Efficient Batch Verification of Short Signatures for a Single-Signer Setting without Random Oracles

The blockchain-enabled internet of medical things (IoMT) is an emerging paradigm that could provide strong trust establishment and ensure the traceability of data sharing in the IoMT networks. One of the fundamental building blocks for Blockchain is Elliptic Curve Digital Signature Algorithm (ECDSA). Nevertheless, when processing a large number of transactions, the verification of multiple signatures will incur cumbersome overhead to the nodes in Blockchain. Although batch verification is able to provide a promising approach that verifies multiple signatures simultaneously and efficiently, the upper bound of batch size is limited to small-scale and the efficiency will drop rapidly as the batch size grows in the state-of-the-art ECDSA batch schemes. Meanwhile, most of the existing researches only focus on improving the efficiency of batch verification algorithms in various cryptosystem while ignoring the identification of invalid signatures, which could cause severe performance degradation when the batch verification fails. Motivated by these observations, this paper proposes an efficient and large-scale batch verification scheme with group testing technology based on ECDSA. The application of the presented protocols in Bitcoin and Hyperledger Fabric has been analyzed as supportive and effective. When the batch verification returns a false result, we utilize group testing technology to improve the efficiency of identifying invalid signatures. Comprehensive simulation results demonstrate that our protocol outperforms the related ECDSA batch verification schemes.

The notion of certificateless cryptography is aimed to eliminate the use of certificates in traditional public key cryptography and also to solve the key-escrow problem in identity-based cryptography. Many kinds of security models have been designed for certificateless cryptography and many new schemes have been introduced based on the correspondence of the security models. In generally speaking, a stronger security model can ensure a certificateless cryptosystem with a higher security level, but a realistic model can lead to a more efficient scheme. In this paper, we focus on the efficiency of a certificateless signature (CLS) scheme and introduce an efficient CLS scheme with short signature size. On one hand, the security of the scheme is based on a realistic model. In this model, an adversary is not allowed to get any valid signature under false public keys. On the other hand, our scheme is as efficient as BLS short signature scheme in both communication and computation and, therefore, turns out to be more efficient than other CLS schemes proposed so far. We provide a rigorous security proof of our scheme in the random oracle model. The security of our scheme is based on the k-CAA hard problem and a new discovered hard problem, namely the modified k-CAA problem. Our scheme can be applied to systems where signatures are typed in by human or systems with low-bandwidth channels and/or low-computation power.

Recently, Boneh et al. proposed the concept of an aggregate signature, introduced security models for such signatures, and also presented some applications. An aggregate signature scheme is a digital signature that supports aggregation: Given n signatures on n distinct messages from n distinct users, it is possible to aggregate all these signatures into a single short signature. This single signature, along with the n original messages will convince verifiers that the n users did indeed sign the n original messages respectively, i.e., user i signed message Mi for i = 1, ..., n. In this paper, however, we find that their security model has some defects. The capacity that the adversaries possess was constrained according to the standard security definition of signatures. We propose an improvement of the Boneh’s scheme by presenting a new security model and giving a formal proof in random oracle model.

Recently, Vehicle Ad Hoc Networks (VANETs) have been increasingly developed in Intelligent Transportation Systems (ITSs). However, VANETs are vulnerable to security issues because of the open-medium nature of Vehicle-To-Vehicle (V2V) and Vehicle-To-Infrastructure (V2I) communication. Recently, many studies have proposed security schemes to address these issues. However, many of these schemes have massive computational overheads, especially in the process of batch verification method, which verifies multiple messages simultaneously. In this article, a Lightweight Security Without Using Batch Verification Method (LSWBVM) scheme is proposed based on Elliptic Curve Cryptography (ECC). The proposed LSWBVM scheme uses the XOR operation and general hash function during mutual authentication. Meanwhile, to verify a large number of messages, the proposed scheme uses an efficient single verification instead of batch verification in a high traffic density-area. BAN logic proves that the LSWBVM achieves the security goals to mutually authenticate between the nodes. The security analysis indicates that the LSWBVM satisfies the security requirements, such as: identity privacy preserving, tractability and revocability; and secure non-forgery under the random oracle model in an adaptively chosen message attack. The preference evaluation shows that the single verification of proposed LSWBVM is more efficient when compared with batch verification of the related works.

