Fog computing extends the cloud computing to the network edge and allows deploying a new type of semioffline services, which can provide real‐time transactions between two entities, while the central cloud server is offline and network edge devices are online. For an e‐payment system and e‐voting with such feature, proxy blind signature is a cornerstone to protect users’ privacy. However, the signature based on number theorem, such as hard mathematical problems on factoring problem, discrete logarithm problem, and bilinear pairings, cannot defeat quantum computers attack. Meanwhile, these schemes need to depend on complex public key infrastructure. Thus, we construct an identity‐based proxy blind signature scheme based on number theorem research unit lattice, which can defeat quantum computers attack and does not need to depend on public key infrastructure. The security of the proposed scheme is dependent on Ring‐Small Integer Solution problem over number theorem research unit lattice. The proposed scheme meets the properties of blind signature and proxy signature. Then we compare the proposed scheme with other existing proxy blind signature schemes; the result shows that the proposed scheme outperforms ZM scheme except in proxy signer’s signature size and can be more secure than TA scheme and MMHP scheme.
Fog computing extends the cloud computing to the network edge and allows deploying a new type of semioffline services, which can provide real‐time transactions between two entities, while the central cloud server is offline and network edge devices are online. For an e‐payment system and e‐voting with such feature, proxy blind signature is a cornerstone to protect users’ privacy. However, the signature based on number theorem, such as hard mathematical problems on factoring problem, discrete logarithm problem, and bilinear pairings, cannot defeat quantum computers attack. Meanwhile, these schemes need to depend on complex public key infrastructure. Thus, we construct an identity‐based proxy blind signature scheme based on number theorem research unit lattice, which can defeat quantum computers attack and does not need to depend on public key infrastructure. The security of the proposed scheme is dependent on Ring‐Small Integer Solution problem over number theorem research unit lattice. The proposed scheme meets the properties of blind signature and proxy signature. Then we compare the proposed scheme with other existing proxy blind signature schemes; the result shows that the proposed scheme outperforms ZM scheme except in proxy signer’s signature size and can be more secure than TA scheme and MMHP scheme.
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.
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.
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.
With the development of wireless sensor networks, IoT devices are crucial for the Smart City; these devices change people's lives such as e-payment and e-voting systems. However, in these two systems, the state-of-art authentication protocols based on traditional number theory cannot defeat a quantum computer attack. In order to protect user privacy and guarantee trustworthy of big data, we propose a new identity-based blind signature scheme based on number theorem research unit lattice, this scheme mainly uses a rejection sampling theorem instead of constructing a trapdoor. Meanwhile, this scheme does not depend on complex public key infrastructure and can resist quantum computer attack. Then we design an e-payment protocol using the proposed scheme. Furthermore, we prove our scheme is secure in the random oracle, and satisfies confidentiality, integrity, and non-repudiation. Finally, we demonstrate that the proposed scheme outperforms the other traditional existing identity-based blind signature schemes in signing speed and verification speed, outperforms the other lattice-based blind signature in signing speed, verification speed, and signing secret key size.
Summary Proxy signature scheme is an important cryptographic primitive, for an entity can delegate his signing right to another entity. Although identity‐based proxy signature schemes based on conventional number‐theoretic problems have been proposed for a long time, the researchers have paid less attention to lattice‐based proxy signature schemes that can resist quantum attack. In this paper, we first propose an identity‐based proxy signature scheme over Number Theory Research Unit (NTRU)‐lattice. We proved that the proposed paradigm is secure under the hardness of the γ‐shortest vector problem on the NTRU lattice in random oracle model; furthermore, the comparison with some existing schemes shows our scheme is more efficient in terms of proxy signature secret key size, proxy signature size, and computation complexity. As the elemental problem of the proposed scheme is difficult even for quantum computation model, our scheme can work well in quantum age.
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.