Modern Cryptography

Cryptography is the art and science of using mathematical methods to preserve message security. There are two types of cryptography, namely classical and modern cryptography. Nowadays, most people would rather use modern cryptography than classical cryptography because it is harder to break than the classical one. One of classical algorithm is the Zig-zag algorithm that uses the transposition technique: the original message is unreadable unless the person has the key to decrypt the message. To improve the security, the Zig-zag Cipher is combined with RC4+ Cipher which is one of the symmetric key algorithms in the form of stream cipher. The two algorithms are combined to make a super-encryption. By combining these two algorithms, the message will be harder to break by a cryptanalyst. The result showed that complexity of the combined algorithm is θ(n2), while the complexity of Zig-zag Cipher and RC4+ Cipher are θ(n2) and θ(n), respectively.

Interactive behaviors are ubiquitous in modern cryptography, but are also present in $$\lambda $$ -calculi, in the form of higher-order constructions. Traditionally, however, typed $$\lambda $$ -calculi simply do not fit well into cryptography, being both deterministic and too powerful as for the complexity of functions they can express. We study interaction in a $$\lambda $$ -calculus for probabilistic polynomial time computable functions. In particular, we show how notions of context equivalence and context metric can both be characterized by way of traces when defined on linear contexts. We then give evidence on how this can be turned into a proof methodology for computational indistinguishability, a key notion in modern cryptography. We also hint at what happens if a more general notion of a context is used.

On the Concept of Trusted Computing and Software Watermarking: A Computational Complexity Treatise

Quantum cryptography has become a subject of widespread interest. In particular, quantum key distribution, which provides a secure key agreement by using quantum systems, is believed to be the most important application of quantum cryptography. Quantum key distribution has the potential to achieve the “unconditionally” secure infrastructure. We also have many cryptographic tools that are based on “modern cryptography” at the present time. They are being used in an effort to guarantee secure communication over open networks such as the Internet. Unfortunately, their ultimate efficacy is in doubt. Quantum key distribution systems are believed to be close to practical and commercial use. In this paper, we discuss what we should do to apply quantum cryptography to our communications. We also discuss how quantum key distribution can be combined with or used to replace cryptographic tools based on modern cryptography.

This study explores the intersection of algebraic topology and modern cryptography, shedding light on how topological concepts can enhance cryptographic techniques. By leveraging algebraic structures and their applications, it introduces novel perspectives on cryptographic frameworks. The research suggests that reorganizing cryptographic components through algebraic binary relations can lead to more secure and efficient systems. Blending theoretical insights with practical implementations, the study demonstrates how topological principles can address contemporary cryptographicchallenges. Furthermore, it underscores the significance of interdisciplinary collaboration by highlighting advancements in secure communication and data integrity. In an increasingly digital era, the findings advocate for the integration ofmathematical frameworks into cryptographic processes, paving the way for innovative security solutions. By establishing algebraic topology as a foundational element in strengthening the resilience and adaptability of cryptographic systems, this work fosters interdisciplinary research and the exploration of new paradigms in secure information processing.

The Diffie-Hellman problem as a cryptographic primitive plays an important role in modern cryptology. The Bit Security or Hard-Core Bits of Diffie-Hellman problem in arbitrary finite cyclic group is a long-standing open problem in cryptography. Until now, only few groups have been studied. Hyperelliptic curve cryptography is an alternative to elliptic curve cryptography. Due to the recent cryptanalytic results that the best known algorithms to attack hyperelliptic curve cryptosystems of genus \(g<3\) are the generic methods and the recent implementation results that hyperelliptic curve cryptography in genus 2 has the potential to be competitive with its elliptic curve cryptography counterpart. In this paper, we generalize Boneh and Shparlinksi’s method and result about elliptic curve to the case of Jacobians of hyperelliptic curves. We prove that the least significant bit of each coordinate of hyperelliptic curves Diffie-Hellman secret value in genus 2 is hard as the entire Diffie-Hellman value, and then we also show that any bit is hard as the entire Diffie-Hellman value. Finally, we extend our techniques and results to hyperelliptic curves of any genus.

Abstract—Modular design is a common approach for dealing with complex tasks in modern cryptology. The critical of this approach is that designing a secure hybrid protocol. In this paper, we study password-based key exchange in the three-party setting within the UC framework and design a hybrid protocol that UC-securely realizes such task. That is, we firstly define an appropriate ideal functionality F3-pwKE for password-based three-party key exchange. Next we partition the task into two sub-tasks, three-party key distribution and password-based two-party key exchange, and propose relevant two ideal functionalities, F3-KD, FpwKE. Finally, we present a (F3-KD, FpwKE)-hybrid protocol for password-based three-party key exchange that is proved to be UC-secure with respect to non- adaptive party corruption.

