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Quantum Information Processing

Quantum homomorphic aggregate signature based on quantum Fourier transform

Teng Chen, Dianjun Lu, Zhi-Ming Deng, Weixin Yao

Published Mar 28, 2024• 7 citations
Publisher

Abstract

Abstract With the rapid development of computer and internet technology, quantum signature plays an extremely important role in modern secure communication. Quantum homomorphic aggregate signature, as an important guarantee of quantum signature, plays a significant role in reducing storage, communication, and computing costs. This article draws on the idea of quantum multi-party summation and proposes a quantum homomorphic aggregate signature scheme based on quantum Fourier transform. Our scheme uses $n$-particle entangled states as quantum channels, with different particles of each entangled state sent separately. This ensures secure transmission of signatures and messages with fewer entangled particles during transmission, further improving the efficiency of quantum signatures. Meanwhile, our scheme generates private keys for each participating party by randomly constructing key generation matrixes. Different signers perform quantum Fourier transforms and basis exchange operations on entangled particles based on different messages and private keys to generate signatures. In addition, the aggregator does not need to measure and verify the signature particles after receiving signatures from different signers, and the group addition operation process has additive homomorphism. Security analysis shows that our scheme has unforgeability, non-repudiation, and can resist various attacks such as entanglement measurement attacks, intercept-resend attacks, private key sequence attacks, and internal attacks by aggregator.

DOI
10.1007/s11128-024-04341-w

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Abstract With the rapid development of computer and internet technology, quantum signature plays an extremely important role in modern secure communication. Quantum homomorphic aggregate signature, as an important guarantee of quantum signature, plays a significant role in reducing storage, communication, and computing costs. This article draws on the idea of quantum multi-party summation and proposes a quantum homomorphic aggregate signature scheme based on quantum Fourier transform. Our scheme uses nnn-particle entangled states as quantum channels, with different particles of each entangled state sent separately. This ensures secure transmission of signatures and messages with fewer entangled particles during transmission, further improving the efficiency of quantum signatures. Meanwhile, our scheme generates private keys for each participating party by randomly constructing key generation matrixes. Different signers perform quantum Fourier transforms and basis exchange operations on entangled particles based on different messages and private keys to generate signatures. In addition, the aggregator does not need to measure and verify the signature particles after receiving signatures from different signers, and the group addition operation process has additive homomorphism. Security analysis shows that our scheme has unforgeability, non-repudiation, and can resist various attacks such as entanglement measurement attacks, intercept-resend attacks, private key sequence attacks, and internal attacks by aggregator.
A quantum homomorphic aggregation signature scheme is proposed based on GHZ states, combined with homomorphic aggregation techniques. The scheme has the following features: Firstly, by changing the existing quantum homomorphic signature scheme which generally uses Bell state as the signature particle, and choosing GHZ state as the signature particle, it can realize the signature of the multi-bit messages by preparing fewer quantum resources; Secondly, the idea of classical aggregated signature is introduced, where multiple message signatures are aggregated into a single signature by quantum entanglement swapping technique, and the verifier can determine the validity of all signatures by only one verification; At the same time, the verification of individual signatures by the aggregator is realized, and dishonest behaviors among the signature members can be detected in time; Finally, the whole signature process satisfies the basic homomorphic property. Compared with the existing quantum homomorphic signature scheme, this scheme can effectively reduce the consumption of quantum resources, improving the efficiency of signature verification and enhancing the reliability of the signature. The security analysis shows that the scheme has the verifiability, unforgeability and non-repudiation.
Abstract With the development of cloud computing in recent years, homomorphic signatures have become a research hotspot in modern cryptography. This article proposes a quantum homomorphic signature scheme with verifiable identity based on four-particle Cluster states, starting from the identity verification of the signers. Compared with Shang’s scheme (Shang et al 2015 Quantum Inf. Process. 14 393–410), our scheme uses four-particle Cluster states as quantum channels and achieves identity verification of the signers through the use of X operation and quantum measurement techniques. Meanwhile, our scheme extends the length of message M to 2n bits and uses random numbers during the signature process, which makes the scheme more secure. Security analysis shows that our scheme can ensure the security of the keys and the unforgeability of the signatures.
Abstract With the continuous development of quantum technology, researchers are constantly improving the research on quantum signatures. In the public-key cryptosystem, a quantum group signature scheme based on four-particle Cluster states is proposed. In this scheme, the four-particle Cluster states are used as quantum channels. The signer randomly generates his private key according to the public key generated by the group manager, and uses the private key to sign. The verifier uses the public key to verify the signature. The features of the scheme are as follows: the public key and private key can be reused, thus reducing the number of keys that need to be saved by the communication parties; The length of the message to be signed does not need to be the same as the length of the public and private keys, which increases the flexibility of the signature; The random sequence is used in the signature process to ensure the unpredictability of the key, thus improving the security of the scheme; The scheme has unforgeability and non-repudiation.
In this paper, a quantum secure multi-party summation scheme with a third party based on quantum Fourier transform (QFT) is put forward, where the third party cannot be permitted to cooperate with others but is allowed for all kinds of attacks. Under the help of third party, [Formula: see text] users can calculate the addition modulo [Formula: see text] of their private integer strings. The third party generates two-level single qubit and its product state as the initial quantum resource, produces the traveling particles with QFT and the controlled-not (CNOT) operations, and sends the traveling particles out to the first users; then, [Formula: see text] users encode their private integer sequences by performing the phase shifting operations on the travelling particles one after another; and finally, the third party decodes out the summation of the private integer sequences from [Formula: see text] users through CNOT operations and inverse quantum Fourier transform (IQFT). This protocol only adopts two-level single particle state and its product state as initial quantum resource, only needs [Formula: see text]-level single particle measurement and does not need to perform quantum entanglement swapping. Security analysis indicates that this protocol can overcome not only the outside attack but also the participant attack.
Abstract With the upgrading of communication technology and the rapid development of quantum computing, the classical digital signature schemes are faced with unprecedented challenges, so the research on quantum digital signature is imperative. In this paper, we propose a multi-proxy signature scheme based on controlled quantum teleportation of five-qubit entangled state. In this scheme, quantum fourier transform is used as an encryption method to encrypt message, which improves the quantum efficiency compared with the quantum one-time pad. The five-qubit maximally entangled state which is qubit threshold quantum error correction required is used as the quantum channel to ensure the stability of the scheme. Security analysis shows that our scheme is unforgeable and undeniable, and it can resist the intercept-resend attack.
Abstract With the continuous development of quantum technology, the quantum signature as an application of quantum cryptography has received great attention. In this paper, we propose a public-key quantum group blind signature scheme based on single-qubit rotations. In this scheme, the group manager generates a public key. Each group member randomly generates his own private key according to the public key. The signer uses his private key and random sequence to generate the signature. The verifier uses the public key to verify the correctness of the quantum signature. The public and private keys can be reused, which simplifies the key management of the signature system. In this scheme, the random sequence is used to enhance the security of the scheme. At the same time, the quantum efficiency is improved by using single-qubit rotations. The security analysis shows that our scheme can ensure the security of the keys, the unforgeability and the non-deniability of the signature.