Public Key and Digital Signature for Blockchain Technology

Authentication of public keys in asymmetric cryptography is an important objective to fulfil. Identity-based schemes are an efficient solution for this scenario. There are various identity-based schemes that are based on either factoring problem or DLP problem, but these problems can be solved in polynomial time using quantum computers. Multivariate cryptography is one of the main alternatives for the construction of post-quantum digital signature schemes. Digital signature construction needs modest computations in multivariate public key cryptography, so these schemes are considered quite efficient. In this paper, we present a new identity-based signature scheme in which the signature size and user key size are relatively small. The design of our proposed signature scheme is based on MQDSS construction.KeywordsMultivariate public key cryptographyMQ problemIdentity-based signature scheme

The Internet of Things (IoT) revolutionizes how we interact with smart devices. However, ensuring security in IoT systems presents complex challenges due to their centralized architecture and inherent limitations. The increasing attention towards blockchain technology stems from its decentralized structure, transparency, immutable records, and cryptographic hash functions, particularly when combined with the Internet of Things (IoT). Cryptographic hash algorithms are essential to blockchain technology, ensuring secure data transmission by linking private and public keys through mathematical functions. Existing cryptographic algorithms typically produce variable hash values accessible to a single node and support input key sizes up to 128 bytes. However, larger key sizes can reduce transaction accuracy, lower key entropy, decrease throughput, and increase transaction complexity. Conversely, smaller key sizes increase vulnerability to attacks. To overcome these challenges, several advancements have been proposed. A modified key signature scheme extends the key size to 256 bytes, achieving 82.6% accuracy, a time complexity of 1.68 nanoseconds, and a throughput of 15.24 kilobytes per 200 nanoseconds. However, this scheme operates on a single-node basis, limiting accessibility. These advancements aim to bolster security in IoT data transmission by integrating encryption techniques with blockchain technology. The performance of the modified signature scheme is analyzed through transaction parameters such as accuracy, time complexity, throughput, and hash output with cryptographic hash functions like SHA224, SHA256, SHA384, SHA512, MD5, SHA3-224, SHA3-256, SHA3-384, SHA3-512, and ECDSA. From this analysis, the elliptic curve cryptography algorithm gives higher accuracy and throughput with less time complexity.

In public-key encryption, the secrecy of the public key is not required, but the authenticity of the public key is necessary to guarantee its integrity and to avoid spoofing and playback attacks. A user’s public key can be authenticated (signed) by a certificate authority that verifies that a public key belongs to a specific user. In this chapter, digital certificates, which are used to validate public keys, and certificate authorities are discussed. When public-key is used, it is necessary to have a comprehensive system that provides public key encryption and digital signature services to ensure confidentiality, access control, data integrity, authentication, and non-repudiation. That system, public-key infrastructure or PKI, is also discussed in this chapter.

We propose a new quantum-safe digital signature algorithm called Multivariate Polynomial Public Key Digital Signature (MPPK/DS). The core of the algorithm is based on the modular arithmetic property that for a given element g, greater than equal to two, in a prime Galois field GF(p) and two multivariate polynomials P and Q, if P is equal to Q modulo p-1, then g to the power of P is equal to g to the power of Q modulo p. MPPK/DS is designed to withstand the key-only, chosen-message, and known-message attacks. Most importantly, making secret the element g disfavors quantum computers’ capability to solve the discrete logarithm problem. The security of the MPPK/DS algorithm stems from choosing a prime p associated with the field GF(p), such that p is a sum of a product of an odd prime number q multiplied with a power x of two and one. Given such a choice of a prime, choosing even coefficients of the publicly available polynomials makes it hard to find any private information modulo p-1. Moreover, it makes it exponentially hard to lift the solutions found modulo q to the ring of integers modulo p-1 by properly arranging x and q. However, finding private information modulo the components q and power x of two is an NP-hard problem since it involves solving multivariate equations over the chosen finite field. The time complexity of searching a private key from a public key or signatures is exponential over GF(p). The time complexity of perpetrating a spoofing attack is also exponential for a field GF(p). MPPK/DS can achieve all three NIST security levels with optimized choices of multivariate polynomials and the generalized safe prime p.


