Abstract
Tian and Huang proposed a lattice-based CLS scheme based on the hardness of the SIS problem and proved, in the random oracle model, that the scheme is existentially unforgeable against strong adversaries. Their security proof uses the general forking lemma under the assumption that the underlying hash function H is a random oracle. We show that the hash function in the scheme is neither one-way nor collision-resistant in the view of a strong Type 1 adversary. We point out flaws in the security arguments and present attack algorithms that are successful in the strong Type 1 adversarial model using the weak properties of the hash function.
Highlights
The notion of certificateless signature (CLS) has been introduced by Al-Riyami and Paterson [1] in 2003 as a variant of identity-based signature (IBS) to eliminate the key escrow problem inherent in IBS and assuage the certificate management of regular signatures
In 2015, Tian and Huang [9] proposed a lattice-based CLS scheme and proved under the SIS assumption that the scheme is existentially unforgeable against strong adversaries, in the random oracle
We show that the CLS scheme is insecure against strong Type 1 adversaries by providing effective attack algorithms
Summary
The notion of certificateless signature (CLS) has been introduced by Al-Riyami and Paterson [1] in 2003 as a variant of identity-based signature (IBS) to eliminate the key escrow problem inherent in IBS and assuage the certificate management of regular signatures. To solve the key escrow problem, a user’s private key in a CLS scheme is not generated by the KGC alone. In 2015, Tian and Huang [9] proposed a lattice-based CLS scheme and proved under the SIS assumption that the scheme is existentially unforgeable against strong adversaries, in the random oracle. We discuss security flaws in the CLS scheme of Tian and Huang by scrutinizing misuses of the hash function in the security arguments. We show that the hash function is neither one-way nor collision-resistant in the view of a strong Type 1 adversary This means that the hash function defined from H cannot be modelled as a random oracle and this indicates critical flaws in the security argument.
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