A novel method for developing post-quantum cryptoschemes and a practical signature algorithm

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.

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.

Predicate encryption (PE), formalized by Katz et al., is a new paradigm of public-key encryption that conceptually captures the public-key encryption that supports fine-grained access control policy. Because of the nature of PE, it is used for cloud storage so that users can retrieve encrypted data without revealing any information about the data to cloud servers and other users. Although lots of PE schemes have been studied, the predicate-hiding security is seldom considered; that is, the user’s secret key may leak sensitive information of the predicate. Additionally, the security of the current predicate-hiding PE schemes relies on the discrete logarithm assumption which cannot resist the quantum attacks in the future. In this paper, we propose a generic PE for inner product under symmetric-key setting, called private IPE, from specific key-homomorphic pseudorandom function (PRF). The rigorous proofs are provided to show that the construction is payload-hiding, attribute-hiding, and predicate-hiding secure. With the advantage of the generic construction, if the underlying PRF can resist quantum attacks, then, through our proposed generic construction, a quantum-resistant private IPE can be obtained.

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

Efficient forward secure identity-based shorter signature from lattice

Password-based authenticated key exchange (PAKE) allows participants sharing low-entropy passwords to agree on cryptographically strong session keys over insecure networks. In this paper, we present two PAKE protocols from lattices in the two-party and three-party settings, respectively, which can resist quantum attacks and achieve mutual authentication. The protocols in this paper achieve two rounds of communication by carefully utilizing the splittable properties of the underlying primitive, a CCA (Chosen-Ciphertext Attack)-secure public key encryption (PKE) scheme with associated nonadaptive approximate smooth projection hash (NA-ASPH) system. Compared with other related protocols, the proposed two-round PAKE protocols have relatively less communication and computation overhead. In particular, the two-round 3PAKE is more practical in large-scale communication systems.

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.

We consider a problem which was stated in a request for comments made by NIST in the FIPS97 document. The question is the following: Can we have a digital signature public key infrastructure where the public (signature verification) keys cannot be abused for performing encryption? This may be applicable in the context of, say, exportable/escrow cryptography. The basic dilemma is that on the one hand, (1) to avoid framing by potentially misbehaving authorities we do not want them to ever learn the “signing keys” (e.g., Japan at some point declared a policy where signature keys may be required to be escrowed), and on the other hand (2) if we allow separate inaccessible public signature verification keys, these keys (based on trapdoor functions) can be used as “shadow public-keys,” and hence can be used to encrypt data in an unrecoverable manner. Any solution within the “trapdoor function” paradigm of Diffie and Hellman does not seem to lead to a solution which will simultaneously satisfy (1) and (2).The cryptographic community so far has paid very limited attention to the problem. In this work, we present the basic issues and suggest a possible methodology and the first scheme that may be used to solve much of the problem. Our solution takes the following steps: (1) it develops the notion of a nested trapdoor which our methodology is based on, (2) we implement this notion based on a novel composite “double-decker” exponentiation technique which embeds the RSA problem within it (the technique may be of independent interest), (3) we analyze carefully what can be and what cannot be achieved regarding the open problem by NIST (our analysis is balanced and points out possibilities as well as impossibilities), and (4) we give a secure signature scheme within a public key infrastructure, wherein the published public key can be used for signature verification only (if it is used for encryptions, then the authorities can decrypt the data). The security of our scheme is based on RSA. We then argue how the scheme’s key cannot be abused (statically) based on an additional assumption. We also show that further leakages and subliminal leakages when the scheme is in (dynamic) use are not added substantially beyond what is always possible by a simple adversary; we call this notion competitive leakage. We also demonstrate such simple leaking adversary.We hope that our initial work will stimulate further thoughts on the non-trivial issue of signature-only signatures.KeywordsSignature SchemeRandom OracleRandom Oracle ModelCovert ChannelDigital Signature SchemeThese 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.

