Biblio

Methods for implementing integer arithmetic operations of addition, subtraction, and multiplication in the system of residual classes are considered. It is shown that their practical use in computer systems can significantly improve the performance of the implementation of arithmetic operations. A new method has been developed for raising numbers represented in the system of residual classes to an arbitrary power of a natural number, both in positive and in negative number ranges. An example of the implementation of the proposed method for the construction of numbers represented in the system of residual classes for the value of degree k = 2 is given.

The security of current key exchange protocols such as Diffie-Hellman key exchange is based on the hardness of number theoretic problems. However, these key exchange protocols are threatened by weak random number generators, advances to CPU power, a new attack from the eavesdropper, and the emergence of a quantum computer. Quantum Key Distribution (QKD) addresses these challenges by using quantum properties to exchange a secret key without the risk of being intercepted. Recent developments on the QKD system resulted in a stable key generation with fewer errors so that the QKD system is rapidly becoming a solid commercial proposition. However, although the security of the QKD system is guaranteed by quantum physics, its careless implementation could make the system vulnerable. In this paper, we proposed the first side-channel attack on plug-and-play QKD system. Through a single electromagnetic trace obtained from the phase modulator on Alice's side, we were able to classify the electromagnetic trace into four classes, which corresponds to the number of bit and basis combination in the BB84 protocol. We concluded that the plug-and-play QKD system is vulnerable to side-channel attack so that the countermeasure must be considered.

Nowadays public-key cryptography is based on number theory problems, such as computing the discrete logarithm on an elliptic curve or factoring big integers. Even though these problems are considered difficult to solve with the help of a classical computer, they can be solved in polynomial time on a quantum computer. Which is why the research community proposed alternative solutions that are quantum-resistant. The process of finding adequate post-quantum cryptographic schemes has moved to the next level, right after NIST's announcement for post-quantum standardization. One of the oldest quantum-resistant proposition goes back to McEliece in 1978, who proposed a public-key cryptosystem based on coding theory. It benefits of really efficient algorithms as well as a strong mathematical background. Nonetheless, its security has been challenged many times and several variants were cryptanalyzed. However, some versions remain unbroken. In this paper, we propose to give some background on coding theory in order to present some of the main flawless in the protocols. We analyze the existing side-channel attacks and give some recommendations on how to securely implement the most suitable variants. We also detail some structural attacks and potential drawbacks for new variants.

In this paper, we propose a new color image encryption and compression algorithm based on the DNA complementary rule and the Chinese remainder theorem, which combines the DNA complementary rule with quantum chaotic map. We use quantum chaotic map and DNA complementary rule to shuffle the color image and obtain the shuffled image, then Chinese remainder theorem from number theory is utilized to diffuse and compress the shuffled image simultaneously. The security analysis and experiment results show that the proposed encryption algorithm has large key space and good encryption result, it also can resist against common attacks.

Route selection is a very sensitive activity for mobile ad-hoc network (MANET) and ranking of multiple routes from source node to destination node can result in effective route selection and can provide many other benefits for better performance and security of MANET. This paper proposes an evaluation model based on analytical hierarchy process (AHP), fuzzy sets and technique for order performance by similarity to ideal solution (TOPSIS) to provide a useful solution for ranking of routes. The proposed model utilizes AHP to acquire criteria weights, fuzzy sets to describe vagueness with linguistic values and triangular fuzzy numbers, and TOPSIS to obtain the final ranking of routes. Final ranking of routes facilitates selection of best and most reliable route and provide alternative options for making a robust Mobile Ad-hoc network.