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Journal of Sichuan University

Lattice-based Proxy Signature Scheme in the Standard Model

Ming-Xian Li

Published Jan 1, 2014• 1 citation
OpenAlex

Abstract

The provably secure public-key cryptosystems in the standard model are more practical,but the provably secure lattice-based proxy signature schemes in the standard model have not been constructed up to now. A new lattice-based proxy signature scheme was constructed by using the Boyen's preimage sampling algorithm. The proposed proxy signature scheme was proved to satisfy the existential unforgeability against adaptive chosen-message attacks based on the hardness of the small integer solution( SIS) problem in the standard model. Finally,the computational performance of the proposed proxy signature scheme was compared with that of the existing lattice-based proxy signature schemes. The comparative results showed that the proposed proxy signature scheme has higher efficiency.

Related papers

Lattice-based Proxy Signature Scheme in the Standard Model

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Abstract:The provably secure public-key cryptosystems in the standard model are more practical, but the provably secure lattice-based proxy signature schemes in the standard model have not been constructed up to now. A new lattice-based proxy signature scheme was constructed by using the Boyen’s preimage sampling algorithm.The proposed proxy signature scheme was proved to satisfy the existential unforgeability against adaptive chosen-message attacks based on the hardness of the small integer solution (SIS) problem in the standard model.Finally,the computational performance of the proposed proxy signature scheme was compared with that of the existing lattice-based proxy signature schemes.The comparative results showed that the proposed proxy signature scheme has higher efficiency.

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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.

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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.

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By using trapdoor functions with preimage sampling,lattice's growth,and lattice basis randomization in the bonsai tree,a lattice-based proxy signature scheme was proposed.The security of the proxy signature is based on the hardness of average-case SIS(Small Integer Solution) and ISIS(Inhomogeneous Small Integer Solution).It is also existential unforgeability under adaptive chosen-message attack in the random oracle.Compared with the schemes based on factoring or discrete log,the public and secret keys of our scheme are larger,but it requires only linear operation on small integers.

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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.

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

Lili Zhang, Yanqin Ma

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.

Mathematical Problems in Engineering•Jan 1, 2014•21 citations
The provably secure public-key cryptosystems in the standard model are more practical,but the provably secure lattice-based proxy signature schemes in the standard model have not been constructed up to now. A new lattice-based proxy signature scheme was constructed by using the Boyen's preimage sampling algorithm. The proposed proxy signature scheme was proved to satisfy the existential unforgeability against adaptive chosen-message attacks based on the hardness of the small integer solution( SIS) problem in the standard model. Finally,the computational performance of the proposed proxy signature scheme was compared with that of the existing lattice-based proxy signature schemes. The comparative results showed that the proposed proxy signature scheme has higher efficiency.
Abstract:The provably secure public-key cryptosystems in the standard model are more practical, but the provably secure lattice-based proxy signature schemes in the standard model have not been constructed up to now. A new lattice-based proxy signature scheme was constructed by using the Boyen’s preimage sampling algorithm.The proposed proxy signature scheme was proved to satisfy the existential unforgeability against adaptive chosen-message attacks based on the hardness of the small integer solution (SIS) problem in the standard model.Finally,the computational performance of the proposed proxy signature scheme was compared with that of the existing lattice-based proxy signature schemes.The comparative results showed that the proposed proxy signature scheme has higher efficiency.
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.
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.
By using trapdoor functions with preimage sampling,lattice's growth,and lattice basis randomization in the bonsai tree,a lattice-based proxy signature scheme was proposed.The security of the proxy signature is based on the hardness of average-case SIS(Small Integer Solution) and ISIS(Inhomogeneous Small Integer Solution).It is also existential unforgeability under adaptive chosen-message attack in the random oracle.Compared with the schemes based on factoring or discrete log,the public and secret keys of our scheme are larger,but it requires only linear operation on small integers.
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.
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.