Cryptanalysis and improvement of a certificateless aggregate signature scheme

In this paper, a provably secure short certificateless proxy signature scheme is presented. It is an efficient proxy signature scheme with the shortest signature length compared with the other existing proxy signature schemes from pairings. It satisfies all the properties required for a proxy signature. We also provide complete security proofs for our new scheme. Our scheme is proved secure in the random oracle model with the assumption that the Computational Diffie-Hellman problem is infeasible.

Kakvi and Kiltz (EUROCRYPT'12) proposed the first tight security reduction for RSA full domain hash signature scheme (RSA-FDH) with public exponent e < N1/4 in the random oracle (RO) model, and they left an open problem which called for a tightly secure RSA-FDH for N1/4 < e < N. In this paper, we consider the improved RSA (iRSA) trapdoor functions, introduced by Cao (Science in China'01), are functions that the security can be strictly proved to be equivalent to the factoring. We show that iRSA-FDH has a tight security reduction for e < N. Technically we construct iRSA lossy trapdoor functions, and then we apply the lossiness of the iRSA trapdoor functions to obtain tight security reductions for iRSA-FDH in the RO model. Finally, we propose a tightly secure blind signature scheme based on our iRSA lossy trapdoor functions in the RO model.

Electronic voting is an alternative mechanism of ballot based voting which empowers voters to cast their secret and secure vote electronically over a public channel. Many onward-thinking countries are adopting the electronic voting system to upgrade their election process. E-voting system is more complicated to construct. Thus it expects more security as compared to the postal voting system. The objective of the paper is twofold. Firstly, we proposed an efficient blind signature scheme using the identity-based cryptosystem in the random oracle model. The proposed scheme uses the combination of Boldyreva’s blind signature scheme and Choon-Cheon’s Identity-based signature. Additionally, we reduce its security to the Gap Diffie-Hellman Complexity (GDH). Under the adaptive chosen message and ID attacks it is secure against existential forgery attack. We show our proposed system performed better as compared to existing systems. Secondly, we construct an E-voting system based on our ID-based blind signature and Boneh’s short signature scheme (EVS-ID-BS) that fulfills the E-voting security requirements. To the best of our knowledge, EVS-ID-BS is the first practical implementation of E-voting system based on ID-BS Scheme which is constructed in the random oracle model. Proposed EVS-ID-BS scheme provides batch verifiability for a significantly large number of voters, needs less bandwidth cost and require less interaction with election authority.

Aggregate signature is widely used in special occasions where the signatures on many different messages generated by many different users need to be compressed into one single signature. This paper presents an efficient certificate-based aggregate signature (CBAS) scheme from bilinear pairing. In the random oracle model, the new scheme is proven existentially unforgeable against adaptive chosen message attacks under the computational Diffie-Hellman assumption. The signature verification of the new scheme only needs constant pairing computations, which improves the efficiency of communication and computation, and it is more suitable for the applications in resource-constrained network environment.

In this chapter, we mainly introduce signature schemes under the q-SDH hardness assumption and the CDH assumption. We start by introducing the Boneh-Boyen short signature scheme [21] and then its variant, namely the Gentry scheme, which is modified from his IBE scheme [47]. Most stateless signature schemes without random oracles must produce signatures at least 320 bits in length for 80-bit security.

SummaryIn a short signature scheme, the length of signature is much smaller than that of the general signature. Short signatures are widely used in low‐computation, low‐storage, and low‐bandwidth communication environments. The proof of security of all certificateless short signature schemes currently known is given in the random oracle model. In this paper, a new certificateless short signature scheme is constructed, and it is proved to be unforgeable in the standard model. Taken into account the computation costs, the scheme performs only one pairing operation, so it is more efficient than previous ones.