With the increase of computing power of quantum computers, classical cryptography schemes such as RSA and ECC are no longer secure in the era of quantum computers. The Cryptosystem based on coding has the advantage of resisting quantum computing and has a good application prospect in the future. McEliece Public Key Cryptography is a cryptosystem based on coding theory, whose security can be reduced to the decoding problem of general linear codes and can resist quantum attacks. Therefore, this paper proposes a cryptosystem based on the Polar-LDPC Concatenated Codes, which is an improvement on the original McEliece cipher scheme. The main idea is to take the generation matrix of Polar code and LDPC code as the private key, and the product of their hidden generation matrix as the public key. The plain text is encoded by Polar code and LDPC code in turn to obtain the encrypted ciphertext. The decryption process is the corresponding decoding process. Then, the experimental data presented in this paper prove that the proposed scheme can reduce key size and improve security compared with the original McEliece cryptosystem under the condition of selecting appropriate parameters. Moreover, compared with the improvement schemes based on McEliece proposed in recent years, the proposed scheme also has great security advantages.


 
 
 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

With the continuous development of quantum technology, the quantum signature as an application of quantum cryptography has received great attention. In this paper, we propose a public-key quantum group blind signature scheme based on single-qubit rotations. In this scheme, the group manager generates a public key. Each group member randomly generates his own private key according to the public key. The signer uses his private key and random sequence to generate the signature. The verifier uses the public key to verify the correctness of the quantum signature. The public and private keys can be reused, which simplifies the key management of the signature system. In this scheme, the random sequence is used to enhance the security of the scheme. At the same time, the quantum efficiency is improved by using single-qubit rotations. The security analysis shows that our scheme can ensure the security of the keys, the unforgeability and the non-deniability of the signature.

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.

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.

A new group signature with one time secret key is proposed. The main merits are that it only needs the trusted center issuing the partial secret key one time for each group member; and that the group member can generate his different secret key each time when he wants to sign a message. The group public key is constant and the size of the signature is independent of the number of group members. The total computation cost of signature and verification requires only 8 modular exponentiations.

In 1984, Shamir proposed the concept of the ID-based cryptosystem (IBC). Instead of generating and publishing a public key for each user, the ID-based scheme permits each user to choose his name or network address as his public key. This is advantageous to public-key cryptosystems because the public-key verification is so easy and direct. In such a way, a large public key file is not required. Since new cryptographic schemes always face security challenges and many integer factorization and discrete logarithm based cryptographic systems have been deployed, therefore, the purpose of this paper is to design a transformation process that can transfer the entire integer factorization problem and discrete logarithm problem based cryptosystems into the ID-based systems rather than re-invent a new system. We consider the security against a conspiracy of some entities in the proposed system and show the possibility of establishing a more secure system. Rapid advances in computer technology and the development of the Internet are changing the way, we conduct our daily and business lives. Secrecy is an important issue with respect to sensitive data transferred over insecure public channels. In an open network environment, secret session key needs to be shared between two users before it establishes a secret communication. While the number of users in the network is increasing, key distribution will become a serious problem. In 1976, Diffie and Hellman (4) introduced the concept of the public key distribution system (PKDS). In the PKDS, each user needs to select a secret key and compute a corresponding public key and store in the public directory. The common secrete session key, which will be shared between two users can then be determined by either user, based on his own secret key and the partner's public key. Although the PKDS provides an elegant way to solve the key distribution problem, the major concern is the authentication of the public keys used in the cryptographic algorithm. Many attempts have been made to deal with the public key authentication issue. Kohnfelder (5) used the RSA digital signature scheme to provide public key certification. His system involves two kinds of public key cryptography: one is in modulo p, where p is a large prime number; the other is in modulo N, where N = pq, and p and q are large primes. Blom (7) proposed a symmetric key generation system (SKGS) based on secret sharing schemes. The problems of SKGS however, are the difficulty of choosing a suitable threshold value and the requirement of large memory space for storing the secret shadow of each user. In 1984, Shamir (1) introduced the concept of an identity. In this system, each user needs to visit key authentication center (KAC) and identify himself before joining the network. Once a user's identity is accepted, the KAC will provide him with a secret key.