A post-quantum digital signature scheme on groups with four-dimensional cyclicity

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.

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.

Recently, the notion of the key-insulated public- key system has been suggested to protect the security of users' private keys. A general idea of this system is changing the user's private key along with the time, but the user's public key remains unchanged. In this paper, we propose a new identity (ID)-based key-insulated signature scheme from bilinear pairings. As compared with the recently proposed ID-based key-insulated signature schemes, our proposed scheme has better performance in the batch verifying phase. For security analysis, our scheme is a provably secure key-insulated signature scheme in the random oracle model and under the computational Diffie-Hellman assumption. Meanwhile, to demonstrate the additional advantage of a key-insulated signature, we present a novel application based on the proposed scheme, called full delegation ID-based proxy signature scheme with time restriction. To our best knowledge, no such a proxy signature scheme is proposed until now.

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.

Наведено порівняльний аналіз відомих протоколів узгодження таємного ключа через відкритий канал звʼязку. Запропоновано узагальнення відомого протоколу з використанням некомутативного множення матриць над простим скінченним полем на випадок довільного скінченного поля. A symmetric cryptosystem requires a secret key agreed by both parties. The Diffie-Hellman protocol was originally proposed for its exchange via an open communication channel. It is based on the computational complexity of the discrete logarithm problem in certain finite groups (the multiplicative group of a finite field, the group of points of an elliptic curve over a finite field). The availability of a powerful quantum computer will allow solving the discrete logarithm problem in these groups. Therefore, the issue of construction of secret key exchange protocols that will be resistant to attacks using a quantum computer has become urgent. The paper provides a comparative analysis of known protocols for a secret key exchange via an open communication channel. A generalization of the known protocol using non-commutative matrix multiplication over a prime finite field for the case of an arbitrary finite field is proposed. In this protocol, two high order elements from the general linear group over a finite field should be used, which satisfy an additional condition. It consists in the fact that each of the matrices cannot be reduced to a diagonal form by conjugation transformation. This condition follows from the considerations of avoiding an attack on the protocol. It is shown how to construct such elements. For the proposed generalization of the protocol, the sizes of public and private keys, secret key, the size of the finite field, which ensure the appropriate level of security, are calculated. The dimensions of matrices (elements of the general linear group) that we use are also given. The generalization of the protocol to the case of an arbitrary finite field increases the flexibility of choosing protocol parameters to ensure the desired level of security.

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.

Analysis of a perspective variant of post-quantum electronic signature based on algebraic lattices of Dilithium is carried out. The central task of the analysis is to study the resistance of Dilithium to fault attacks, in particular differential ones. First, information is given about the ES scheme itself and its security, fault attacks, their development to differential fault attacks. Possibilities of carrying out these attacks and criteria of their successful execution are considered. The places of the ES algorithm that need protection against fault attacks were identified, such as hash function (the moment of access to it and operation of polynomials multiplying), the stage of loading the private key, the function of expanding seed. Also, nonce reuse and partial nonce reuse when generating keys poses a significant threat, and by carrying out such an attack, the attacker can fully recover the long-term Dilithium private key. Attacks countermeasures are formed based on the sources analysis, their advantages and negative effects are presented. Methods of protection against such attacks are: re-calculation of the signature; verification of signature after signing, which is three times faster than the previous method; introducing additional randomness to the deterministic noise sampling; checking the value of secret and false components (nonce); calculating the average value and variance of the sample, and checking them for belonging to a given range. The results of this work provide researchers with a guide for the development of secure post-quantum electronic signature schemes.

A Distributed Key Generation (DKG)p rotocol is an essential component of any threshold cryptosystem. It is used to initialize the cryptosystem and generate its private and public keys, and it is used as a subprotocol, for example to generate a one-time key pair which is a part of any threshold El-Gamal-like signature scheme. Gennaro et al. showed [GJKR99] that a widely-known non-interactive DKG protocol suggested by Pedersen does not guarantee a uniformly random distribution of generated secret keys even in the static adversary model. Furthermore, Gennaro et al. proposed to replace this protocol with one that guarantees a uniform distribution of the generated key but requires an extra round of reliable broadcast communication.We investigate the question whether some discrete-log based threshold cryptosystems remain secure when implemented using the more efficient DKG protocol of Pedersen, in spite of the fact that the adversary can skew the distribution of the secret key generated by this protocol. We answer this question in the positive. We show that threshold versions of some schemes whose security reduces to the hardness of the discrete logarithm problem, remain secure when implemented with Pedersen DKG. We exemplify this claim with a threshold Schnorr signature scheme.However, the resulting scheme has less efficient security reduction (in the random oracle model)from the hardness of the discrete logarithm problem than the same scheme implemented with the computationally more expensive DKG protocol of Gennaro et al. Thus our results imply a trade-o. in the design of threshold versions of certain discrete-log based schemes between the round complexity of a protocol and the size of the modulus.KeywordsThreshold cryptographydistributed key generationdiscrete logarithmexact securityrandom oracle model