 
 
 History of Seal and Printing Cultures Implications of the four important Chinese inventions, the compass, gun powder, papermaking, and printing, have far-reaching significance for human civilisation. The Chinese seal is intimately related to printing. Seals have the practical function of duplicating impressions of words or patterns. This process shares a very similar concept to printing on a small scale. Printing originated from the function of seals for making duplicated impressions, and for this reason Wang believes that seals constitute the prototype of printing. Seals in Traditional Commere Seals in certain Asian countries, such as Taiwan and Japan, play a vital role similar to that played by signatures in Western society. Particularly, the Chinese seal has been an integral part of Chinese heritage and culture. Wong states that seals usually symbolise tokens of promise in Chinese society. Ancient seals in their various forms have played a major role in information systems, in terms of authority, authentication, identification, certified proof, and authenticity, and have also been used for tamper-proofing, impression duplication, and branding purposes. To illustrate, clay sealing has been applied to folded documents to detect when sealed documents have been exposed or tampered with. Interestingly, one of the features of digital signature technology is also designed to achieve this purpose. Wong records that when the commodity economy began to develop and business transactions became more frequent, seals were used to prove that particular goods had been certified by customs. Moreover, when the goods were subject to tax by the government, seals were applied to the goods to prove the levy paid. Seals continue to be used in Chinese society as personal identification and in business transactions, official and legal documents, administrative warrants and charters. Paper-based Contract Signing with Seal Certificates In Taiwan and Japan, in certain circumstances, when two parties wish to formalise a contract, the seals of the two parties must be affixed to the contract. As Figure 1 illustrates, seal certificates are required to be attached to the signed and sealed contract for authentication as well as the statement of intent of a voluntary agreement in Taiwan. Figure 1. Example of a contract attached with the seal certificates A person can have more than one seal; however, only one seal at a time is allowed to be registered with a jurisdictional registration authority. The purpose of seal registration is to prevent seal forgery and to prove the identity of the seal owner. Namely, the seal registration process aims to associate the identity of the seal owner with the seal owner’s nominated seal, through attestation by a jurisdictional registration authority. Upon confirmation of the seal registration, the registration authority issues a seal certificate with both the seals of the registration authority and the registration authority executive. Digital Signatures for Electronic Commerce Handwritten signatures and tangible ink seals are highly impractical within the electronic commerce environment. However, the shift towards electronic commerce by both the public and private sector is an inevitable trend. ‘Trust’ in electronic commerce is developed through the use of ‘digital signatures’ in conjunction with a trustworthy environment. In principle, digital signatures are designed to simulate the functions of handwritten signatures and traditional seals for the purposes of authentication, data integrity, and non-repudiation within the electronic commerce environment. Various forms of Public Key Infrastructure (PKI) are employed to ensure the reliability of using digital signatures so as to ensure the integrity of the message. PKI does not, however, contribute in any way to the signatory’s ability to verify and approve the content of an electronic document prior to the affixation of his/her digital signature. Shortcomings of Digital Signature Scheme One of the primary problems with existing digital signatures is that a digital signature does not ’feel’ like, or resemble, a traditional seal or signature to the human observer; it does not have a recognisably individual or aesthetic quality. Historically, the authenticity of documents has always been verified by visual examination of the document. Often in legal proceedings, examination of both the affixed signature or seal as an integral part of the document will occur, as well as the detection of any possible modifications to the document. Yet, the current digital signature regime overlooks the importance of this sense of visualisation. Currently, digital signatures, such as the OpenPGP (Pretty Good Privacy) digital signature, are appended to an electronic document as a long, incomprehensible string of arbitrary characters. As shown in Figure 2, this offers no sense of identity or ownership by simple visual inspection. Figure 2. Example of a PGP signature To add to this confusion for the user, a digital signature will be different each time the user applies it. The usual digital signature is formed as an amalgam of the contents of the digital document and the user’s private key, meaning that a digital signature attached to an electronic document will vary with each document. This again represents a departure from the traditional use of the term ‘signature’. A digital signature application generates its output by firstly applying a hash algorithm over the contents of the digital document and then encrypting that hash output value using the user’s private cryptographic key of the normal dual-key pair provided by the Public Key cryptography systems. Therefore, digital signatures are not like traditional signatures which an individual can identify as being uniquely theirs, or as a recognisable identity attributable to an individual entity. New Visualised Digital Signature Scheme Liu et al. have developed the visualised digital signature scheme to enhance existing digital signature schemes through visualisation; namely, this scheme makes the intangible digital signature virtually tangible. Liu et al.’s work employs the visualised digital signature scheme with the aim of developing visualised signing and verification in electronic situations. The visualised digital signature scheme is sustained by the digital certificate containing both the certificate issuer’s and potential signer’s seal images. This thereby facilitates verification of a signer’s seal by reference to the appropriate certificate. The mechanism of ensuring the integrity and authenticity of seal images is to incorporate the signer’s seal image into an X.509 v3 certificate, as outlined in RFC 3280. Thus, visualised digital signature applications will be able to accept the visualised digital certificate for use. The data structure format of the visualised digital certificate is detailed in Liu. The visualised signing and verification processes are intended to simulate traditional signing techniques incorporating visualisation. When the signer is signing the document, the user interface of the electronic contracting application should allow the signer to insert the seal from the seal image file location into the document. After the seal image object is embedded in the document, the document is referred to as a ’visually sealed’ document. The sealed document is ready to be submitted to the digital signing process, to be transmitted with the signer’s digital certificate to the other party for verification. The visualised signature verification process is analogous to the traditional, sealed paper-based document with the seal certificate attached for verification. In history, documents have always required visual stimulus for verification, which highlights the need for visual stimulus evidence to rapidly facilitate verification. The user interface of the electronic contracting application should display the visually sealed document together with the associated digital certificate for human verification. The verifier immediately perceives the claimed signer’s seal on the document, particularly when the signer’s seal is recognisable to the verifier. This would be the case particularity where regular business transactions between parties occur. Significantly, having both the issuing CA’s and the signer’s seal images on the digital certificate instils confidence that the signer’s public key is attested to by the CA, as shown in Figure 3. This is unlike the current digital signature verification process which presents long, meaningless strings to the verifier. Figure 3. Example of a new digital certificate presentation Conclusions Seals have a long history accompanying the civilisation of mankind. In particular, certain business documents and government communities within seal-culture societies still require the imprints of the participating entities. Inevitably, the use of modern technologies will replace traditional seals and handwritten signatures. Many involved in implementing electronic government services and electronic commerce care little about the absence of imprints and/or signatures; however, there is concern that the population may experience difficulty in adapting to a new electronic commerce system where traditional practices have become obsolete. The purpose of the visualised digital signature scheme is to explore enhancements to existing digital signature schemes through the integration of culturally relevant features. This article highlights the experience of the use and development of Chinese seals, particularly in visualised seals used in a recognition process. Importantly, seals in their various forms have played a major role in information systems for thousands of years. In the advent of the electronic commerce, seal cultures still remain in the d

