Homomorphic signcryption with public plaintext-result checkability

Signcryption originally proposed by Zheng (CRYPTO 0 97) is a useful cryptographic primitive that provides strong confidentiality and integrity guarantees. This article ad-dresses 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:

[1]  Yi Mu,et al.  Provably Secure (Broadcast) Homomorphic Signcryption , 2019, Int. J. Found. Comput. Sci..

[2]  Giovanni Di Crescenzo,et al.  Implementing Conjunction Obfuscation Under Entropic Ring LWE , 2018, 2018 IEEE Symposium on Security and Privacy (SP).

[3]  Shai Halevi,et al.  Implementing BP-Obfuscation Using Graph-Induced Encoding , 2017, CCS.

[4]  Yi Mu,et al.  Provably Secure Homomorphic Signcryption , 2017, ProvSec.

[5]  Denise Demirel,et al.  Linearly Homomorphic Authenticated Encryption with Provable Correctness and Public Verifiability , 2017, C2SI.

[6]  Kartik Nayak,et al.  HOP: Hardware makes Obfuscation Practical , 2017, NDSS.

[7]  Alex J. Malozemoff,et al.  5Gen: A Framework for Prototyping Applications Using Multilinear Maps and Matrix Branching Programs , 2016, CCS.

[8]  Mark Zhandry,et al.  Semantically Secure Order-Revealing Encryption: Multi-input Functional Encryption Without Obfuscation , 2015, EUROCRYPT.

[9]  Brent Waters,et al.  A Punctured Programming Approach to Adaptively Secure Functional Encryption , 2015, CRYPTO.

[10]  Daniel Wichs,et al.  Leveled Fully Homomorphic Signatures from Standard Lattices , 2015, IACR Cryptol. ePrint Arch..

[11]  Dario Catalano,et al.  Authenticating Computation on Groups: New Homomorphic Primitives and Applications , 2014, ASIACRYPT.

[12]  Rosario Gennaro,et al.  Efficiently Verifiable Computation on Encrypted Data , 2014, CCS.

[13]  Yuval Ishai,et al.  Optimizing Obfuscation: Avoiding Barrington's Theorem , 2014, CCS.

[14]  Bogdan Warinschi,et al.  Homomorphic Signatures with Efficient Verification for Polynomial Functions , 2014, CRYPTO.

[15]  Craig Gentry,et al.  (Leveled) Fully Homomorphic Encryption without Bootstrapping , 2014, ACM Trans. Comput. Theory.

[16]  Vinod Vaikuntanathan,et al.  Efficient Fully Homomorphic Encryption from (Standard) LWE , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[17]  Shafi Goldwasser,et al.  Functional Signatures and Pseudorandom Functions , 2014, Public Key Cryptography.

[18]  Abhi Shelat,et al.  Computing on Authenticated Data , 2012, Journal of Cryptology.

[19]  Chunming Tang,et al.  Efficient Non-Interactive Verifiable Outsourced Computation for Arbitrary Functions , 2014, IACR Cryptol. ePrint Arch..

[20]  Elaine Shi,et al.  Adaptively Secure Fully Homomorphic Signatures Based on Lattices , 2014, IACR Cryptol. ePrint Arch..

[21]  Michael Backes,et al.  Verifiable delegation of computation on outsourced data , 2013, CCS.

[22]  Brent Waters,et al.  Candidate Indistinguishability Obfuscation and Functional Encryption for all Circuits , 2013, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science.

[23]  Vinod Vaikuntanathan,et al.  Functional Encryption with Bounded Collusions via Multi-party Computation , 2012, CRYPTO.

[24]  Amit Sahai,et al.  On the (im)possibility of obfuscating programs , 2001, JACM.

[25]  Vinod Vaikuntanathan,et al.  How to Delegate and Verify in Public: Verifiable Computation from Attribute-based Encryption , 2012, IACR Cryptol. ePrint Arch..

[26]  Dan Boneh,et al.  Homomorphic Signatures for Polynomial Functions , 2011, EUROCRYPT.

[27]  Brent Waters,et al.  Functional Encryption: Definitions and Challenges , 2011, TCC.

[28]  Yael Tauman Kalai,et al.  Improved Delegation of Computation using Fully Homomorphic Encryption , 2010, IACR Cryptol. ePrint Arch..

[29]  Craig Gentry,et al.  Non-interactive Verifiable Computing: Outsourcing Computation to Untrusted Workers , 2010, CRYPTO.

[30]  Craig Gentry,et al.  Fully Homomorphic Encryption over the Integers , 2010, EUROCRYPT.

[31]  Adam O'Neill,et al.  Definitional Issues in Functional Encryption , 2010, IACR Cryptol. ePrint Arch..

[32]  Craig Gentry,et al.  Fully homomorphic encryption using ideal lattices , 2009, STOC '09.

[33]  Yuliang Zheng,et al.  Digital Signcryption or How to Achieve Cost(Signature & Encryption) << Cost(Signature) + Cost(Encryption) , 1997, CRYPTO.