IntroductionBlockchain technology has attracted much attention due to its decentralization, transparency and security. Initially applied in the financial field, it has now expanded to various fields such as Internet of Things (IoT), electronic cash and healthcare. However, the open nature of blockchain has raised potential security concerns about sensitive transaction data, and the increasing number of transactions requires low-latency solutions. Most blockchain applications still rely on the lightweight Elliptic Curve Digital Signature Algorithm (ECDSA). Due to complex operations such as vectorized multiplication and modular inversion, this may introduce significant additional overhead.MethodsTo address these issues, a new scheme named KTP-ECDSA is proposed. This scheme is based on the improved two-parameter Elliptic Curve Digital Signature Algorithm (TP-ECDSA) and the KGLP algorithm. In both the signing and verification processes, this scheme eliminates modular inverse operations and reduces scalar multiplications during the verification stage by using batch verification.ResultThe experimental results show that, compared with the traditional ECDSA, KTP-ECDSA has achieved a speed increase of over 50% in both independent verification and batch verification, significantly improving the efficiency of signature verification.DiscussionBy adopting the KTP-ECDSA algorithm and using the digital signature batch verification method, multiple signatures can be verified simultaneously, thus reducing the computational burden of the traditional single-verification method. This greatly increases the overall transaction throughput and improves resource utilization efficiency.

In cloud and edge computing, senders of data often want to be anonymous, while recipients of data always expect that the data come from a reliable sender and they are not redundant. Linkable ring signature (LRS) can not only protect the anonymity of the signer, but also detect whether two different signatures are signed by the same signer. Today, most lattice-based LRS schemes only satisfy computational anonymity. To the best of our knowledge, only the lattice-based LRS scheme proposed by Torres et al. can achieve unconditional anonymity. But the efficiency of signature generation and verification of the scheme is very low, and the signature length is also relatively long. With the preimage sampling, trapdoor generation, and rejection sampling algorithms, this study proposed an efficient LRS scheme with unconditional anonymity based on the e-NTRU problem under the random oracle model. We implemented our scheme and Torres et al.'s scheme, as well as other four efficient lattice-based LRS schemes. It is shown that under the same security level, compared with Torres et al.'s scheme, the signature generation time, signature verification time, and signature size of our scheme are reduced by about 94.52%, 97.18%, and 58.03%, respectively.

Internet of Things (IoT) is made up of various smart devices for the exchange of sensed data through online services. Direct contact with people through smart devices to define parameters for healthcare and send them to a centralized repository. At the time of data exchange, messages need to be secure between a source (sender) and target (receiver) in order to confront human malicious attacks. Various signature-based schemes are presented in the literature to provide secure communication. Smart apps, however, require lightweight activities by maintaining critical security strengths. The key challenge in signature-based methods is more incurred computational expense for signing and checking process involving large numbers. In this article, a new lightweight provably secure partial discrete logarithm (DL) based subtree-based short signature with fuzzy user data sharing for human-centered IoT systems is introduced and it's security analysis is demonstrated on random oracle (RO) model. The presented scheme provides assurance of better security than other standing short-signature schemes. For low-storage, low-computation environments and low-bandwidth communication, the presented new provably secure and lightweight subtree-based short-signature scheme is needed. The results demonstrate the strength of proposed scheme, as opposed to existing works.

Verifying multiple digital signatures in a batch to reduce verification time and computation has caught the interest of many researchers since many years. There are various batch verification schemes proposed for various popular digital signature algorithms such as DSS, RSA, ECDSA and other signature schemes. If there are any bad signatures in the given batch of signatures, then the batch verification test fails but the test does not indicate the location of the bad signature. In literature, there are very few efficient schemes, which locate the index of the bad signature/s in the given batch. These existing schemes perform poorly when the bad signature/s count is unknown or when the entire batch of signatures is faulty. To overcome these disadvantages, we propose a new Low-Density Parity-Check (LDPC) based verification scheme to locate the index of the bad signature/s. Our proposed scheme outperforms the other bad signature identification schemes. The comparative analysis of our scheme with the other schemes is provided. The primary advantage of the scheme is, it removes all the transmission errors in the received batch of signatures.