Chaos and Cellular Automata-Based Substitution Box and Its Application in Cryptography

Substitution boxes are the key factor in symmetric-key cryptosystems that determines their ability to resist various cryptanalytic attacks. Creating strong substitution boxes that have multiple strong cryptographic properties at the same time is a challenging task for cryptographers. A significant amount of research has been conducted on S-boxes in the past few decades, but the resulting S-boxes have been found to be vulnerable to various cyberattacks. This paper proposes a new method for creating robust S-boxes that exhibit superior performance and possess high scores in multiple cryptographic properties. The hybrid S-box method presented in this paper is based on Chua’s circuit chaotic map, two-dimensional cellular automata, and an algebraic permutation group structure. The proposed 16×16 S-box has an excellent performance in terms of security parameters, including a minimum nonlinearity of 102, the absence of fixed points, the satisfaction of bit independence and strict avalanche criteria, a low differential uniformity of 5, a low linear approximation probability of 0.0603, and an auto-correlation function of 28. The analysis of the performance comparison indicates that the proposed S-box outperforms other state-of-the-art S-box techniques in several aspects. It possesses better attributes, such as a higher degree of inherent security and resilience, which make it more secure and less vulnerable to potential attacks

An SVP attack on Vortex

In [BS22], the authors proposed a lattice based hash function that is useful for building zero-knowledge proofs with superior performance. In this short note we analysis the underlying lattice problem with the classic shortest vector problem, and show that 2 out of 15 proposed parameter sets for this hash function do not achieve the claimed security

Optical visual encryption using focused beams and convolutional neural networks

The target of this paper is to implement an optically-based visual encryption system able to work with a large set of optical codes. The optical setup comprises a holographic system designed to generate spirally-polarized highly focused fields and an imaging module able to perform polarimetric analysis. In a previous stage, the optical system is numerically simulated in order to produce synthetic polarimetric distributions that are used to train a convolutional neural network. Interestingly, the way the network is trained depends on the selected state of polarization. Then, secret codes are split in two XOR-connected ones that are optically processed. The corresponding experimental polarimetric distribution is obtained and transmitted to the corresponding recipients, that can recover the code by interrogating the neural network. Finally, combining the two pieces of information, the encrypted message can be decoded

Theoretical Computer Science and Discrete Mathematics

This book includes 15 articles published in the Special Issue "Theoretical Computer Science and Discrete Mathematics" of Symmetry (ISSN 2073-8994). This Special Issue is devoted to original and significant contributions to theoretical computer science and discrete mathematics. The aim was to bring together research papers linking different areas of discrete mathematics and theoretical computer science, as well as applications of discrete mathematics to other areas of science and technology. The Special Issue covers topics in discrete mathematics including (but not limited to) graph theory, cryptography, numerical semigroups, discrete optimization, algorithms, and complexity

A Novel Technique for Secure Data Cryptosystem Based on Chaotic Key Image Generation