The Internet of Things (IoT) and Cloud computing are gaining popularity due to their numerous advantages, including the efficient utilization of internet and computing resources. In recent years, many more IoT applications have been extensively used. For instance, Healthcare applications execute computations utilizing the user’s private data stored on cloud servers. However, the main obstacles faced by the extensive acceptance and usage of these emerging technologies are security and privacy. Moreover, many healthcare data management system applications have emerged, offering solutions for distinct circumstances. But still, the existing system has issues with specific security issues, privacy-preserving rate, information loss, etc. Hence, the overall system performance is reduced significantly. A unique blockchain-based technique is proposed to improve anonymity in terms of data access and data privacy to overcome the above-mentioned issues. Initially, the registration phase is done for the device and the user. After that, the Geo-Location and IP Address values collected during registration are converted into Hash values using Adler 32 hashing algorithm, and the private and public keys are generated using the key generation centre. Then the authentication is performed through login. The user then submits a request to the blockchain server, which redirects the request to the associated IoT device in order to obtain the sensed IoT data. The detected data is anonymized in the device and stored in the cloud server using the Linear Scaling based Rider Optimization algorithm with integrated KL Anonymity (LSR-KLA) approach. After that, the Timestamp-based Public and Private Key Schnorr Signature (TSPP-SS) mechanism is used to permit the authorized user to access the data, and the blockchain server tracks the entire transaction. The experimental findings showed that the proposed LSR-KLA and TSPP-SS technique provides better performance in terms of higher privacy-preserving rate, lower information loss, execution time, and Central Processing Unit (CPU) usage than the existing techniques. Thus, the proposed method allows for better data privacy in the smart healthcare network.

