• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• v.9 no.1
• /
• pp.928-930
• /
• 2005

With an increasing importance of the information security issues, the efficienct calculation process in terms of finite field level is becoming more important in the Elliptic curve cryptosystems. Serial multiplication architectures are based on the Mastrovito's serial multiplier structure. In this paper, we manipulate the numerical expressions so that we could suggest a 3-times as fast as (3x) the Mastrovito's multiplier using the polynomial basis. The architecture was implemented with HDL, to be evaluated and verified with EDA tools. The implemented 3x GF (Galois Field) multiplier showed 3 times calculation speed as fast as the Mastrovito's, only with the additional partial-sum generation processing unit.

• International Journal of Computer Science & Network Security
• /
• v.21 no.8
• /
• pp.17-27
• /
• 2021

Non-abelian group based cryptosystems are a latest research inspiration, since they offer better security due to their non-abelian properties. In this paper, we propose a novel approach to non-abelian group based public-key cryptographic protocols using semidirect products of finite groups. An intractable problem of determining automorphisms and generating elements of a group is introduced as the underlying mathematical problem for the suggested protocols. Then, we show that the difficult problem of determining paths and cycles of Cayley graphs including Hamiltonian paths and cycles could be reduced to this intractable problem. The applicability of Hamiltonian paths, and in fact any random path in Cayley graphs in the above cryptographic schemes and an application of the same concept to two previous cryptographic protocols based on a Generalized Discrete Logarithm Problem is discussed. Moreover, an alternative method of improving the security is also presented.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.9 no.1
• /
• pp.135-146
• /
• 1999

Most public key cryptosystems are constructed based on a modular exponentiation, which is further decomposed into a series of modular multiplications. We design a new systolic array multiplier to speed up modular multiplication using Montgomery algorithm. This multiplier with simple circuit for each processing element will save about 14% logic gates of hardware and 20% execution time compared with previous one.

• International Journal of Computer Science & Network Security
• /
• v.21 no.4
• /
• pp.289-300
• /
• 2021

Non-abelian group based Cryptography is a field which has become a latest trend in research due to increasing vulnerabilities associated with the abelian group based cryptosystems which are in use at present and the interesting algebraic properties associated that can be thought to provide higher security. When developing cryptographic primitives based on non-abelian groups, the researchers have tried to extend the similar layouts associated with the traditional underlying mathematical problems and assumptions by almost mimicking their operations which is fascinating even to observe. This survey contributes in highlighting the different analogous extensions of traditional assumptions presented by various authors and a set of open problems. Further, suggestions to apply the Hamiltonian Cycle/Path Problem in a similar direction is presented.

• The KIPS Transactions:PartC
• /
• v.13C no.2 s.105
• /
• pp.137-146
• /
• 2006

Because the traditional public key-based cryptosystems are unsuitable for the sensor node with limited computational and communication capability, a secure communication between two neighbor sensor nodes becomes an important challenging research in sensor network security. Therefore several session key establishment protocols have been proposed for that purpose. In this paper, we analyzed and compared the existing session key establishment protocols based on the criterions of generation strategy and uniqueness of the session key, connectivity, overhead of communication and computation, and vulnerability to attacks. Based on the analysis results, we specify the requirements for the secure and efficient protocols for establishing session keys. Then, we propose an advanced protocol to satisfy the specified requirements and verify the superiority of our protocol over the existing protocols through the detailed analysis.

• Journal of Information Processing Systems
• /
• v.6 no.3
• /
• pp.335-346
• /
• 2010