S-box structures used in the encryption architecture are of great importance for constructing powerful block encryption systems, which hold an important place in modern cryptology. The design of S-boxes with sound cryptographic characteristics is of utmost importance for constructing powerful encryption systems. In this study, an S-box design algorithm based on time-delay chaotic systems is proposed. The proposed algorithm is considered relative to other algorithms in the literature as more useful according to such criteria as simplicity and efficient implementation. Theoretical analysis and computer simulations demonstrated that the proposed algorithm meets all the performance requirements for the S-box design criteria, and also verified the efficient and practical structure of the algorithm.

Summary form only given. Along with the rapid development and wide application of Internet technique, the research about communication security becomes a very important topic in theory and the practice. For the explicitness and large information content of images, much attention has been paid to the security of image storing and transmission in communication. As one of the key technique of digital image security problem, the digital image scrambling technique can be seem as one of the method for digital image encryption and used for digital image hiding, digital watermark, precondition, and after-treatment process of numerical resume for image deposit. Most digital image scrambling technique are based on the Arnold transformation, magic square, and fractal etc. By the Arnold transformation, the image becomes more and more complicity, but the image is recovered in a certain moment. In this way, the hiding purpose for image in communication can be reached. The periodicity of the two-dimensional Arnold transformation was discussed in many literatures. The necessary and sufficient condition about the existence of periodicity for the general Arnold matrix transformation had been given in literatures. The periodicity of n-dimensional Arnold transformation had been discussed in literatures. Some new image scrambling method based on three-dimensional Arnold transformation had been given in literatures. In this paper, we extend the conclusion about the periodicity of n-dimensional Arnold transformation, apply it in digital image scrambling, and give the key-dependent digital image scrambling scheme. For the n-dimensional transformation, the necessary and sufficient condition about the existence of periodicity is gcd(|A|, N)=1, where |A|=det(A) and A is the transformation matrix, N is module. We define the transformation satisfied above character to n-dimensional Arnold-type transformation. Obviously, we can derive the conclusion that the n-dimensional Arnold-type transformation is periodic. Using properties of the similar matrixes, we can derive the following conclusion. For a given module N, if the n-dimensional Arnold-type transformation matrix A is similar to B, then the period of transformation A is equal to that of transformation B. There is a shortcoming for the application of the Arnold transformation in digital image hiding. The security of the algorithm is based on the assumption that the attacker doesn't know about the algorithm (i.e. the attacker don't know the transformation matrix). If the attacker know about the algorithm, it is easy to recover the image. So this algorithm doesn't fill the requirement of the modern cryptography. However, we can apply the above n-dimensional Arnold-type transformation to avoid this lack. It can ensure the security of the digital image scrambling by the secrete key even the algorithm is public. We select a n-dimensional invertible matrix as the secrete key, then derive transformation matrix. In this paper, we extend the conclusion which about the Arnold transformation in the former paper using the property of the similar matrix and a digital image scrambling scheme is proposed by a kind of Arnold-type transformation in order to raise the security of the image scrambling.

Cryptography is the practice of securing information through the use of codes, ciphers, and other methods of encryption. It is an essential aspect of modern communication, enabling the secure transmission of data over networks and protecting sensitive information from unauthorized access. Cryptography has been used throughout history to protect messages from interception and decipherment. In ancient times, cryptography was used by military leaders and diplomats to communicate confidential information. Over time, cryptographic techniques have become more sophisticated, and modern cryptography now employs complex algorithms and mathematical principles.Today, cryptography is used in various applications, including online banking, e-commerce, secure messaging, and government communication. Cryptography also plays a critical role in securing sensitive information such as medical records, personal data, and intellectual property.As technology continues to evolve, the importance of cryptography will only increase. Cryptography ensures the confidentiality, integrity, and authenticity of data, and it is an essential tool for protecting digital assets and maintaining trust in the online world. Literature Review: Cryptography has been a subject of interest in computer science and mathematics for decades. The literature on cryptography is vast and covers a wide range of topics, including encryption algorithms, key management, and protocols for secure communication. One of the earliest and most well-known encryption algorithms is the Caesar cipher, which was used by Julius Caesar to encode his messages. Since then, numerous encryption techniques have been developed, including symmetric-key cryptography and public-key cryptography.Symmetric-key cryptography involves the use of a single key for both encryption and decryption, while public-key cryptography uses two keys, one for encryption and one for decryption.In recent years, research on post-quantum cryptography has gained significant attention due to the potential threat quantum computers pose to current encryption methods. Post- quantum cryptography aims to develop algorithms that are resistant to quantum attacks.