أحدثت التطورات في تكنولوجيا المعلومات والاتصالات، خلال العقود الماضية، تغييراً كبيراً في نمط نقل معلومات الأشخاص عبر الإنترنت/الشبكات أو تخزينها. لذا، فإن أحد التحديات الرئيسية هو الحفاظ على هذه المعلومات بصورة آمنة ضد الهجمات. أدرك العديد من الباحثين والمؤسسات أهمية وفوائد التشفير في تحقيق الكفاءة والفاعلية بمختلف جوانب الاتصال الآمن.يتبنى هذا العمل تقنية جديدة لنظام تشفير البيانات الآمن على أساس نظرية الفوضى. تولد الخوارزمية المقترحة مصفوفة مفاتيح ثنائية الأبعاد لها ذات أبعاد الصورة الأصلية والتي تتضمن أرقاما عشوائية تم الحصول عليها من الخريطة الفوضوية اللوجستية أحادية الأبعاد وفق معطيات معاملات التحكم، والتي تتم معالجتها بعد ذلك من خلال تحويل الأجزاء العشرية منها عن طريق دالة إلى مجموعة من الأرقام غير المتكررة التي تؤدي إلى عدد هائل من الاحتمالات الغير قابلة للتوقع (مفكوك ناتج ضرب الصفوف في الأعمدة). يتم إجراء بعثرة مزدوجة للصفوف والأعمدة لقيم الأرقام لعدد محدد من المراحل. بعد ذلك، يتم تنفيذ عمليات XOR بين مصفوفة المفاتيح والصورة الأصلية، والتي تمثل حلاً فعالاً لتشفير البيانات لأي نوع من الملفات (النصية، الصورية، الصوتية، الفيديوية، ... إلخ).أثبتت النتائج أن تقنية التشفير المقترحة تعتبر جدا واعدة وفقا لمعايير القياسات الأمنية حيث أدت إلى تسطيح Histogram للصور المشفرة مقارنة بما هو عليه بالصور الأصلية، في حين أن متوسطات MSE عالية جدا (10115.48) و PSNR منخفضة جدا (8.17)، إلى جانب مؤشر Correlation هو قريب من الصفر و Entropy القريبة من 8 (7.997).The advancements in Information and Communication Technology (ICT), within the previous decades, has significantly changed people’s transmit or store their information over the Internet or networks. So, one of the main challenges is to keep these information safe against attacks. Many researchers and institutions realized the importance and benefits of cryptography in achieving the efficiency and effectiveness of various aspects of secure communication.This work adopts a novel technique for secure data cryptosystem based on chaos theory. The proposed algorithm generate 2-Dimensional key matrix having the same dimensions of the original image that includes random numbers obtained from the 1-Dimensional logistic chaotic map for given control parameters, which is then processed by converting the fractional parts of them through a function into a set of non-repeating numbers that leads to a vast number of unpredicted probabilities (the factorial of rows times columns). Double layers of rows and columns permutation are made to the values of numbers for a specified number of stages. Then, XOR is performed between the key matrix and the original image, which represent an active resolve for data encryption for any type of files (text, image, audio, video, … etc). The results proved that the proposed encryption technique is very promising when tested on more than 500 image samples according to security measurements where the histograms of cipher images are very flatten compared with that for original images, while the averages of Mean Square Error is very high (10115.4) and Peak Signal to Noise Ratio is very low (8.17), besides Correlation near zero and Entropy close to 8 (7.9975)

Twin Column Parity Mixers and Gaston - A New Mixing Layer and Permutation

We introduce a new type of mixing layer for the round function of cryptographic permutations, called circulant twin column parity mixer (CPM), that is a generalization of the mixing layers in KECCAK-f and XOODOO. While these mixing layers have a bitwise differential branch number of 4 and a computational cost of 2 (bitwise) additions per bit, the circulant twin CPMs we build have a bitwise differential branch number of 12 at the expense of an increase in computational cost: depending on the dimension this ranges between $3$ and $3.34$ XORs per bit. Our circulant twin CPMs operate on a state in the form of a rectangular array and can serve as mixing layer in a round function that has as non-linear step a layer of S-boxes operating in parallel on the columns. When sandwiched between two ShiftRow-like mappings, we can obtain a columnwise branch number of 12 and hence it guarantees 12 active S-boxes per two rounds in differential trails. Remarkably, the linear branch numbers (bitwise and columnwise alike) of these mappings is only 4. However, we define the transpose of a circulant twin CPM that has linear branch number of 12 and a differential branch number of 4. We give a concrete instantiation of a permutation using such a mixing layer, named Gaston. It operates on a state of $5 \times 64$ bits and uses $\chi$ operating on columns for its non-linear layer. Most notably, the Gaston round function is lightweight in that it takes as few bitwise operations as the one of NIST lightweight standard ASCON. We show that the best 3-round differential and linear trails of Gaston have much higher weights than those of ASCON. Permutations like Gaston can be very competitive in applications that rely for their security exclusively on good differential properties, such as keyed hashing as in the compression phase of Farfalle

Noisy three-player dilemma game: Robustness of the quantum advantage

Games involving quantum strategies often yield higher payoff. Here, we study a practical realization of the three-player dilemma game using the superconductivity-based quantum processors provided by IBM Q Experience. We analyze the persistence of the quantum advantage under corruption of the input states and how this depends on parameters of the payoff table. Specifically, experimental fidelity and error are observed not to be properly anti correlated, i.e., there are instances where a class of experiments with higher fidelity yields a greater error in the payoff. Further, we find that the classical strategy will always outperform the quantum strategy if corruption is higher than half.Comment: Persistence of the quantum advantage under corruption of the input states is analyzed for a 3-player dilemma game implemented using superconductivity-based quantum processor