The present study investigates the difficulty of solving the mathematical problem, namely the DLP (Discrete Logarithm Problem) for ephemeral keys. The DLP is the basis for many public key cryptosystems. The ephemeral keys are used in such systems to ensure security. The DLP defined on a prime field $Z^*_p of random prime is considered in the present study. The most effective method to solve the DLP is the ICM (Index Calculus Method). In the present study, an efficient way of computing the DLP for ephemeral keys by using a new variant of the ICM when the factors of p-1 are known and small is proposed. The ICM has two steps, a pre-computation and an individual logarithm computation. The pre-computation step is to compute the logarithms of a subset of a group and the individual logarithm step is to find the DLP using the precomputed logarithms. Since the ephemeral keys are dynamic and change for every session, once the logarithms of a subset of a group are known, the DLP for the ephemeral key can be obtained using the individual logarithm step. Therefore, an efficient way of solving the individual logarithm step based on the newly proposed precomputation method is presented and the performance is analyzed using a comprehensive set of experiments. The ephemeral keys are also solved by using other methods, which are efficient on random primes, such as the Pohlig-Hellman method, the Van Oorschot method and the traditional individual logarithm step. The results are compared with the newly proposed individual logarithm step of the ICM. Also, the DLP of ephemeral keys used in a popular password key exchange protocol known as Chang and Chang are computed and reported to launch key recovery attack.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.14 no.9
• /
• pp.3841-3857
• /
• 2020

RSA is one of the best well-known public key cryptosystems. This methodology is widely used at present because there is not any algorithm which can break this system that has all strong parameters within polynomial time. However, it may be easily broken when at least one parameter is weak. In fact, many weak parameters are already found and are solved by some algorithms. Some examples of weak parameters consist of a small private key, a large private key, a small prime factor and a small result of the difference between two prime factors. In this paper, the new weakness of RSA is proposed. Assuming Euler's totient value, Φ (n), can be rewritten as Φ (n) = ad + b, where d is the private key and a, b ∈ ℤ, if a divides both of Φ (n) and b and the new exponent for the decryption equation is a small integer, this condition is assigned as the new weakness for breaking RSA. Firstly, the specific algorithm which is created for this weakness directly is proposed. Secondly, two equations are presented to find a, b and d. In fact, one of two equations must be implemented to find a and b at first. After that, the other equation is chosen to find d. The experimental results show that if this weakness has happened and the new exponent is small, original plaintext, m, will be recovered very fast. Furthermore, number of steps to recover d are very small when a is large. However, if a is too large, d may not be recovered because m which must be always written as m = h^a is higher than modulus.

• Journal of KIISE:Computer Systems and Theory
• /
• v.30 no.1
• /
• pp.50-58
• /
• 2003

Among finite field arithmetic operations, the $AB^2$ operation is known as an efficient basic operation for public key cryptosystems over $GF(2^m)$,Division/Inversion is computed by performing the repetitive AB$^2$ multiplication. This paper presents two new $AB^2$algorithms and their systolic realizations in finite fields $GF(2^m)$.The proposed algorithms are based on the MSB-first scheme using standard basis representation and the proposed systolic architectures for $AB^2$ multiplication have a low hardware complexity and small latency compared to the conventional approaches. Additionally, since the proposed architectures incorporate simplicity, regularity, modularity, and pipelinability, they are well suited to VLSI implementation and can be easily applied to inversion architecture. Furthermore, these architectures will be utilized for the basic architecture of crypto-processor.

• Smart Media Journal
• /
• v.12 no.2
• /
• pp.76-82
• /
• 2023

In the 4th industrial revolution, the blockchain that distributes and manages data through a P2P network is used as a new decentralized networking paradigm in various fields such as manufacturing, culture, and public service. However, with the advent of quantum computers, quantum algorithms that are able to break existing cryptosystems such as hash function, symmetric key, and public key cryptography have been introduced. Currently, because most major blockchain systems use an elliptic curve cryptography to generate signatures for transactions, they are insecure against the quantum adversary. For this reason, the research on the quantum-resistant blockchain that utilizes lattice-based cryptography for transaction signatures is needed. Therefore, in this paper, we propose a blind signature scheme for the blockchain in which the contents of the signature can be verified later, as well as signing by hiding the contents to be signed using lattice-based cryptography with the property of quantum resistance. In addition, we prove the security of the proposed scheme using a random oracle model.

• Journal of Korea Society of Industrial Information Systems
• /
• v.9 no.4
• /
• pp.41-46
• /
• 2004

This paper presents a new semi- systolic architecture for $AB^2$ operation. First of all the previous architecture proposed by Lee et al. is analysed and then we present a new algorithm and it's architecture for $AB^2$ operation based on AOP (all one polynomial) to solve the shortcomings in the architecture. Proposed architecture has an efficient configuration than other previous architectures. It is useful for implementing the exponentiation architecture, which is the core operation in public-key cryptosystems.