short—only one (two) ring element(s). The ciphertext (signature) is also short—only two (three) ring elements. Meanwhile, as the case of NTRUEncrypt, our IBE scheme could encrypt n bits in each encryption process. These properties may make our schemes have more advantages for some IoT applications over postquantum world in theory.

Highlights

Nowadays, Internet of things (IoT) plays an extremely important role by comprising millions of smart and connected devices to o er bene ts in a wide range of situations, for example, smart cities, smart grads, smart tra c, and smart buildings. e corresponding techniques have been unprecedentedly developed and adopted due to the quick evolution of smart devices and the continuous investment of leading communities
Identity-based cryptography is a type of public key cryptography in which the public key of a user is some unique information about the identity of the user
Ough the efficiency of our identity-based encryption schemes (IBE) and identity-based signature schemes (IBS) schemes may be not satisfactory when we set parameters to achieve the provably security, our results give a high-level implication that we can heuristically design IBE and IBS over any cyclotomic field with small parameters and construct a lightweight cryptosystem, which can be used in some IoT applications

Summary

Introduction

Internet of things (IoT) plays an extremely important role by comprising millions of smart and connected devices to o er bene ts in a wide range of situations, for example, smart cities, smart grads, smart tra c, and smart buildings. e corresponding techniques have been unprecedentedly developed and adopted due to the quick evolution of smart devices and the continuous investment of leading communities. Ough the efficiency of our IBE and IBS schemes may be not satisfactory when we set parameters to achieve the provably security, our results give a high-level implication that we can heuristically design IBE and IBS over any cyclotomic field with small parameters (for example, settings of the classical NTRU-based cryptography [20]) and construct a lightweight cryptosystem, which can be used in some IoT applications. Our construction provides an important support for designing IBE and IBS over general cyclotomic rings with relative small parameters (with no provably secure guarantee, but the key generation algorithm is PPT by our results) and analyzing the security from the view of attacks. How to reduce the magnitudes of parameters of provably secure identity-based cryptographic primitives and improve the efficiency of these schemes are important and meaningful open problems.

Preliminaries

Identity-Based Encryption Schemes

Identity-Based Signature Schemes