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Quantum-Resistant Identity-Based Signature with Message Recovery and Proxy Delegation

Xiuhua Lu, Qiaoyan Wen, Wei Yin, Kaitai Liang, Zhengping Jin, Emmanouil Panaousis, Jiageng Chen

Published Feb 20, 2019• 6 citations

Abstract

Digital signature with proxy delegation, which is a secure ownership enforcement tool, allows an original signer to delegate signature rights to a third party called proxy, so that the proxy can sign messages on behalf of the original signer. Many real-world applications make use of this secure mechanism, e.g., digital property transfer. A traditional digital signature mechanism is required to bind a message and its signature together for verification. This may yield extra cost in bandwidth while the sizes of message and signature are relatively huge. Message recovery signature, enabling to reduce the cost of bandwidth, embeds a message into the corresponding signature; therefore, only the signature will be transmitted to the verifier and the message can further be recovered from the signature. In this paper, we, for the first time, propose a novel digital signature scheme in the identity-based context with proxy delegation and message recovery features and, more importantly, our scheme is quantum resistant, in a particular lattice-based signature. Our scheme achieves delegation information and signature existential unforgeability against adaptive chosen warrant and identity. Compared with the seminal lattice-based message recovery signature, our scheme is independent from public key infrastructure, realizes delegation transfer of signature rights, and compresses signature length ulteriorly. To the best of our knowledge, this paper is the first of its type.

DOI: 10.3390/sym11020272

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Digital signature with proxy delegation, which is a secure ownership enforcement tool, allows an original signer to delegate signature rights to a third party called proxy, so that the proxy can sign messages on behalf of the original signer. Many real-world applications make use of this secure mechanism, e.g., digital property transfer. A traditional digital signature mechanism is required to bind a message and its signature together for verification. This may yield extra cost in bandwidth while the sizes of message and signature are relatively huge. Message recovery signature, enabling to reduce the cost of bandwidth, embeds a message into the corresponding signature; therefore, only the signature will be transmitted to the verifier and the message can further be recovered from the signature. In this paper, we, for the first time, propose a novel digital signature scheme in the identity-based context with proxy delegation and message recovery features and, more importantly, our scheme is quantum resistant, in a particular lattice-based signature. Our scheme achieves delegation information and signature existential unforgeability against adaptive chosen warrant and identity. Compared with the seminal lattice-based message recovery signature, our scheme is independent from public key infrastructure, realizes delegation transfer of signature rights, and compresses signature length ulteriorly. To the best of our knowledge, this paper is the first of its type.

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.

Proxy-signcryption is a variation of an ordinary signcryption scheme and has been used in many applications where the delegation of rights is quite common. In a proxy-signcryption scheme, an original signcrypter needs to delegate his signcryption capability to a proxy signcrypter to signcrypt messages on behalf of the original signcrypter. By combining the functionalities of proxy signature with identity-based signcryption, in this paper, we propose a novel identity-based proxy-signcryption scheme (IBPSC) from lattice assumptions in the random oracle model. Meanwhile, the security requirements of our IBPSC scheme have been analysed, and our scheme can even resist quantum computer attacks. Compared with existing IBPSC schemes, our scheme is more secure and more efficient. To the best of our knowledge, there is still no relevant IBPSC scheme based on lattice, which is an interesting stepping stone in the post-quantum cryptographic communication.

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.

Proxy signature plays an important role in distributed systems, mobile agent applications, distributed shared object systems, global distribution networks and mobile communications etc., since it allows the original signer to delegate another proxy signer to sign the message instead of himself. However, the proxy signature schemes constructed on the number theory cannot resist quantum computers attack and depend on the public key infrastructure. To mitigate these problems, the alternative schemes are Identity-based proxy signature constructed on lattice. In this paper, an identity-based proxy signature scheme based on Number theorem research unit (NTRU) lattice is proposed and proven secure in the random oracle. Compared with the other existing identity-based proxy signature schemes, the proposed scheme outperforms them in terms of original signer's signature size and signing key size and proxy signer's signing key size.

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.

Proxy signature is one of the important primitives of public-key cryptography and plays an essential role in delivering security services in modern communications. However, existing post quantum proxy signature schemes with larger signature sizes might not be fully practical for some resource-constrained devices (e.g., Internet of Things devices). A signature scheme with message recovery has the characteristic that part or all of the message is embedded in the signature, which can reduce the size of the signature. In this paper, we present a new identity-based proxy signature scheme over an NTRU lattice with message recovery (IB-PSSMR), which is more efficient than the other existing identity-based proxy signature schemes in terms of the size of the signature and the cost of energy. We prove that our scheme is secure under a Short Integer Solution (SIS) assumption that is as hard as approximating several worst-case lattice problems in the random oracle model. We also discussed some application scenarios of IB-PSSMR in blockchain and Internet of Things (IOT). This paper provides a new idea for the design of lattice signature schemes in low resource constrained environments.