Abstract
Non-committing encryption (NCE) was introduced by Canetti et al. (STOC ’96). Informally, an encryption scheme is non-committing if it can generate a dummy ciphertext that is indistinguishable from a real one. The dummy ciphertext can be opened to any message later by producing a secret key and an encryption random coin which “explain” the ciphertext as an encryption of the message. Canetti et al. showed that NCE is a central tool to achieve multi-party computation protocols secure in the adaptive setting. An important measure of the efficiently of NCE is the ciphertext rate, that is the ciphertext length divided by the message length, and previous works studying NCE have focused on constructing NCE schemes with better ciphertext rates.
We propose an NCE scheme satisfying the ciphertext rate 
based on the decisional Diffie-Hellman (DDH) problem, where 
is the security parameter. The proposed construction achieves the best ciphertext rate among existing constructions proposed in the plain model, that is, the model without using common reference strings. Previously to our work, an NCE scheme with the best ciphertext rate based on the DDH problem was the one proposed by Choi et al. (ASIACRYPT ’09) that has ciphertext rate 
. Our construction of NCE is similar in spirit to that of the recent construction of the trapdoor function proposed by Garg and Hajiabadi (CRYPTO ’18).
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Notes
- 1.
- 2.
Usually, a chameleon hash function is required to be collision resistant, but we omit it since it is implied by the security of chameleon encryption defined later.
- 3.
and 
do not use 
for 
such that 
, but for simplicity, we generate whole 
.
and 
do not use 
for 
such that 
, but for simplicity, we generate whole 
.References
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Acknowledgements
A part of this work was supported by NTT Secure Platform Laboratories, JST OPERA JPMJOP1612, JST CREST JPMJCR14D6, JSPS KAKENHI JP16H01705, JP17H01695, JP19J22363.
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Yoshida, Y., Kitagawa, F., Tanaka, K. (2019). Non-Committing Encryption with Quasi-Optimal Ciphertext-Rate Based on the DDH Problem. In: Galbraith, S., Moriai, S. (eds) Advances in Cryptology – ASIACRYPT 2019. ASIACRYPT 2019. Lecture Notes in Computer Science(), vol 11923. Springer, Cham. https://doi.org/10.1007/978-3-030-34618-8_5
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