Security Vulnerabilities of Four Signature Schemes From NTRU Lattices and Pairings

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.