Almost Tightly-Secure Re-Randomizable and Replayable CCA-secure Public Key Encryption
Re-randomizable Replayable CCA-secure public key encryption (Rand-RCCA PKE) schemes guarantee security against chosen-ciphertext attacks while ensuring the useful property of re-randomizable ciphertexts. We introduce the notion of multi-user and multi-ciphertext Rand-RCCA PKE and we give the first construction of such a PKE scheme with an almost tight security reduction to a standard assumption. Our construction is structure preserving and can be instantiated over Type-1 pairing groups. Technically, our work borrows ideas from the state of the art Rand-RCCA PKE scheme of Faonio et al. (ASIACRYPT’19) and the adaptive partitioning technique of Hofheinz (EUROCRYPT’17). Additionally, we show (1) how to turn our scheme into a publicly-verifiable (pv) Rand-RCCA scheme and (2) that plugging our pv-Rand-RCCA PKE scheme into the MixNet protocol of Faonio et al. we can obtain the first almost tightly-secure MixNet protocol.
From Polynomial IOP and Commitments to Non-malleable zkSNARKs
We study sufficient conditions to compile simulation-extractable zkSNARKs from information-theoretic interactive oracle proofs (IOP) using a simulation-extractable commit-and-prove system for its oracles. Specifically, we define simulation extractability for opening and evaluation proofs of polynomial commitment schemes, which we then employ to prove the security of zkSNARKS obtained from polynomial IOP proof systems. To instantiate our methodology, we additionally prove that KZG commitments satisfy our simulation extractability requirement, despite being naturally malleable. To this end, we design a relaxed notion of simulation extractability that matches how KZG commitments are used and optimized in real-world proof systems. The proof that KZG satisfies this relaxed simulation extractability property relies on the algebraic group model and random oracle model.