An Efficient Linearly Homomorphic Signature Scheme with a Designated Combiner

With the widespread adoption of digital signature technology, when a signer needs to perform numerous signature activities but has limited computing power, the efficiency of the general signature scheme can be severely restricted. To address this challenge, the linearly homomorphic signature scheme with a designated combiner (LHSDC) allows the signer to transfer the primary computing task to a cloud server, thereby reducing the computational burden on the signer. The signature algorithm of LHSDC comprises two parts: the homomorphic compression function and the binding function. However, due to the high computational requirements of these two parts, existing schemes still suffer from low efficiency for signers. In this paper, an efficient linearly homomorphic signature scheme with a designated combiner (ELHSDC) is presented, which is tailored for secure proxy signature scenarios. Firstly, we enhance the homomorphic compression function in the signature algorithm by reducing the number of exponential operations required from n to 1. Secondly, we simplify the binding function of the signature algorithm by enabling the signer to directly generate a secret parameter that is shared with the designated combiner, thus eliminating the need for public and private keys for the designated combiner. As a result of the above improvements, our scheme significantly reduces the signer’s amount of calculation during a complete signature process by reducing (n-1) exponential operations, 1 pairing operation, and 2 hash operations, at the expense of only 1 multiplication operation. Finally, the scheme is proved secure against existential forgery on adaptively chosen message attacks under the random oracle model.

I. Introduction

As one of the core technologies of cryptography, digital signature [1] can provide authenticity, integrity, and undeniable services for information. However, due to the defect that the original signature becomes invalid once the message is changed, the general digital signature scheme cannot be used to solve the problem of pollution attacks in network coding. In the way of studying how to solve the pollution attack problem based on the public key method, scholars have proposed a series of signature schemes with linear homomorphism in turn [2] –[5]. However, these signature schemes do not formally define linearly homomorphic signature scheme (LHSS) and cannot sign multiple files with the same public key in the schemes. Until 2009, the work of Boneh et al. [6] filled these gaps. In an LHSS, for l message-signature pairs , any entities can obtain the legal signature of the message only by calculating without knowing the signer’s private key. Today, the main applications of LHSS include network coding, electronic health systems [7], block chains [8], and the Internet of things [9].