Proceedings of the
The Nineteenth International Conference on Computational Intelligence and Security (CIS 2023)
December 1 – 4, 2023, Haikou, China
Threshold Decryption of LWE Cryptosystem Over Zpk
1Zhejiang Lab, China 2School of Cyberspace, Hangzhou Dianzi University, China.
ABSTRACT
With the widespread adoption of digital signature in cryptocurrencies, there has been a growing interest in threshold cryptography. While several threshold decryption and signature schemes have been explored in the literature, there
has been relatively limited research on threshold post-quantum cryptography, particularly in the context of latticebased cryptography. In this paper, a novel approach is proposed to do threshold decryption for the PVW's (Peikert, Vaikuntanathan and
Waters) LWE (Learning With Errors) cryptosystem using Shamir's secret sharing technique. Additionally, an efficient (t;N)-threshold lattice-based key generation protocol and a PVW's LWE (t;N)-threshold decryption protocol are presented, both of that
are secure under specific computational assumptions. To enable distributed sharing of the decryption key, a secret sharing scheme tailored for secrets in Zpk is developed. Within this scheme, we extend Zpk to a
Galois ring and subsequently devise a secret sharing mechanism for this ring.
Keywords: Lattice-based cryptography, Threshold decryption, Secret sharing, Galois ring, LWE, Key
generation.
Download PDF
1Zhejiang Lab, China 2School of Cyberspace, Hangzhou Dianzi University, China.
ABSTRACT
With the widespread adoption of digital signature in cryptocurrencies, there has been a growing interest in threshold cryptography. While several threshold decryption and signature schemes have been explored in the literature, there has been relatively limited research on threshold post-quantum cryptography, particularly in the context of latticebased cryptography. In this paper, a novel approach is proposed to do threshold decryption for the PVW's (Peikert, Vaikuntanathan and Waters) LWE (Learning With Errors) cryptosystem using Shamir's secret sharing technique. Additionally, an efficient (t;N)-threshold lattice-based key generation protocol and a PVW's LWE (t;N)-threshold decryption protocol are presented, both of that are secure under specific computational assumptions. To enable distributed sharing of the decryption key, a secret sharing scheme tailored for secrets in Zpk is developed. Within this scheme, we extend Zpk to a Galois ring and subsequently devise a secret sharing mechanism for this ring.
Keywords: Lattice-based cryptography, Threshold decryption, Secret sharing, Galois ring, LWE, Key generation.
Download PDF