This review chapter provides an in-depth exploration of various aspects of data security, ranging from foundational principles to advanced techniques. It sheds light on the importance of maintaining confidentiality, integrity, and availability of data and presents a comprehensive overview of technologies and methodologies that can be employed to achieve robust data security. In today's digital age, ensuring the security and protection of data has become paramount. This research chapter explores various topics related to data security, including confidentiality, integrity, and availability. It also delves into the role of blockchain technology, zero-trust architecture, secure coding practices, legal and ethical considerations, homomorphic encryption, secure multi-party computation, hash functions and digital signatures, secure communication protocols, cryptocurrency and blockchain security, as well as cryptanalysis and side-channel attacks.It highlights various techniques and technologies that can be employed to protect data confidentiality, including encryption and access control mechanisms. Blockchain technology has emerged as a groundbreaking solution for enhancing data security. Zero-trust architecture challenges traditional security models by adopting a holistic and dynamic approach to data protection. Secure coding practices and DevSecOps play a vital role in developing secure software applications. The chapter investigates the importance of integrating security measures throughout the software development lifecycle. It emphasizes the adoption of secure coding practices and the implementation of DevSecOps methodologies to build resilient and secure software systems. Legal and ethical considerations are crucial when addressing data security. Homomorphic encryption and secure multi-party computation are advanced cryptographic techniques that allow data to be processed securely while encrypted. The chapter examines the principles and applications of these techniques, highlighting their significance in scenarios where privacy is paramount. Hash functions and digital signatures form the backbone of data authentication and integrity. The chapter discusses the properties and applications of hash functions and digital signatures in verifying the integrity and authenticity of data. Secure communication protocols are essential for protecting data during transmission. The chapter explores various secure communication protocols, such as Transport Layer Security (TLS), and examines their role in ensuring data confidentiality, integrity, and authenticity. Cryptocurrency and blockchain security focus on the secure storage and transfer of digital assets. The research chapter investigates the security considerations specific to cryptocurrencies and explores how block chain technology can mitigate vulnerabilities and ensure the trustworthiness of transactions. Cryptanalysis and side-channel attacks are threats to cryptographic systems. The chapter discusses these attack techniques, highlighting their potential risks and the measures that can be taken to counter them.

Blockchain Technology The term ‘blockchain technology’ typically refers to the transparent, trust enabled, publicly accessible ledger that allows us to securely transfer the ownership of units of value using public key encryption and consensus methods. The technology uses decentralized consensus to maintain the network, which means it is not centrally controlled by a bank, corporation, or government, but is governed by the participants in the network itself. In fact, the larger the network grows and becomes increasingly decentralized, the more secure it becomes. The Bitcoin Network is the first successful implementation of “public blockchain”.

Anonymous channels or similar techniques that achieve sender's anonymity play important roles in many applications, e.g. electronic voting. However, they will be meaningless if cryptographic primitives containing sender's identity are carelessly used during the transmission. In computationally secure settings, this problem may be easily overcome by using public key encryption and group signatures. However, in an unconditionally secure setting, in which no computational difficulty is assumed, this is not an easy case as such. As the increasing computational power approaches the point where security policy can no longer assume the difficulty of solving factoring or discrete logarithm problems, it must shift its focus to assuring the solvency of unconditionally secure schemes that provide long-term security. The main contribution of this paper is to study the security primitives for the above problem. In this paper, we first define the unconditionally secure asymmetric encryption scheme, which is an encryption scheme with unconditional security and where it is impossible for a receiver to deduce the identity of a sender from the encrypted message. We also investigate tight lower bounds on required memory sizes from an information theoretic viewpoint and show an optimal construction based on polynomials. It is remarkable to see that these bounds are considerably different from those in Shannon's model of the conventional unconditionally secure symmetric encryption. Other than the polynomial-based scheme, we also show a construction based on combinatorial theory, a non-malleable scheme and a multi-receiver scheme. Then, we define and formalize the group authentication code (GA-code), which is an unconditionally secure authentication code with anonymity like group signatures. In this scheme, any authenticated user will be able to generate and send an authenticated message while the receiver can verify the legitimacy of the message---that it has been sent from a legitimate user but at the same time retains his anonymity. However, by cooperating with the group authority, such as in the case of disputes, the receiver is able to obtain information of the user's identity. For GA-code, we show two concrete constructions.