Article Free AccessOne-way functions are necessary and sufficient for secure signatures Author: J. Rompel Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MAView Profile Authors Info & Claims STOC '90: Proceedings of the twenty-second annual ACM symposium on Theory of ComputingApril 1990 Pages 387–394https://doi.org/10.1145/100216.100269Published:01 April 1990Publication History 433citation1,331DownloadsMetricsTotal Citations433Total Downloads1,331Last 12 Months122Last 6 weeks33 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

: Cryptographic hash functions are fundamental primitives in modern cryptography and have many security applications (data integrity checking, cryptographic protocols, digital signatures, pseudo random number generators etc.). At the same time novel hash functions are designed (for instance in the framework of the SHA-3 contest organized by the National Institute of Standards and Technology (NIST)), the cryptanalysts exhibit a set of statistical metrics (propagation criterion, frequency analysis etc.) able to assert the quality of new proposals. Also, rules to design good hash functions are now known and are followed in every reasonable proposal of a new hash scheme. This article investigates the ways to build on this experiment and those metrics to generate automatically compression functions by means of Evolutionary Algorithms (EAs). Such functions are at the heart of the construction of iterative hash schemes and it is therefore crucial for them to hold good properties. Actually, the idea to use nature-inspired heuristics for the design of such cryptographic primitives is not new: this approach has been successfully applied in several previous works, typically using the Genetic Programming (GP) heuristic [1]. Here, we exploit a hybrid meta-heuristic for the evolutionary process called Gene Expression Programming (GEP) [2] that appeared far more efficient computationally speaking compared to the GP paradigm used in the previous papers. In this context, the GEPHashSearch framework is presented. As it is still a work in progress, this article focuses on the design aspects of this framework (individuals definitions, fitness objectives etc.) rather than on complete implementation details and validation results. Note that we propose to tackle the generation of compression functions as a multi-objective optimization problem in order to identify the Pareto front i.e. the set of non-dominated functions over the four fitness criteria considered. If this goal is not yet reached, the first experimental results in a mono-objective context are promising and open the perspective of fruitful contributions to the cryptographic community.

Semantic-security of individual plaintext bits given the corresponding ciphertext is a fundamental notion in modern cryptography. We initiate the study of this basic problem for Order-Preserving Encryption (OPE), asking “what plaintext information can be semantically hidden by OPE encryptions?” OPE has gained much attention in recent years due to its usefulness for secure databases, and has received a thorough formal treamtment with innovative and useful security notions. However, all previous notions are one-way based, and tell us nothing about partial-plaintext indistinguishability (semantic security).

The security of a file is a matter of concern in maintaining the confidentiality of information, especially those containing information that only the authorized parties may know about. Sending files or information without security will risk tapping and the information contained therein, can be easily known by unauthorized parties. One important thing in maintaining the confidentiality and security of files is the encryption process. Then based on techniques in cryptography, one of the methods that will be used in securing text files with the Spritz algorithm. Modern cryptography is more trusted by scientists than classical cryptography because it has a good level of security. Classical cryptography only does randomization from A-Z while modern cryptography operates in bit mode. The modern algorithm used is the Spritz algorithm. The Spritz algorithm is a variant of the RC4 algorithm, the security level of the Spritz algorithm is better than RC4

The addition chain for a given exponent $n$ is an increasing sequence of positive integers: its first term is $1$, and each subsequent term is obtained by adding the previous two terms which can be the same , so that the last element of the sequence is equal to $n$. Constructing the shortest addition chain for a fixed exponent $n$ is the most efficient method for computing $x^n$ in some group under multiplication. Therefore, the addition chain plays a crucial role in modern cryptography. It can improve the computational efficiency of cryptographic algorithms that require fast exponentiation, such as RSA, ElGamal, Paillier, and ECC, etc. However, the problem of finding the shortest additive chain is textbf{NP}-Complete. Moreover, the existing evolutionary algorithms can not work well for finding short addition chains for large integers. This paper integrates genetic algorithms with the window method to obtain an efficient strategy for the addition chain problem involving large integers. We do experiments on an RSA-1536 modulus to verify the efficiency and practicability of our algorithm.