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Quantum Information Processing

Quantum gate encryption and quantum signature scheme based on public identity information

Y. C. Xu, jinqing Li, Xiaoqiang Di, Shilun Qiu

Published Feb 18, 2026• 0 citations
Publisher
DOI
10.1007/s11128-026-05105-4

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Public key encryption with equality test (PKEET) enables the testing whether two ciphertexts encrypt the same message. Identity-based encryption with equality test (IBEET) simplify the certificate management of PKEET, which leads to many potential applications such as in smart city applications or Wireless Body Area Networks. Lee et al. (ePrint 2016) proposed a generic construction of IBEET scheme in the standard model utilising a 3-level hierachy IBE together with a one-time signature scheme, which can be instantiated in lattice setting. Duong et al. (ProvSec 2019) proposed the first direct construction of IBEET in standard model from lattices. However, their scheme achieve CPA security only. In this paper, we improve the Duong et al.'s construction by proposing an IBEET in standard model which achieves CCA2 security and with smaller ciphertext and public key size.
Identity-based cryptography is a type of public key cryptography with simple key management procedures. To our knowledge, till now, the existing identity-based cryptography based on NTRU is all over power-of-2 cyclotomic rings. Whether there is provably secure identity-based cryptography over more general fields is still open. In this paper, with the help of the results of collision resistance preimage sampleable functions (CRPSF) over cyclotomic fields, we give concrete constructions of provably secure identity-based encryption schemes (IBE) and identity-based signature schemes (IBS) based on NTRU over any cyclotomic field. Our IBE schemes are provably secure under adaptive chosen-plaintext and adaptive chosen-identity attacks, meanwhile, our IBS schemes are existentially unforgeable against adaptively chosen message and adaptively chosen identity attacks for any probabilistic polynomial time (PPT) adversary in the random oracle model. The securities of both schemes are based on the worst-case approximate shortest independent vectors problem (SIVPγ) over corresponding ideal lattices. The secret key size of our IBE (IBS) scheme is short—only one (two) ring element(s). The ciphertext (signature) is also short—only two (three) ring elements. Meanwhile, as the case of NTRUEncrypt, our IBE scheme could encrypt n bits in each encryption process. These properties may make our schemes have more advantages for some IoT applications over postquantum world in theory.
Based on the Hadamard operator and Bell states, an identity-based public-key quantum signature scheme is proposed. In our scheme, the signer’s identity is used as her public key. Her private keys are generated by the trusted private key generator (PKG). Given a quantum signature, the verifier can verify the validity of the quantum signature by the signer’s identity information without any public-key certificate. So, our quantum signature has the advantages of the identity-based signature system. On the other hand, in our scheme, it need not use the long-term quantum memory. The verifier need not perform any quantum swap test or state comparison algorithm. What is more, our quantum signature is secure against PKG’s forgery attack. And the disputation of losing quantum signature can be arbitrated by PKG. Therefore, our scheme is relatively more practical and efficient than the similar schemes.