Security Vulnerabilities of Four Signature Schemes From NTRU Lattices and Pairings

Abstract

Certificateless cryptography solves the certificate management problem in public-key cryptography and the key-escrow problem in identity-based cryptography. Xie et al. proposed a certificateless signature scheme using NTRU lattices. They proved that their scheme was existential unforgeable for Type I and Type II adversaries under the intractability of the Small Integer Solution (SIS) problem on NTRU lattices in the random oracle model. Subsequently, Hung et al. proposed a revocable certificateless signature scheme on NTRU lattices that gave a revocation method via public channels to revoke illegal or compromised users. They also proved that their scheme was existential unforgeable for Type I, Type II and Type III adversaries under the intractability of the SIS problem. Recently, Wang et al. proposed a certificateless aggregate signature scheme from bilinear pairings and Rezaeibagha et al. proposed a new lightweight certificateless scheme for Industrial Internet of Things from bilinear pairings. The security of their schemes was proven for Type I and Type II adversaries under the intractability of some mathematical problems. In this paper, we show that the two schemes on NTRU lattices are insecure against Type I or Type II adversaries. We also point out invalidity of Wang et al.'s scheme and vulnerability of Rezaeibagha et al.'s scheme against Type I attacks. We then suggest some improvements to prevent our attacks. INDEX TERMS Certificateless signature scheme, certificateless aggregate signature scheme, revocation, type I adversary, type II adversary.

An Efficient Scheme for Industrial Internet of Things Using Certificateless Signature

“…e authors claim that their scheme is safe against type I and type II adversaries. However, Shim [47] proved the invalidity of the designed scheme against the type I adversary. Also, the security of [37] is based on BPG which does not correspond to the resourcelimited setting of IIoT due to heavy pairing operations.…”

Provably Secure Lattice-Based Self-Certified Signature Scheme

“…Tian and Huang [26] and others propose several lattice-based certificateless signatures schemes, which do not need the certificate too. However, they cannot prevent insider attack, and there exist other flaws [27,28]. Hence, in this paper, we aim to propose a provably secure self-certified signature scheme over lattice.…”