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Lecture notes in computer science

Quantum-Secure (Non-)Sequential Aggregate Message Authentication Codes

Shingo Sato, Junji Shikata

Published Jan 1, 2019• 2 citations
Publisher
DOI
10.1007/978-3-030-35199-1_15

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In the forward secure sequential aggregate (FssAgg) signature scheme, the signer combines signatures generated in different intervals under different secret keys incrementally and sequentially in a layered “onion-like” fashion with the first signature innermost in the aggregate. In contrast with general (not forward-secure) aggregate signature schemes which aggregate signatures from multiple signers, a FssAgg signature scheme aggregates signatures of a single signer not the signatures of different signers, so the verifier uses a single public key to verify the entire aggregate. With the advantages of forward secure signature and the aggregate signature at the same time, the FssAgg signature scheme has been widely applied in logging systems and blockchain since it was proposed in 2007. Although there have been several FssAgg signature schemes, all of them are based on the classic number theory problem, which are no longer secure in the quantum era. So looking for the quantum-immune FssAgg signature is much urgent. Based on the small integer solution over lattice, a FssAgg signature in the standard model is proposed. In order to improve the efficiency, this paper uses the fixed-dimensional lattice basis delegation technique to update the keys, and the forward security is achieved. This paper uses the message addition technique and the pre-image sampling technique to embed the message and the small integer solution into the signature process, and the existentially unforgeability of the scheme is also guranteed in the standard model.

•Oct 1, 2021•0 citations
For detecting and identifying forgeries in communications, a non-adaptive group-testing aggregate message authentication code (naGT-AMAC) introduced by Hirose and Shikata at ISPEC 2018 is considered to be an efficient way when band-width is limited. In this paper, following the previous work in the classical case, we formalize quantum security of the naGT-AMAC scheme. Then we prove that the generic construction of naGT-AMAC satisfies the quantum security under the quantum security of the component MAC. The proof goes naturally along the way of the classical case. Then, we report the performance of software implementation. A method of constructing d-disjunct matrices is employed, which serves as a concrete example of an naGT-AMAC scheme. It turns out that, in the case that the number of messages is 1000 and d=10, the execution time is less than 0.5 seconds.
Aggregated signatures are a type of digital signatures that allow individual signatures obtained by different signers for different messages to be combined into a single signature that provides authenticity, integrity, and non-repudiation for all signed messages. In this case, the length of the resulting aggregated signature is much less than the sum of the lengths of the individual signatures. Sequential aggregated signatures are a subtype of aggregated signatures and allow individual signatures to be combined only during the signing procedure. Signatures of this type can be used in a variety of applications, including secure routing protocols, secure logging, sensor networks, public key infrastructure, blockchain. In this paper we present a new post-quantum aggregated signature scheme with lazy verification that eliminates the need for checking the current sequential aggregated signature during the signature process, which expands its possible application as compared to existing sequential post-quantum signature schemes. The proposed signature scheme is based on post-quantum HFEv- one-way trapdoor permutation, which is known to be resistant to quantum attacks; and Unified Framework of Gentry, O'Neill and Reyzin for obtaining lazy verification using an ideal cipher that can be implemented using the Feistel network and a block cipher. For the presented scheme we provide formal proofs of its security using Bellare-Rogaway game model: the security of the scheme was reduced to the security of a HFEv- one-way trapdoor permutation. We also present a set of parameters for the proposed scheme to meet 80 and 120-bit security levels.
In the forward secure sequential aggregate (FssAgg) signature scheme, the signer combines signatures generated in different intervals under different secret keys incrementally and sequentially in a layered “onion-like” fashion with the first signature innermost in the aggregate. In contrast with general (not forward-secure) aggregate signature schemes which aggregate signatures from multiple signers, a FssAgg signature scheme aggregates signatures of a single signer not the signatures of different signers, so the verifier uses a single public key to verify the entire aggregate. With the advantages of forward secure signature and the aggregate signature at the same time, the FssAgg signature scheme has been widely applied in logging systems and blockchain since it was proposed in 2007. Although there have been several FssAgg signature schemes, all of them are based on the classic number theory problem, which are no longer secure in the quantum era. So looking for the quantum-immune FssAgg signature is much urgent. Based on the small integer solution over lattice, a FssAgg signature in the standard model is proposed. In order to improve the efficiency, this paper uses the fixed-dimensional lattice basis delegation technique to update the keys, and the forward security is achieved. This paper uses the message addition technique and the pre-image sampling technique to embed the message and the small integer solution into the signature process, and the existentially unforgeability of the scheme is also guranteed in the standard model.