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IEEE Access

Blind Proxy Re-Signature Scheme Based on Isomorphisms of Polynomials

Huixian Li, Han Zhipeng, Liqin Wang, Liaojun Pang

Published Jan 1, 2018• 4 citations
Publisher

Abstract

Most of the existing blind proxy re-signature schemes are designed based on the traditional public key cryptosystems, whose security relies on the hardness of big integer factoring, discrete logarithm, elliptic curve discrete logarithm, and so on. However, these problems will be unsecure when facing the attack of quantum computers. Motivated by these concerns, we proposed a blind proxy re-signature scheme based on the problem of isomorphisms of polynomials, which can resist quantum attack, and gave its security proof under the random oracle model. In the proposed scheme, the message can be kept blind by using the hash function, and the delegatee's identity can be kept anonymous by using the problem of isomorphisms of polynomials. Compared with the existing schemes, the new scheme has more secure properties, such as quantum resistance, high efficiency, message blindness, and delegatee anonymity. It is concluded that the proposed scheme has a good application prospect in the future quantum computing environment with low-power hardware.

DOI
10.1109/access.2018.2869041

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Most of the existing blind proxy re-signature schemes are designed based on the traditional public key cryptosystems, whose security relies on the hardness of big integer factoring, discrete logarithm, elliptic curve discrete logarithm, and so on. However, these problems will be unsecure when facing the attack of quantum computers. Motivated by these concerns, we proposed a blind proxy re-signature scheme based on the problem of isomorphisms of polynomials, which can resist quantum attack, and gave its security proof under the random oracle model. In the proposed scheme, the message can be kept blind by using the hash function, and the delegatee's identity can be kept anonymous by using the problem of isomorphisms of polynomials. Compared with the existing schemes, the new scheme has more secure properties, such as quantum resistance, high efficiency, message blindness, and delegatee anonymity. It is concluded that the proposed scheme has a good application prospect in the future quantum computing environment with low-power hardware.
Blind signatures have been widely applied when privacy preserving is required, and the delegation of blind signature rights and a proxy blind signature (Proxy-BS) become necessary when the signer cannot sign. Existing Proxy-BS schemes are based on traditional cryptographically hard problems, and they cannot resist quantum attacks. Moreover, most current Proxy-BS schemes depend on public key infrastructure (PKI), which leads to high certificate storage and management overhead. To simplify key management and resist quantum attacks, we propose a post-quantum secure identity-based proxy blind signature (ID-Proxy-BS) scheme on a lattice using a matrix cascade technique and lattice cryptosystem. Under the random oracle model (ROM), the security of the proposed scheme is proved. Security shows that the proposed scheme assures security against quantum attacks and satisfies the correctness, blindness, and unforgeability. In addition, we apply the ID-Proxy-BS scheme on a lattice to e-voting and propose a quantum-resistant proxy e-voting system, which is resistant to quantum attacks and achieves the efficiency of e-voting.
Those existing proxy signature schemes are mainly based on the assumed hardness of Big Integer Factoring problem and Discrete Logarithm problem. So they can't resist quantum attacks. This proxy signature scheme is based on the assumed hardness of some lattice problem, which can resist quantum attack. The key pair of proxy signer was generated using basis delegation technology. Combined with GPV basic signature scheme, the proxy signature scheme was constructed. This scheme is satisfied with all the security property of proxy signature schemes. Based on this scheme, variant lattice-based proxy signature schemes will be designed, such as blind proxy signature, multi-grade proxy signature, and identity-based proxy signature etc.
Most of the previous proxy re-encryption schemes rely on the average-case hardness problems such as the integer factorization problems and the discrete logarithm problems. Therefore, they cannot guarantee its security under quantum analysis, since there exist quantum algorithms efficiently solving the factorization and logarithm problems. In the paper, we propose the first proxy re-encryption scheme based on the hard worst-case lattice problems. Our scheme has many useful properties as follows: Unidirectional, collusion-resistant, noninteractive, proxy invisible, key optimal, and nontransitive. We also provided the formal security proof of the proposed scheme in the random oracle model.
The threshold proxy signcryption can implement signature and encryption simultaneously in one logical step, and can be used to realize the decentralized protection of the group signature key, so it is an efficient technology for network security. Currently, most of the existing threshold proxy signcryption schemes are designed based on the traditional public key cryptosystems, and their security mainly depends on the difficulty of the large integer decomposition and the discrete logarithm. However, the traditional public key cryptosystems cannot resist the quantum computer attack, which makes the existing threshold proxy signcryption schemes based on traditional public key cryptosystems insecure against quantum attacks. Motivated by these concerns, we proposed a threshold proxy signcryption scheme based on Multivariate Public Key Cryptosystem (MPKC) which is one of the quantum attack-resistent public key algorithms. Under the premise of satisfying the threshold signcryption requirements of the threshold proxy, our scheme can not only realize the flexible participation of the proxy signcrypters but also resist the quantum computing attack. Finally, based on the assumption of Multivariate Quadratic (MQ) problem and Isomorphism Polynomial (IP) problem, the proof of the confidentiality and the unforgeability of the proposed scheme under the random oracle model is given.
In a proxy signature scheme, an original signer delegates his/her signing capability to a proxy signer and then the proxy signer can sign messages on behalf of the original signer. The security of many proxy signature schemes that have been proposed depends, either directly or indirectly, on either the difficulty of big integers factoring problem or the difficulty of finding discrete logarithm in a finite group. These types of schemes cannot resist quantum attacks. In this paper, we propose a new lattice-based proxy signature scheme which can resist quantum attacks. The proposed scheme is based on the GGH-signature scheme and also satisfies all the security requirements of proxy signature schemes.
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.