Due to the rapid growth of wireless applications, Cognitive Radio (CR) has been considered as a technology to solve spectrum source deficiency by improving effective utilization of limited radio spectrum resources for future wireless communications and mobile computing. However, the unique characteristics of CRNs make security a greater challenge. Moreover, due to the dynamic characteristics of CRNs, a member of CRNs, may join or leave the network at any time. The issue of supporting secure communication in CRNs therefore becomes more serious than for conventional wireless networks. Public key encryption and signature techniques have been adopted here to ensure the security of message transmission in CRNs. This work proposes a digital signature-based trust-oriented scheme to ensure communication by identifying efficient trustworthy users in CRNs. The security analysis is analyzed to guarantee that the proposed approach achieves security proof.

Introduction: Development of practical post-quantum signature schemes is a current challenge in the applied cryptography. Recently, several different forms of the hidden discrete logarithm problem were proposed as primitive signature schemes resistant to quantum attacks. Purpose: Development of a new form of the hidden discrete logarithm problem set in finite commutative groups possessing multi-dimensional cyclicity, and a method for designing post-quantum signature schemes. Results: A new form of the hidden discrete logarithm problem is introduced as the base primitive of practical post-quantum digital signature algorithms. Two new four-dimensional finite commutative associative algebras have been proposed as algebraic support for the introduced computationally complex problem. A method for designing signature schemes on the base of the latter problem is developed. The method consists in using a doubled public key and two similar equations for the verification of the same signature. To generate a pair of public keys, two secret minimum generator systems <G, Q> and <H, V> of two different finite groups G<G, Q> and G<H, V> possessing two-dimensional cyclicity are selected at random. The first public key (Y, Z, U) is computed as follows: Y = Gy1Qy2a, Z = Gz1Qz2b, U = Gu1Qu2g, where the set of integers (y1, y2, a, z1, z2, b, u1, u2, g) is a private key. The second public key (Y¢, Z¢, U¢) is computed as follows: Y¢ = Hy1Vy2a, Z¢ = Hz1Vz2b, U¢ = Hu1Vu2g. Using the same parameters to calculate the corresponding elements belonging to different public keys makes it possible to calculate a single signature which satisfies two similar verification equations specified in different finite commutative associative algebras. Practical relevance: Due to a smaller size of the public key, private key and signature, as well as approximately equal performance as compared to the known analogues, the proposed digital signature scheme can be used in the development of post-quantum signature algorithms.

Public-key encryption is extensively used to provide digital data confidentiality and deliver the security features, such as nonrepudiation (digital signature) and secure key exchange. Conventional public-key schemes are based on mathematical problems with inflexible constraints, and the security of digital contents relies on computational complexity. In the era of emerging technologies, most public-key image encryption schemes are susceptible to various threats. We propose a novel public-key encryption in this article with near-ring criteria and provide confidentiality to private data with the microstates of the Einstein crystal model. The virtual oscillator generated by microstates of initial oscillators for the common secrets with the public-key scheme produces unique states to encrypt digital data. The privacy-preserved structure, that mimics the data stream of digital content with the behavior of the improved Einstein crystal model, describes a system in terms of microstates to generate diffusion in the plain data with unique states of a virtual oscillator. The performance and digital forensic evaluations, such as randomness, histogram uniformity, pixels’ correlation, pixels’ similarity, visual strength, pixels’ incongruity, key sensitivity, linear and differential attacks, noise, and occlusion attacks analyses, certify the resistivity of the proposed algorithm against potential threats and provide superior capacity in comparison to existing methodologies to hostile certain attacks.

