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Quantum Information Processing

Quantum homomorphic encryption scheme based on elliptic curve cryptography

Xiuli Song, Jianbing Zhou, Qian Chen, Tao Wu, Yousheng Zhou

Published May 19, 2025• 3 citations
Publisher
DOI
10.1007/s11128-025-04746-1

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Data aggregation has been one of the most widely researched topics for Wireless Sensor Network (WSN) as it helps in increasing the effective life time of the network and reduces the packet transmission overhead. Besides other challenges, security is one of the serious challenges during data aggregation. Numerous solutions on security for data aggregation for WSN are based on homomorphic encryption technique or Elliptic Curve Cryptography (ECC) based solutions and thus are vulnerable to attacks by quantum machines. This paper presents a post-quantum security solution using lattice cryptography. The proposed solution is applying Learning with Errors over Rings (R-LWE) for encryption of data in the data aggregation process at the gateway module of WSN. Security analysis shows that the proposed scheme provides confidentiality, integrity and authenticity during communication. Performance analysis shows that the proposed scheme is lightweight and shows better performance compared to Elliptic Curve Elgamal (ECEG) cryptography based scheme and symmetric homomorphic based scheme.
We propose and develop new schemes for post-quantum cryptography based on isogenies over elliptic curves. First we show that ordinary elliptic curves are have less than exponential security against quantum computers. These results were used as the motivation for De Feo, Jao and Pl\\^ut's construction of public key cryptosystems using supersingular elliptic curve isogenies. We extend their construction and show that isogenies between supersingular elliptic curves can be used as the underlying hard mathematical problem for other quantum-resistant schemes. For our second contribution, we propose is an undeniable signature scheme based on elliptic curve isogenies. We prove its security under certain reasonable number-theoretic computational assumptions for which no efficient quantum algorithms are known. This proposal represents only the second known quantum-resistant undeniable signature scheme, and the first such scheme secure under a number-theoretic complexity assumption. Finally, we also propose a security model for evaluating the security of authenticated encryption schemes in the post-quantum setting. Our model is based on a combination of the classical Bellare-Namprempre security model for authenticated encryption together with modifications from Boneh and Zhandry to handle message authentication against quantum adversaries. We give a generic construction based on Bellare-Namprempre for producing an authenticated encryption protocol from any quantum-resistant symmetric-key encryption scheme together with any digital signature scheme or MAC admitting any classical security reduction to a quantum-computationally hard problem. We apply the results and show how we can explicitly construct authenticated encryption schemes based on isogenies.
Based on the quantum key distribution protocol of BB84 and elliptic curve cryptography,a new digital signature scheme was proposed.This project used the quantum key as conversation key to make the signature process be highly effective and simple.The certifiable security of this conversation key in the key distribution process combined with the elliptic curve encryption system has provided the dual safekeeping of security to the new scheme and simultaneously achieved mutually authenticated effect.