TY - GEN
T1 - An Improved Threshold Homomorphic Cryptosystem Based on Class Groups
AU - Braun, Lennart
AU - Castagnos, Guilhem
AU - Damgård, Ivan
AU - Laguillaumie, Fabien
AU - Melissaris, Kelsey
AU - Orlandi, Claudio
AU - Tucker, Ida
PY - 2024
Y1 - 2024
N2 - 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, Damgård, 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.
AB - 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, Damgård, 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.
UR - http://www.scopus.com/inward/record.url?scp=85204873037&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-71073-5_2
DO - 10.1007/978-3-031-71073-5_2
M3 - Article in proceedings
SN - 9783031710728
T3 - Lecture Notes in Computer Science
SP - 24
EP - 46
BT - Security and Cryptography for Networks - 14th International Conference, SCN 2024, Amalfi, Italy, September 11-13, 2024, Proceedings, Part II
A2 - Galdi, Clemente
A2 - Phan, Duong Hieu
PB - Springer
ER -