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Mathematical Problems in Engineering

A Lattice‐Based Identity‐Based Proxy Blind Signature Scheme in the Standard Model

Lili Zhang, Yanqin Ma

Published Jan 1, 2014• 21 citations
Publisher

Abstract

A proxy blind signature scheme is a special form of blind signature which allowed a designated person called proxy signer to sign on behalf of original signers without knowing the content of the message. It combines the advantages of proxy signature and blind signature. Up to date, most proxy blind signature schemes rely on hard number theory problems, discrete logarithm, and bilinear pairings. Unfortunately, the above underlying number theory problems will be solvable in the postquantum era. Lattice‐based cryptography is enjoying great interest these days, due to implementation simplicity and provable security reductions. Moreover, lattice‐based cryptography is believed to be hard even for quantum computers. In this paper, we present a new identity‐based proxy blind signature scheme from lattices without random oracles. The new scheme is proven to be strongly unforgeable under the standard hardness assumption of the short integer solution problem (SIS) and the inhomogeneous small integer solution problem (ISIS). Furthermore, the secret key size and the signature length of our scheme are invariant and much shorter than those of the previous lattice‐based proxy blind signature schemes. To the best of our knowledge, our construction is the first short lattice‐based identity‐based proxy blind signature scheme in the standard model.

DOI
10.1155/2014/307637

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A proxy blind signature scheme is a special form of blind signature which allowed a designated person called proxy signer to sign on behalf of original signers without knowing the content of the message. It combines the advantages of proxy signature and blind signature. Up to date, most proxy blind signature schemes rely on hard number theory problems, discrete logarithm, and bilinear pairings. Unfortunately, the above underlying number theory problems will be solvable in the postquantum era. Lattice‐based cryptography is enjoying great interest these days, due to implementation simplicity and provable security reductions. Moreover, lattice‐based cryptography is believed to be hard even for quantum computers. In this paper, we present a new identity‐based proxy blind signature scheme from lattices without random oracles. The new scheme is proven to be strongly unforgeable under the standard hardness assumption of the short integer solution problem (SIS) and the inhomogeneous small integer solution problem (ISIS). Furthermore, the secret key size and the signature length of our scheme are invariant and much shorter than those of the previous lattice‐based proxy blind signature schemes. To the best of our knowledge, our construction is the first short lattice‐based identity‐based proxy blind signature scheme in the standard model.
Blind signature allows a user to get a signature of a signer on an arbitrary message, and the verifier can convince that the signature is indeed signed by the signer without leaking any information about the message. This property is necessary when the user’s privacy needs protection, such as a bank bill, a trade secret, etc. As an alternative of public key infrastructure, the identity-based system can simplify the key management procedures in certificate-based public key systems. Inspired by the requirement of identity-based blind signature in the post quantum world, we research on identity-based blind signature based on hard lattice problems under the random Oracle model. We propose a construction built upon the blind signature by Rückert, and it is proved to be one-more unforgeable against selective identity and chosen message attacks (sID-CMA) and unconditionally blind. The proposed scheme has 2 moves, and its security can be reduced to the small integer solution (SIS) problem.
Proxy signature schemes safely ensure that an original signer transfers the signing right to a proxy signer, and a variety of these schemes have been developed for secure applications. Constructions of proxy signature schemes vary; recently developed schemes utilize lattices to safeguard against quantum attacks. However, existing lattice-based proxy schemes proved secure in the standard model have many public system parameters, reducing the efficiency of these schemes. To solve this problem, we utilize an admissible hash function with compatible algorithms (AHFwCA) and lattice trapdoors as an initial framework to propose a new lattice-based proxy signature scheme. While maintaining a similar key and signature size as prior schemes, this new proxy signature scheme requires fewer public system parameters. Compared with requiring linear basic matrices as public system parameters found in other standard model schemes, the proposed new scheme depends upon logarithmic basic matrices. Under the standard inhomogeneous short integer solution (ISIS) assumption, we prove that the scheme is existentially unforgeable against chosen message attacks and chosen warrant attacks (EUF-CMA-CWA) in the standard model by using the generalized partitioning proof technique. Thus, this paper partially solves the many parameters problem existed in the standard model lattice-based signature schemes.
Currently, most of the identity-based proxy signature schemes are based on large integer factorization and discrete logarithm which are insecure in quantum setting. To this problem, we propose a provably-secure identity-based proxy signature scheme over lattice, which uses preimage sampling technology and lattice basis delegation algorithm in fixed dimension. The proposed scheme was proved to satisfy strong unforgeability against selective identity attacks based on the hardness of the small integer solution (SIS) problem in the standard model. And compared with the existing identity-based proxy signature scheme from lattices, our scheme is more secure under the same efficiency.
Blind multisignature (BMS), first introduced by Horster et al, constitutes a crucial primitive that allows a user to generate a signature of a message from multiple signers, while the signers cannot obtain any information about the message. With these useful properties, blind multisignature is suitable for electronic payments and electronic voting. However, most of the current BMS schemes may be attacked by quantum computers in the future because they are based on traditional number theories, such as discrete logarithm assumption and large integer factor assumption. In this work, we first formalize the notion and the sound security models of the identity-based blind multisignature scheme (IDBMS). Then we present an instantiation based on lattices, along with rigorous proofs of the blindness and unforgeability under the lattice hard assumption (short integer solution, SIS), which is considered to remain secure under quantum computer attacks. To the best of our knowledge, it is the first identity-based quantum-resistant scheme that has the advantages of blind signature and multisignature.
In response to the issues of low security and computational efficiency in current lattice-based proxy blind signature systems, a novel identity-based proxy blind signature scheme utilizing lattices is proposed. This scheme integrates the user's identity information through matrix accumulation operations to serve as the verification public key, simplifying the identity validation process and strengthening both security and privacy measures. The user's private key as well as the proxy signing key are produced through the extended algorithm of the left sampling algorithm, while the rejection sampling algorithm is employed to produce the proxy blind signature. These enhance the space utilisation of keys and signatures. Moreover, the scheme's security is reducible to solving the small integer solution problem, thereby attaining resilience against one-more unforgeability under the adaptive chosen-message attacks within the random oracle model. Compared to other schemes, our scheme features smaller key and signature sizes, resulting in greater efficiency.
So far, most ring signature schemes rely on hard number theory problems, such as discrete logarithm, bilinear pairings and so on. Unfortunately, the above underlying number theory problems will be solvable in the post quantum era. Lattice-based cryptography is a hotspot of research recently, due to its implementation simplicity and provable security reductions. When the hash-and-sign signature scheme was constructed based on the hardness of worst-case lattice problems, provably secure lattice-based ring signature schemes were finally constructed. However, the hash-and-sign ring signatures were rather inefficient (with megabytes long signatures). In this paper, we propose an alternative method for constructing lattice-based and identity-based ring signature scheme which does not use the hash-and-sign methodology. In the random oracle model, the proposed signature scheme based on the problem in general lattices is unforgeable and holds anonymity. Compared with the previous instantiations of the hash-and-sign ring signature schemes, the lengths of secret key, public key and signatures in the proposed scheme are much shorter. The signing algorithm is quite simple, with matrix-vector multiplications and rejection samplings.