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An Improved Threshold Homomorphic Cryptosystem Based on Class Groups

delete2025-09-01
delete0
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OA
AI
L
Lennart Braun *
G
Guilhem Castagnos
I
Ivan Damgård
F
Fabien Laguillaumie
K
Kelsey Melissaris
C
Claudio Orlandi
I
Ida Tucker
DOI：10.1007/s12095-025-00826-2delete
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Abstract

Abstract

En 中文
We present distributed key generation and decryption protocols for an additively homomorphic cryptosystem based on class groups, improving on a similar system proposed by Braun, Damg & aring;rd, and Orlandi at CRYPTO '23. Our key generation is similarly constant round but achieves lower communication complexity than the previous work. This improvement is in part the result of relaxing the reconstruction property required of the underlying integer verifiable secret sharing scheme. This eliminates the reliance on potentially costly proofs of knowledge in unknown order groups. We present a new method to batch zero-knowledge proofs in unknown order groups which strengthens these improvements. We also present a protocol which is proven secure against adaptive adversaries in the single inconsistent player (SIP) model. Our protocols are secure in the universal composability (UC) framework and provide guaranteed output delivery. We demonstrate the relative efficiency of our techniques by presenting the running times and communication costs associated with our implementation of the statically secure protocol and provide a direct comparison with alternate state of the art constructions.
Keywords:
Linearly homomorphic encryption
Threshold encryption
Class groups

Journal

C
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
IF:
1.1
Papers:
63
Citations:
0

Organization

No organization information available