A new quantum-safe multivariate polynomial public key digital signature algorithm

This article examines digital signature as a critical security measure for authentication and verification in electronic transactions, distinguishing them from simpler e-signatures by their use of advanced cryptographic techniques. Digital signature leverage asymmetric cryptography to provide higher security, with various standardised algorithms, such as the Digital Signature Algorithm (DSA) and Rivest- Shamir-Adleman (RSA), forming the foundation of secure systems today. The paper outlines the evolution of digital and electronic signature, from early telegraph-based approvals to the modern applications that facilitate secure digital contracts and communications. Key digital signature algorithms are analysed in detail, highlighting their strengths and weaknesses, including RSA, DSA, Elliptic Curve Digital Signature Algorithm (ECDSA), and Edwards-Curve Digital Signature Algorithm (EdDSA). Additionally, the article addresses the technical and implementation challenges of digital signature algorithms, such as high computational demands, complexities in key management, and difficulties in secure implementation. It concludes with an exploration of future trends, such as the development of efficient and quantum-resistant algorithms, improvements in cryptographic hardware, and new strategies to simplify secure key management. This comprehensive overview provides insights into both current digital signature practices and emerging solutions poised to enhance security and efficiency in an evolving digital landscape.

This paper presents the possibilities of combing public-key encryption and digital signature algorithms which are actually based on different mathematical hard problems. Since the output of the combination produces an Encrypted signed message. In general, most of the currently used public-key algorithms are computationally expensive with relatively lengthy key requirement due to the dependency on the number theory. Therefore, it’s important to show a combinational protocols which are based on different mathematical hard problem. In some sense, difficult to solve. In the combined scheme, we present the powerful and practical encryption digital signature scheme and its security level and execution time.

Research in the field of public key cryptography in general and digital signatures in particular is often considered and evaluated at two levels: The first level is considering the mathematical basis for constructing cryptographic and digital signature algorithms, especially these difficult problems: factorizing a large integer into prime factors, finding root problem, discrete logarithm problem, discrete logarithm problem on elliptic curve... The second level is constructing cryptographic and digital signatures algorithms on these hard problems including RSA, DSA, Schnorr, GOST R34.10-94. At the first level, research focuses mainly on improving algorithms for finding large primes, structures for strong primes and algorithms to attack these problems efficiently. At the second level, the research concentrates on improving the existing algorithms to enhance the safety or effective performance of the algorithm. In this article, the authors propose a solution to improve the security of digital signature schemes, implemented in both levels of digital signatures. At the first level, the authors propose a new hard problem - different from the hard problems used before and hasn’t been solved by anyone so far (except by "brute force attack" method). At the second level, the authors propose a method to construct new digital signature algorithms that can help create not only one but also a family of new digital signature algorithms with high security level for practical applications.

The National Institute of Standards and Technology is in the process of selecting public-key cryptographic algorithms through a public, competition-like process. The new public-key cryptography standards will specify additional digital signature, public-key encryption, and key-establishment algorithms to augment Federal Information Processing Standard (FIPS) 186-4, Digital Signature Standard (DSS), as well as NIST Special Publication (SP) 800-56A Revision 3, Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography, and SP 800-56B Revision 2, Recommendation for Pair-Wise Key Establishment Using Integer Factorization Cryptography. It is intended that these algorithms will be capable of protecting sensitive information well into the foreseeable future, including after the advent of quantum computers. The first round of the NIST Post-Quantum Cryptography Standardization Process began in December 2017 with 69 candidate algorithms that met both the minimum acceptance criteria and submission requirements. The first round lasted until January 2019, during which candidate algorithms were evaluated based on their security, performance, and other characteristics. NIST selected 26 algorithms to advance to the second round for more analysis. The second round continued until July 2020, after which seven 'finalist' and eight 'alternate' candidate algorithms were selected to move into the third round. This report describes the evaluation and selection process, based on public feedback and internal review, of the third-round candidates. The report summarizes each of the 15 third-round candidate algorithms and identifies those selected for standardization, as well as those that will continue to be evaluated in a fourth round of analysis. The public-key encryption and key-establishment algorithm that will be standardized is CRYSTALS-Kyber. The digital signatures that will be standardized are CRYSTALS-Dilithium, Falcon, and SPHINCS+. While there are multiple signature algorithms selected, NIST recommends CRYSTALS-Dilithium as the primary algorithm to be implemented. In addition, four of the alternate key-establishment candidate algorithms will advance to a fourth round of evaluation: BIKE, Classic McEliece, HQC, and SIKE. These candidates are still being considered for future standardization. NIST will also issue a new Call for Proposals for public-key digital signature algorithms to augment and diversify its signature portfolio.

