Pairing Product Equations Research Articles

Strongly‐optimal structure preserving signatures from Type II pairings: synthesis and lower bounds

Recent work on structure-preserving signatures (SPS) studies optimality of these schemes in terms of the number of group elements needed in the verification key and the signature, and the number of pairing-product equations in the verification algorithm. While these measures are crucial for many applications, another important aspect to consider for performance is verification time, which for these schemes is dominated by pairings computation. Although prior work considers optimality in terms of number of pairing-product equations, this measure does not capture the exact number of pairings needed in verification. To fill this gap, we study the minimal number of pairings needed in verification of SPS. First, we prove lower bounds for schemes in the Type~II setting secure under chosen message attacks in the generic group model. We show that three pairings are necessary and at most one of these pairings can be precomputed. Second, we build an automated tool to search for schemes matching our lower bounds. Using this tool, we find a new randomisable SPS in the Type~II setting that is optimal with respect to our lower bound on the number of pairings, and minimal in terms of group operations to be computed during verification.

Efficient oblivious transfer with adaptive queries in UC framework

AbstractWe propose two efficient universally composable adaptivek‐out‐of‐N protocols, secure in the presence of malicious adversary in static corruption model under the Decision Linear and q‐Strong Diffie–Hellman assumptions. Our second scheme additionally requires the hardness of Decision Bilinear Diffie‐Hellman problem. Non‐interactive Groth–Sahai proofs are employed for the verification of pairing product equations. More interestingly, our first scheme facilitates the receiver to verify the correctness of messages recovered. The proposed protocols exhibit significant computational and communication efficiency compared with existing similar schemes in the literature. Copyright © 2016 John Wiley & Sons, Ltd.

Structure-Preserving Signatures and Commitments to Group Elements

A modular approach to constructing cryptographic protocols leads to simple designs but often inefficient instantiations. On the other hand, ad hoc constructions may yield efficient protocols at the cost of losing conceptual simplicity. We suggest a new design paradigm, structure-preserving cryptography, that provides a way to construct modular protocols with reasonable efficiency while retaining conceptual simplicity. A cryptographic scheme over a bilinear group is called structure-preserving if its public inputs and outputs consist of elements from the bilinear groups and their consistency can be verified by evaluating pairing-product equations. As structure-preserving schemes smoothly interoperate with each other, they are useful as building blocks in modular design of cryptographic applications. This paper introduces structure-preserving commitment and signature schemes over bilinear groups with several desirable properties. The commitment schemes include homomorphic, trapdoor and length-reducing commitments to group elements, and the structure-preserving signature schemes are the first ones that yield constant-size signatures on multiple group elements. A structure-preserving signature scheme is called automorphic if the public keys lie in the message space, which cannot be achieved by compressing inputs via a cryptographic hash function, as this would destroy the mathematical structure we are trying to preserve. Automorphic signatures can be used for building certification chains underlying privacy-preserving protocols. Among a vast number of applications of structure-preserving protocols, we present an efficient round-optimal blind-signature scheme and a group signature scheme with an efficient and concurrently secure protocol for enrolling new members.