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Telecommunication Systems

A efficient lattice-based forward-secure linearly homomorphic signature scheme for network coding

Bin Wu, Caifen Wang, Yahong Li, Ning Shi

Published Nov 25, 2024• 2 citations
Publisher

Abstract

Abstract The property that linearly homomorphic signature (LHS) enables linear computation on signed data makes this primitive commonly used to secure the network coding based application against pollution attacks. The security of LHS wholly depends on the security of secret signing keys; once a secret key is compromised, the application system’ security will be broken. However, as relatively insecure mobile devices are increasingly used in network coding application systems, the key exposure issue is becoming more prevalent. On the other hand, with the quantum technology development, some existing LHS schemes based on some traditional number-theoretic primitives are susceptible to quantum cryptanalysis. Hence, facing the dual threats of the exposure of secret keys in reality and the future effiffifficient quantum computers, we integrate forward security into LHS, and present a forward-secure identity-based LHS scheme (FSIBLHS) based on lattice assumptions, which achieves post-quantum security, and even if the current secret key is compromised, the validity of signatures of previous time periods is still guaranteed. We defifine the fifirst security model on forward security of LHS, and prove that the proposed scheme can resist adaptively chosen identity and datasets attack under lattice assumption. Moreover, compared with previous related works, the performance analysis shows that our scheme enjoys a comparable computation cost and has a lower communication cost, and provides higher security and stronger functionality.

