Homomorphic signcryption with public plaintext‐result checkability

Abstract

Signcryption originally proposed by Zheng (CRYPTO 0 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.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Leveled Fully Homomorphic Signcryption From Lattices

“…However, their scheme is only linearly homomorphic. To overcome linear homomorphism, Shimin Li et al [4] constructed two (leveled) fully homomorphic signcryption (FHSC) schemes. However, their schemes can not be constructed from standard assumption since they employ the indistinguishability obfuscation (iO) which can not be built from standard assumption as far as we know.…”

“…For this, Fatemeh Rezaeibagha et al [3] proposed a linearly homomorphic signcryption (HSC) scheme which demonstrates weak unforgeability (WUF) and indistinguishability against chosen plaintext attacks (IND-CPA) based on the Decisional Diffie-Hellman (DDH) assumption. Recently, Shimin Li et al [4] constructed two leveled fully homomorpic signcryption (FHSC) schemes 1 with public plaintextresult checkability. One is in a public evaluation setting which employs FHS, indistinguishability obfuscation (iO) and non-interactive zero knowledge proof.…”

A Linear Homomorphic Proxy Signature Scheme Based on Blockchain for Internet of Things

“…For example, the verifiable encryption HS scheme proposed by Seo et al [30] has been successfully applied to cumulative optimistic fair exchange, and the homomorphic signcryption scheme proposed by Fan et al [31] has been successfully applied to electronic voting, for voters, the use of homomorphic signcryption can complete the encryption and signature of votes in one step. In 2021, Li et al [32] proposed a homomorphic signcryption scheme with verifiable public plaintext results, allowing the evaluation of arbitrary functions on signcrypted data, and allowing anyone to publicly test whether a given ciphertext is a signcrypted file for a message under a key.…”

A Publicly Verifiable Leveled Fully Homomorphic Signcryption Scheme

“…In 2017, Rezaeibagha et al [11] proposed a homomorphic signcryption (HSC) scheme based on the decisional Diffie-Hellman assumption which only supported linear homomorphic operations. Furthermore, Li et al [12] constructed two leveled fully homomorphic signcryption (FHSC) schemes under nonstandard assumptions as they used indistinguishable obfusion, zero knowledge proof, and multiple input function encryption. Recently, Jin et al [13] proposed a leveled FHSC schemes based on lattices.…”