Welcome to the resource topic for
**2021/426**

**Title:**

Generic Plaintext Equality and Inequality Proofs (Extended Version)

**Authors:**
Olivier Blazy, Xavier Bultel, Pascal Lafourcade, Octavio Perez Kempner

**Abstract:**

Given two ciphertexts generated with a public-key encryption scheme, the problem of plaintext equality consists in determining whether the ciphertexts hold the same value. Similarly, the problem of plaintext inequality consists in deciding whether they hold a different value. Previous work has focused on building new schemes or extending existing ones to include support for plaintext equality/inequality. We propose generic and simple zero-knowledge proofs for both problems, which can be instantiated with various schemes. First, we consider the context where a prover with access to the secret key wants to convince a verifier, who has access to the ciphertexts, on the equality/inequality without revealing information about the plaintexts. We also consider the case where the prover knows the encryptionâ€™s randomness instead of the secret key. For plaintext equality, we also propose sigma protocols that lead to non-interactive zero-knowledge proofs. To prove our protocolsâ€™ security, we formalize notions related to malleability in the context of public-key encryption and provide definitions of their own interest.

**ePrint:**
https://eprint.iacr.org/2021/426

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