DOI
10.1007/s11235-024-01227-1

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Abstract The property that linearly homomorphic signature (LHS) enables linear computation on signed data makes this primitive commonly used to secure the network coding based application against pollution attacks. The security of LHS wholly depends on the security of secret signing keys; once a secret key is compromised, the application system’ security will be broken. However, as relatively insecure mobile devices are increasingly used in network coding application systems, the key exposure issue is becoming more prevalent. On the other hand, with the quantum technology development, some existing LHS schemes based on some traditional number-theoretic primitives are susceptible to quantum cryptanalysis. Hence, facing the dual threats of the exposure of secret keys in reality and the future effiffifficient quantum computers, we integrate forward security into LHS, and present a forward-secure identity-based LHS scheme (FSIBLHS) based on lattice assumptions, which achieves post-quantum security, and even if the current secret key is compromised, the validity of signatures of previous time periods is still guaranteed. We defifine the fifirst security model on forward security of LHS, and prove that the proposed scheme can resist adaptively chosen identity and datasets attack under lattice assumption. Moreover, compared with previous related works, the performance analysis shows that our scheme enjoys a comparable computation cost and has a lower communication cost, and provides higher security and stronger functionality.
Group signatures allow users to sign messages on behalf of a group without revealing authority is capable of identifying the user who generated it. However, the exposure of the user's signing key will severely damage the group signature scheme. In order to reduce the loss caused by signing key leakage, Song proposed the first forward-secure group signature. If a group signing key is revealed at the current time period, the previous signing key will not be affected. This means that the attacker cannot forge group signatures regarding messages signed in the past. To resist quantum attacks, many lattice-based forward-secure group signatures have been proposed. However, their key-update algorithm is expensive since they require some costly computations such as the Hermite normal form (HNF) operations and conversion from a full-rank set of lattice vectors into a basis. In this paper, we propose the group signature with forward security from lattice. In comparison with previous works, we have several advantages: Firstly, our scheme is more effective since we only need to sample some vectors independently from a discrete Gaussian during the key-update algorithm. Secondly, the derived secret key size is linear instead of quadratic with the lattice dimensions, which is more friendly towards lightweight applications. Anonymous authentication plays an increasingly critical role in protecting privacy and security in the environment where private information could be collected for intelligent analysis. Our work contributes to the anonymous authentication in the post-quantum setting, which has wide potential applications in the IoT environment.
With the use of a large number of mobile devices, the problem of key leakage becomes more and more serious. In view of the excellent characteristics of lattice cipher and forward-secure digital signature scheme, the construction of identity-based forward-secure digital signature based on lattice technology has become a research hotspot. However, the identity-based forward secure digital signature scheme on the existing grid has the disadvantage of excessive signature length. This paper uses the technique (without trapdoors) of Lyubashevsky and extended Samplepre, an efficient identity-based forward secure signature scheme from lattice is proposed. Its security is based on the Small Integer Solution (SIS) difficulty assumption, and the strong non-forgery of the signature scheme is achieved. Low computing overhead; The analysis results show that, compared with the existing schemes, the key and signature are smaller in size, more efficient in computing, able to resist quantum attacks, and more practical.
Blind signature (BS) plays one of key ingredients in electronic cash or electronic voting system. However, the key exposures bring out very serious problems in insecure mobile devices. Forward-secure blind signatures preserve the validity of past signatures and prevent a forger from forging past signatures even if current secret key has been compromised. In this paper, we propose the first forward-secure identity-based shorter blind signature scheme from lattices which can resist quantum attack, and prove that our scheme satisfies the security requirements of blindness, unforgeability, and forward secrecy in the random oracle model. Furthermore, we also extend our construction to a forward-secure identity-based shorter blind signature in the standard model.
We propose a linearly homomorphic signature scheme that authenticates vector subspaces of a given ambient space. Our system has several novel properties not found in previous proposals: • It is the first such scheme that authenticates vectors defined over binary fields; previous proposals could only authenticate vectors with large or growing coefficients. • It is the first such scheme based on the problem of finding short vectors in integer lattices, and thus enjoys the worst-case security guarantees common to lattice-based cryptosystems. Our scheme can be used to authenticate linear transformations of signed data, such as those arising when computing mean and Fourier transform or in networks that use network coding. Our construction gives an example of a cryptographic primitive — homomorphic signatures over F2 — that can be built using lattice methods, but cannot currently be built using bilinear maps or other traditional algebraic methods based on factoring or discrete log type problems. Security of our scheme (in the random oracle model) is based on a new hard problem on lattices, called k-SIS, that reduces to standard average-case and worst-case lattice problems. Our formulation of the k-SIS problem adds to the “toolbox” of lattice-based cryptography and may be useful in constructing other lattice-based cryptosystems. As a second application of the new k-SIS tool, we construct an ordinary signature scheme and prove it k-time unforgeable in the standard model assuming the hardness of the k-SIS problem. Our construction can be viewed as “removing the random oracle” from the signatures of Gentry, Peikert, and Vaikuntanathan at the expense of only allowing a small number of signatures.
Abstract A forward-secure group signature (FSGS) ensures the unforgeability of signatures in the past time period despite signing secret key is leaked in the current time period. As we know, traditional FSGS schemes are mostly relying on number-theoretic assumptions unable to resist quantum attacks. Therefore, we present an efficient lattice-based fully dynamic (i.e. users can flexibly join or quit the group) forward-secure group signature (DFSGS) by combining an improved version of FSGS scheme proposed by Ling. Based on an efficient zero-knowledge argument, we construct argument of knowledge of the committed value and the plaintext that help with privacy protection. Our DFSGS scheme is proved to be anonymous and forward-secure traceable relying on short integer solution and learning with errors assumptions in random oracle model. Moreover, the lengths of group public key and signature of our DFSGS scheme have been improved, and the length of user secret key has no connection with the quantity of group members.
The security of digital signatures depends significantly on the signature key. Therefore, to reduce the impact of leaked keys upon existing signatures and subsequent ones, a digital signature scheme with strong forward security could be an effective solution. Most existing strong forward-secure digital signature schemes rely on traditional cryptosystems, which cannot effectively resist quantum attacks. By introducing lattice-based delegation technology into the key-iteration process, a two-direction and lattice-based key-iteration algorithm with strong forward security is proposed. In the proposed algorithm, a unique key pair is assigned to the signer in every period. Based on the proposed algorithm, a strong forward-secure signature scheme is further put forward, which achieves resistance to quantum attacks. Performance analysis shows that under the security assumption of the SIS problem on the lattice, the proposed strong forward-secure signature scheme is existentially unforgeable under the random oracle model. Ultimately, based on the proposed strong forward-secure signature scheme, a remote identity-authentication scheme that is resistant to quantum attacks is proposed, ensuring post-quantum security in the user-authentication process.