Leveled Strongly-Unforgeable Identity-Based Fully Homomorphic Signatures

Leveled Adaptively Strong-Unforgeable Identity-Based Fully Homomorphic Signatures

“…• We construct an efficient leveled strongly-unforgeable IBFHS scheme without additional public parameters, which can be used to sign many different datasets, thereby positively answering the open question of constructing a leveled IBFHS scheme with short public parameters in [15]. • We prove that our leveled IBFHS scheme is adaptively secure against chosen identity and message attacks under the small integer solution ( SIS ) assumption in standard lattices.…”

“…Subsequently, Wang et al [15] first extended the notion of HTDF, the underlying primitive of FHS in [16], to identity-based setting, and obtained the identity-based HTDF (IBHTDF) which has better parameters and stronger security. The maximum noise compared with Gorbunov et al's HTDF is roughly reduced from O(m d β) to O(4 d mβ), which will lead to a polynomial modulus q = ploy(λ) when d = O(log λ), where d is the maximum depth of the circuit and λ is the security parameter.…”

“…Our starting point is Wang et al's selectively secure leveled IBFHS scheme [15]. As stated above, although the authors in [15] extend Gorbunov et al's leveled FHS scheme to the identity-based setting with better parameters and stronger security, there are some drawbacks in terms of the security level, size of common parameters, functionality, and efficiency in generating signatures. In this paper, we construct a leveled IBFHS scheme based on the SIS problem on arbitrary lattices, which is strongly-unforgeable against adaptively chosen identity and message attack.…”

“…In addition, as done in [15], we can also use Barrington's theorem [19] to convert the Boolean circuit involved in our IBFHS scheme into a polynomial length, width-5 permutation branch program, which can greatly reduce the size of the evaluated signature from m O(dmax) to O(m • 4 dmax ) for circuits with a maximum depth d max . This process results in a smaller module q, so the efficiency and security of our IBFHS scheme can be further improved.…”

“…However, to the best of our knowledge, constructions of identity-based homomorphic signatures (IBHS) have been few and far between. In particular, a major drawback of the known IBHS scheme is that they either handle only linear functions [11] [12], [13], [14] or they satisfy only the notion of selective security [15], where an adversary announces the identity it will attack at the beginning of the security experiment, or they have the size of large public key parameter that is linearly related to the size of the dataset [15]. In this paper, our goal is to overcome these limitations and construct an identity-based full homomorphic signature (IBFHS) for all circuits, which is strongly unforgeable against adaptively chosen identity and dataset attack, based on the small integer solution (SIS) problem on arbitrary lattices.…”