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 invention of public-key cryptography was of central importance to the field of cryptography and provided answers to many key management problems for large scale networks. For all its benefits, however, public-key cryptography did not provide a comprehensive solution to the key management problem. Indeed, the possibilities brought forth by public-key cryptography heightened the need for sophisticated key management systems to answer questions such as the following:"How can I easily encrypt a file once for a number of different people using public-key cryptography?""If I lose my keys, how can I decrypt all of my files that were encrypted with those keys?""How do I know that I really have Alice’s public key and not the public key of someone pretending to be Alice?""How can I know that a public key is still trustworthy?"The paper discusses public key cryptography and its use in applications such as Key Agreement, Data Encryption and Digital Signature. The paper discusses some public key algorithms such as DH, RSA, and DSA and also gives working explanations of these algorithms.KeywordsShared SecretCertificate AuthorityCipher TextHash CodeDigital CertificateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A SM2 based efficient and lightweight batch verification approach for IC cards

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.

A powerful and practical public-key and digital signature scheme was produced by ElGamal. ElGamal public-key and digital signature scheme were modified from the domain of natural integers, Z, to the domains of Gaussian integers, Z[i], and polynomials over finite fields, F[x]. We implement the classical and modified ElGamal digital signature scheme to compare and to test their functionality, reliability and security. To test the security of the algorithms we use a famous attack algorithm called Baby-Step-Giant algorithm which works in the domain of natural integers. We enhance the Baby-Step-Giant algorithm to work with the modified ElGamal digital signature algorithms.

Identification schemes are used to verify identities of parties and signatures. Recently, systems based on multivariate polynomials have been preferred in identification schemes due to their resistance against quantum attacks. In this paper, we propose a quantum secure $3$-pass identification scheme based on multivariate quadratic polynomials. We compare the proposed scheme with the previous ones in view of memory requirements, communication length, and computation time. We define an efficiency metric by using impersonation probability and computation time. According to the comparison results, the proposed one has the same computation time as that of Monteiro et al. and reduces impersonation probability compared to the work of Sakumoto et al. We also propose a new signature scheme constructed from the proposed identification scheme. In addition, we compare the signature scheme with the previous schemes in view of signature and key sizes. We improve the signature size compared to that given in previous work by Chen et al.

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.

Round 1 of the the NIST post-quantum cryptography (PQC) standardization effort began on November 30th, 2017. The competition aims to select the most promising quantum-resistant algorithms, which are currently secure against large scale quantum computers. Multivariate cryptosystems belong to a promising group of PQC schemes and are based on multivariate polynomials over finite fields. Among them are the Unbalanced Oil and Vinegar (UOV) and Rainbow signature schemes, which have been extensively studied since 1999 and 2005, respectively. The main advantage of UOV is high confidence in its security, and the disadvantages include large key and signature sizes. Rainbow is a multi-layer version of UOV that offers better performance, smaller keys, and smaller signatures. This paper presents a high-speed FPGA implementation for the NIST Round 1 PQC submission of Rainbow. We discuss a high-speed design that uses a parameterized system solver, which can solve an n-byn system in n clock cycles. Compared to the previous state-of-the-art, we reduce the number of required multipliers by almost half, speed up execution, and implement Rainbow for higher security levels. Our design supports many parameter sets, which require operations in the fields GF(16) and GF(256). Additionally, in order to make benchmarking easier and fairer, our design follows a universal PQC hardware API, which allows for fair comparison with other post-quantum signature schemes. This design is being made open-source to increase transparency and speed up further optimization.

Communication in wireless sensor networks uses the majority of a sensor's limited energy. Using aggregation in wireless sensor network reduces the overall communication cost. Security in wireless sensor networks entails many different challenges. Traditional end-to-end security is not suitable for use with in-network aggregation. A corrupted sensor has access to the data and can falsify results. Additively homomorphic encryption allows for aggregation of encrypted values, with the result being the same as the result when unencrypted data was aggregated. Using public key cryptography, digital signatures can be used to achieve integrity. We propose a new algorithm using homomorphic encryption and additive digital signatures to achieve confidentiality, integrity and availability for in-network aggregation in wireless sensor networks. We prove that our digital signature algorithm which is based on the elliptic curve digital signature algorithm (ECDSA) is as secure as ECDSA.

This article proposes the algorithm of generation of public key for digital signature. The algorithm is quantum-resistant because it uses the complexity of solving a system of polynomial equations. It is assumed that in this case a standard hash function is used for the digital signature implementation, which has 384-512 bit output. The digital signature that is formed in this way will allow the blockchain technology to be quantum-resistant.

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.