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SO-CCA secure PKE from pairing based all-but-many lossy trapdoor functions

Dingding Jia 1, 2, 3 Benoît Libert 1, 2, 3
Abstract : In a selective-opening chosen ciphertext (SO-CCA) attack on an encryption scheme, an adversary A has access to a decryption oracle, and after getting a number of ciphertexts, can then adaptively corrupt a subset of them, obtaining the plaintexts and corresponding encryption randomness. SO-CCA security requires the privacy of the remaining plaintexts being well protected. There are two flavors of SO-CCA definition: the weaker indistinguishability-based (IND) and the stronger simulation-based (SIM) ones. In this paper, we study SO-CCA secure PKE constructions from all-but-many lossy trapdoor functions (ABM-LTFs) in pairing-friendly prime order groups. Concretely, we construct two ABM-LTFs with O(n/ log λ) size tags for n bits inputs and security parameter λ, which lead to IND-SO-CCA secure PKEs with ciphertext size O(n/ log λ) to encrypt n bits messages. In addition, our second ABM-LTF enjoys tight security, so as the resulting PKE. by equipping a lattice trapdoor for opening randomness, we show our ABM-LTFs are SIM-SO-CCA compatible.
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https://hal.inria.fr/hal-03380672
Contributor : Benoit Libert Connect in order to contact the contributor
Submitted on : Friday, October 15, 2021 - 4:56:48 PM
Last modification on : Saturday, October 16, 2021 - 3:47:35 AM

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Dingding Jia, Benoît Libert. SO-CCA secure PKE from pairing based all-but-many lossy trapdoor functions. Designs, Codes and Cryptography, Springer Verlag, 2021, 89 (5), pp.895-923. ⟨10.1007/s10623-021-00849-9⟩. ⟨hal-03380672⟩

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