Highly-Secure Backdoors: Internet of Traitorous Things (IoTT)

Data exchange has been rapidly increased recently by increasing the use of mobile networks. Sharing information (text, image, audio and video) over unsecured mobile network channels is liable for attacking and stealing. Encryption techniques are the most suitable methods to protect information from hackers. Hill cipher algorithm is one of symmetric techniques, it has a simple structure and fast computations, but weak security because sender and receiver need to use and share the same private key within a non-secure channel. Therefore, a novel hybrid encryption approach between elliptic curve cryptosystem and hill cipher (ECCHC) is proposed in this paper to convert Hill Cipher from symmetric technique (private key) to asymmetric one (public key) and increase its security and efficiency and resist the hackers. Thus, no need to share the secret key between sender and receiver and both can generate it from the private and public keys. Therefore, the proposed approach presents a new contribution by its ability to encrypt every character in the 128 ASCII table by using its ASCII value direct without needing to assign a numerical value for each character. The main advantages of the proposed method are represented in the computation simplicity, security efficiency and faster computation.

Several researchers have proposed the use of threshold cryptographic model to enable secure communication in ad hoc networks without the need of a trusted center. In this model, the system remains secure even in the presence of a certain threshold t of corrupted/malicious nodes.In this paper, we show how to perform necessary public key operations without node-specific certificates in ad hoc networks. These operations include pair-wise key establishment, signing, and encryption. We achieve this by using Feldman’s verifiable polynomial secret sharing (VSS) as a key distribution scheme and treating the secret shares as the private keys. Unlike in the standard public key cryptography, where entities have independent private/public key pairs, in the proposed scheme the private keys are related (they are points on a polynomial of degree t) and each public key can be computed from the public VSS information and node identifier. We show that such related keys can still be securely used for standard signature and encryption operations (using resp. Schnorr signatures and ElGamal encryption) and for pairwise key establishment, as long as there are no more that t collusions/corruptions in the system.The proposed usage of shares as private keys can also be viewed as a threshold-tolerant identity-based cryptosystem under standard (discrete logarithm based) assumptions.

In this paper, we propose two authenticated key distribution protocols and one conference key protocol using identity-based, self-certified public keys. These proposed protocols have the following properties:(i) No extra public key certificates and computational efforts are required for verification of authenticity for public keys.(ii) Key establishment and validation of the desired public keys are integrated in a logically single step.(iii) Each registering user can use his derived private key to check the validity of his public key issued by the system authority.(iv) The system authority cannot access to users' private keys. Hence, all private keys cannot be compromised in case of disruption or corruption of the system authority.(v) The proposed protocols provide the security property of key authentication whereby one user is assured that no other user aside from specifically identified user (s) may gain access to the derived shared key/conference key.

This paper proposes a novel hybrid public/private key cryptography scheme based on perfect Gaussian integer sequences (PGISs) of period $N=pq$ . First, a review study of construction degree-4 PGIS is addressed. We show that circular convolution over PGISs is a trapdoor one-way permutation function that enables simultaneous cipher encryption and digital signatures. To implement the proposed cipher encryption scheme, a private PGIS is assigned as the encryption key sequence for circular convolution with the plaintext to generate the ciphertext. The reverse decryption key sequence involves the time reflection and complex conjugation of the encryption sequence, which can be regenerated using a pair of public and private keys. The security level of the proposed scheme is the same as that of the Rivest-Shamir-Adleman (RSA) system; however, the capacity of a cryptosystem based on PGISs may outperform that of based on RSA, because abundant PGISs are available. Simulation results show that the approximation error when finite digits are used to represent the irrational coefficients of a normalized PGIS can be relatively small compared with the noise. This contributes to the simplicity of this scheme’s implementation. With the fast development of IoT (internet of things), the adaptation and applicability of the proposed scheme to IoT platforms are also addressed, where lightweight cryptographic functions are preferable due to the limited resources of IoT devices.

Methods and results from the representation theory of finite di- mensional algebras have led to many interactions with other areas of mathe- matics. Such areas include the theory of Lie algebras and quantum groups, commutative algebra, algebraic geometry and topology, and in particular the new theory of cluster algebras. The aim of this workshop was to further de- velop such interactions and to stimulate progress in the representation theory of algebras.

This paper describes an algorithm for secure transmission of information via open communication channels based on the discrete logarithm problem. The proposed algorithm also provides sender identification (digital signature). It is twice as fast as the RSA algorithm and requires fifty per cent fewer exponentiations than the ElGamal cryptosystems. In addition, the algorithm requires twice less bandwidth than the ElGamal algorithm. Numerical examples illustrate all steps of the proposed algorithm: system design (selection of private and public keys), encryption, transmission of information, decryption and information recovery.