Combining Public-Key Encryption with Digital Signature Scheme

A public-key encryption algorithm and a practical hybrid scheme are proposed in this paper. This algorithm uses the advanced transform techniques, i.e. the Number Theoretic Transforms (NTTs) to diffuse data, and uses a non-linear technique based on the Elliptic Curve Discrete Logarithm Problem (ECDLP) to confuse data. The main advantage of the proposed algorithm is its high efficiency and capability. The plaintext can be encrypted in blocks in parallel, thus saves computational time. The proposed algorithm also can be easily applied in a hybrid scheme for practical applications.

With the development of modern communication technology, an increasing number of people are choosing to communicate end-to-end over the network. However, the risk of information leakage and data tampering has also increased, and the issue of information confidentiality has become an increasing concern. Among the existing encryption algorithms, symmetric encryption algorithms cannot securely manage the key and share the key between communication parties; ECC and other public key encryption algorithms have problems such as slow encryption and decryption speed, low encryption strength, etc. In addition, key management is still not guaranteed to be very secure; conventional hybrid encryption algorithms need to manage two different types of keys, and key management may be very complicated and prone to key leakage or theft. Based on the problems of the above algorithms, this paper proposes RSA-Co-CP-ABE Architecture, which uses socket communication, encrypts the RSA public key passed from Client to Server with CP-ABE, encrypts the confidential message with the public key passed from Client at Server, and finally sends the encrypted message to Client. This scheme has higher flexibility than the traditional symmetric encryption and public key encryption schemes, and by using CP-ABE encryption, it can realize attribute-based access control. And RSA encryption can make the scheme make a better balance between encryption and decryption efficiency and encryption strength. In addition, because the communication is transmitted in full cipher text during the communication, the scheme can effectively resist tampering or stealing by man-in-the-middle attacks.

Wireless radio frequency identification (RFID) has been widely used as the core technology of the Internet of Things, but it also brings many potential security risks. In this paper, two typical RFID security authentication protocols are analyzed in depth. The results show that the two protocols have security risks, and two targeted attack methods are proposed. Next, two RFID security authentication protocols which can resist the DoS, replay, and tracing attacks are designed. The first protocol uses index grouping and dynamic renewal mechanism. Since the Rabin public key encryption algorithm verification only requires square and modulo operations, the second protocol introduces the public key encryption algorithm into the cost-sensitive RFID tag, and formally verifies the functionality of the proposed scheme by SPIN. Furthermore, the security of the protocol is proven by the BAN logic. The grouping index method can effectively improve the ability to locate tags in a large database and enhance the practicability of the protocol. The introduction of the Rabin public key algorithm improves the security of the protocol under the condition of cost control.

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.

Improving the computational efficiency of modular operations for embedded systems

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.

The beyond 5G networks (B5G) are characterized by high throughputs at extremely low latencies and better energy consumptions. This has seen them being deployed as the backbone of numerous Internet of Things (IoT) application domains such as smart homes, smart cities and in intelligent transport systems. Massive and private data flows in these ultra-dense networks and hence the need to protect them. As such, the Third-Generation Partnership Project (3GPP) has defined Authentication and Key Agreement (AKA) protocols for secure signaling and packet exchanges in these networks. However, these AKA protocols are susceptible to numerous attacks, such as impersonation and packet replays. This has seen the development of numerous schemes based on techniques such as public key cryptography, biometrics, group signatures and blockchain. Unfortunately, these schemes fail to offer the required levels of security and privacy protection at low execution time, energy and bandwidths. In this paper, a protocol is developed that leverages on the message authentication codes, symmetric cryptography and elliptic curve cryptography. It is shown that the proposed protocol is secure under the Dolev–Yao model. In terms of performance, it exhibited the lowest execution time and has the lowest bandwidth requirements.KeywordsAuthenticationCryptographyDolev–YaoECCKey agreementPrivacySecurity

In this paper, we present an evaluation of possible ARM instruction set extension for elliptic curve cryptography (ECC) over binary finite fields GF(2/sup m/). The use of elliptic curve cryptography is becoming common in embedded domain, where its reduced key size at a security level equivalent to standard public-key methods (such as RSA) allows for power consumption savings and more efficient operation. ARM processor was selected because it is widely used for embedded system applications. We developed an ECC benchmark set with three widely used public-key algorithms: Diffie-Hellman for key exchange, digital signature algorithm, as well as El-Gamal method for encryption/decryption. We analyzed the major bottlenecks at function level and evaluated the performance improvement, when we introduce some simple architectural support in the ARM ISA. Results of our experiments show that the use of a word-level multiplication instruction over binary field allows for an average 33% reduction of the total number of dynamically executed instructions, while execution time improves by the same amount when projective coordinates are used.

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.

In order to improve the security in the process of audio files in Internet communication, first Construct a generating chaotic sequence of six dimensional cellular neural network model, according to the principle of RSA asymmetric encryption algorithm, proposes a location of any number as a transmission key(Coordinate key) in the chaotic sequence and using the public key and RSA encryption algorithm for it. Then the number corresponding to this key position, as the starting point of Chebyev chaotic mapping, and to generate encryption sequence. Finally encrypt the original audio and send to receiver with the transport key. In order to verify the practicability of the algorithm, we made a simulation experiment, the complexity of the test the transmission key and comparison of the original audio and the encryption audio waveform figure, and proves the feasibility of this kind of encryption algorithm through the correlation analysis, spectrum analysis and sensitivity analysis. There is the broad prospect and the important application of chaotic and RSA encryption technology.

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.

Cryptanalysis of the Wu–Dawson Public Key Cryptosystem

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 efficiency with which an integer may be factored into its prime factors determines several public key cryptosystems’ security in use today. Although there is a quantum-based technique with a polynomial time for integer factoring, on a traditional computer, there is no polynomial time algorithm. We investigate how to enhance the wheel factoring technique in this paper. Current wheel factorization algorithms rely on a very restricted set of prime integers as a base. In this study, we intend to adapt this notion to rely on a greater number of prime integers, resulting in a considerable improvement in the execution time. The experiments on composite numbers n reveal that the proposed algorithm improves on the existing wheel factoring algorithm by about 75%.

Mobile devices now serve to pay for goods and services by means of the transmission of data, a system known as mobile payments. Mobile payment is receiving growing attention globally, from consumers to merchants, as an alternative to using cash, check, or credit cards. Most encryption techniques applied in mobile payment are based on traditional public key infrastructure. However, the traditional public key encryption algorithm has higher requirements for hardware, which is not suitable for mobile terminals of limited computing resources. In addition, these public key encryption algorithms are vulnerable to quantum computing attacks and the availability of practical quantum computer is approaching faster than previously believed. Since mobile payment is facing more and more security issues, how to complete the payment process effectively and securely becomes a problem urgently to be solved. In this paper, we firstly analyze the problem of the signature scheme for mobile payment and propose an improved signature scheme based on the Number Theory Research Unit (NTRU). The results of the experiment show that the proposed signature scheme is secure and efficient which can raise the speed and probability of generating reasonable signature value. Second, we introduce a new public key infrastructure NTRU-WPKI and design a third-party mobile payment model based on NTRU-WPKI to increase the efficiency and security. Finally, by doing the overall simulation, we prove that our model is highly effective and secure.