PurposeThe practical purpose of this research is to propose a candidate for post-quantum signature standard that is free of significant drawback of the finalists of the NIST world competition, which consists in the large size of the signature and the public key. The practical purpose is to propose a fundamentally new method for development of algebraic digital signature algorithms.Design/methodology/approachThe proposed method is distinguished by the use of two different finite commutative associative algebras as a single algebraic support of the digital signature scheme and setting two different verification equation for a single signature. A single public key is computed as the first and the second public keys, elements of which are computed exponentiating two different generators of cyclic groups in each of the algebras.FindingsAdditionally, a scalar multiplication by a private integer is performed as final step of calculation of every element of the public key. The same powers and the same scalar values are used to compute the first and the second public keys by the same mathematic formulas. Due to such design, the said generators are kept in secret, providing resistance to quantum attacks. Two new finite commutative associative algebras, multiplicative group of which possesses four-dimensional cyclicity, have been proposed as a suitable algebraic support.Originality/valueThe introduced method is novel and includes new techniques for designing algebraic signature schemes that resist quantum attacks. On its base, a new practical post-quantum signature scheme with relatively small size of signature and public key is developed.

Blockchain is an up-and-coming technology, and it is exploring its existence in all our day-to-day lives, particularly for business applications. Due to this, security has become a major and a higher priority concern during the transaction process of data, cryptocurrency, etc. Achieving integrity, authentication, and non-repudiation with blockchain technology through digital signatures are the factors for its success. Hence, we imply a novel hybrid chaotic map–based proactive RSA/digital signature scheme for a better securable transaction of blocks compared to earlier works. Faster encryption and decryption could be expected by this novel approach. This could surely be resistant to brute force attacks, chosen plain text attacks and chosen cipher text attacks. OPENMP and OPENSSL libraries could be employed for good performance and security in a multicore platform. Chaotic map theory has its unique characteristics in the design of highly secure asymmetric encryption and decryption processes, with lesser computational cost in lesser time. The strength of RSA lies in the prime factorization of larger prime numbers in the generation of public and private keys. RSA has a severe backlog in computational time; while the length of the prime number is longer, to ensure higher security, the longer one is preferable. Hence to speedup the factorization process, chaotic mapping theory has been synchronized with the RSA cryptosystem. Second, chaotic mapping theory provides an enhanced avalanche effect, which leads to a two-factor RSA encryption process. Chaotic maps are highly sensitive to initial values and control parameters. The unique feature of inclusion of chaotic maps is that any slight change in the initial conditions of the plain text would cause a remarkable deviation in the message digest. This nature would make the hacker limit their prediction ability. Computational time, cost, and level of resistance to attacks are the factors to be considered to measure the efficiency of our new approach when compared to other RSA approaches. The work was simulated using MATLAB and it is proved that that the proposed RSA with hybrid GLT chaotic maps is 1.53 times and 1.27 times faster than the existing ones.

There is no quantum election protocol that can fulfil the eight requirements of an electronic election protocol, i.e., completeness, robustness, privacy, legality, unreusability, fairness, verifiability, and receipt-freeness. To address this issue, we employ the general construction of quantum digital signature and quantum public key encryption, in conjunction with classic public key encryption, to develop and instantiate a general construction of quantum election protocol. The proposed protocol exhibits the following advantages: (i) no pre-shared key between any two participants is required, and no trusted third party or anonymous channels are required. The protocol is suitable for large-scale elections with numerous candidates and voters and accommodates the situation in which multiple voters vote simultaneously. (ii) It is the first protocol that dismantles the contradiction between verifiability and receipt-freeness in a quantum election protocol. It satisfies all eight requirements stated earlier under the physical assumptions that there exists a one-way untappable channel from the administrator to the voter and that there is no collusion between any of the three parties in the protocol. Compared with current election protocols with verifiability and receipt-freeness, this protocol relies upon fewer physical assumptions. (iii) This construction is flexible and can be instantiated into an election scheme having post-quantum security by applying cryptographic algorithms conveying post-quantum security. Moreover, utilizing quantum digital signature and public key encryption yields a good result: the transmitted ballots are in quantum states, so owing to the no-cloning theorem, ballot privacy is less likely to be compromised, even if private keys of the signature and public key encryption are leaked after the election. However, in existing election protocols employing classic digital signatures and public key encryption, ballot privacy can be easily violated if attackers obtain private keys. Thus, our construction enhances privacy.