Homomorphic signcryption with public plaintext‐result checkability

Signcryption originally proposed by Zheng (CRYPTO′97) is a useful cryptographic primitive that provides strong confidentiality and integrity guarantees. This article addresses the question whether it is possible to homomorphically compute arbitrary functions on signcrypted data. The answer is affirmative and a new cryptographic primitive, homomorphic signcryption (HSC) with public plaintext‐result checkability is proposed that allows both to evaluate arbitrary functions over signcrypted data and makes it possible for anyone to publicly test whether a given ciphertext is the signcryption of the message under the key. Two notions of message privacy are also investigated: weak message privacy and message privacy depending on whether the original signcryptions used in the evaluation are disclosed or not. More precisely, the contributions are two‐fold: (i) two different definitions of HSC with public plaintext‐result checkability is provided for arbitrary functions in terms of syntax, unforgeability and message privacy depending on if the homomorphic computation is performed in a private or in a public evaluation setting, (ii) two HSC constructions are proposed: one for a public evaluation setting and another for a private evaluation setting and security is formally proved.