Symmetric-key algorithms are a type of encryption method where the same key is used for both encryption and decryption of data. This means that the sender and the receiver must both possess the same secret key, and its security is paramount because anyone who has access to the key can decrypt the data. ### Key Characteristics: 1. **Same Key for Encryption and Decryption**: The same secret key is used for both the processes, which simplifies the encryption and decryption process.

Equihash is a proof-of-work (PoW) algorithm designed to be memory-hard, which means it requires a significant amount of memory to compute, making it more resistant to specialized hardware such as ASICs (Application-Specific Integrated Circuits). It is primarily used for cryptocurrencies that aim to promote decentralization and reduce the advantages of mining with specialized equipment. The algorithm was proposed by Alex Biryukov and Dmitry Khovratovich in 2016.

Crypto++ is a free and open-source cryptographic library written in C++. It provides a wide array of cryptographic algorithms and protocols, which are essential for building secure applications. The library includes implementations of various symmetric and asymmetric encryption algorithms, hashing functions, message authentication codes, random number generation, and more. Crypto++ is designed for performance and portability, making it suitable for use on different platforms and architectures.

Cryptographic agility refers to the design property of a system or protocol that allows it to support multiple cryptographic algorithms and key sizes, enabling it to adapt to new cryptographic standards and advances in technology. This is particularly important because cryptographic algorithms can become vulnerable over time due to advances in computational power, cryptanalysis, or the emergence of new threats (such as quantum computing).

Modular exponentiation is a mathematical operation that computes the value of \( b^e \mod m \), where \( b \) is the base, \( e \) is the exponent, and \( m \) is the modulus. It is particularly useful in fields such as cryptography, number theory, and computer science, especially when working with large numbers, because it allows for efficient computation without having to compute the potentially enormous number \( b^e \) directly.

ISMACryp is an encryption standard developed for securing data in information systems. Specifically, it is based on the principles of the ISO/IEC 18033-3 standard, which pertains to the encryption of data and is related to symmetric key algorithms. ISMACryp is part of a family of cryptographic methods designed to provide confidentiality and integrity of information.

Locality-Sensitive Hashing (LSH) is a technique used to reduce the dimensionality of data while preserving the locality of points in a high-dimensional space. It is especially useful for tasks like nearest neighbor search and similarity detection in large datasets. ### Key Features of LSH: 1. **Locality Preservation**: LSH maps similar input items to the same "buckets" with high probability, while dissimilar items are mapped to different buckets.

A Linear Feedback Shift Register (LFSR) is a type of sequential circuit that consists of a shift register and a linear feedback mechanism. It is widely used in digital systems for a variety of applications, including pseudorandom number generation, cryptography, error detection and correction, and digital signal processing.

Ring Learning With Errors (Ring-LWE) is a crucial concept in modern cryptography, particularly in the realm of post-quantum cryptography. It is built upon the Learning With Errors (LWE) problem, which is a well-known problem believed to be hard to solve even for quantum computers. The Ring-LWE problem leverages the structure of polynomial rings, making it more efficient than standard LWE while maintaining similar levels of security.

A Substitution-Permutation Network (SPN) is a type of symmetric key cipher used for the encryption and decryption of data. It combines two fundamental operations: substitution, which alters the bits in a specified manner, and permutation, which rearranges those bits. This approach is integral to many modern block ciphers and is designed to provide strong security properties through diffusion and confusion. ### Key Components of a Substitution-Permutation Network 1.

A chosen-plaintext attack (CPA) is a type of cryptographic attack in which the attacker has the capability to choose arbitrary plaintexts to be encrypted and has access to their corresponding ciphertexts. This ability allows the attacker to gain information about the encryption algorithm and (potentially) the secret key used in the encryption process.

A differential-linear attack is a cryptanalysis technique used to analyze block ciphers. It combines two different methods of cryptanalysis: differential cryptanalysis and linear cryptanalysis. ### Key Concepts: 1. **Differential Cryptanalysis**: This method focuses on how differences in input pairs can produce differences in the output pairs after passing through the encryption process. It involves studying how specific input differences propagate through the rounds of the cipher and how they affect the output difference.

Side-channel attacks are techniques used to extract sensitive information from a system by analyzing the indirectly related data rather than exploiting direct vulnerabilities. These attacks often take advantage of the physical implementation of a system, rather than flaws in its algorithms or protocols. ### Types of Side-Channel Information: 1. **Timing Information**: Variations in the time taken to execute cryptographic algorithms based on the input data can reveal secrets.

An Adaptive Chosen-Ciphertext Attack (CCA) is a type of cryptographic attack model where the attacker has the ability to choose ciphertexts and obtain their corresponding plaintexts, potentially multiple times, in a manner that adapts based on the information learned from previous queries. This is a more powerful attack model than a standard chosen-ciphertext attack, as it allows the attacker to refine their strategy based on the feedback received from the decryption of the chosen ciphertexts.

Spacecraft attitude control refers to the techniques and systems used to manage and control the orientation of a spacecraft in space. The "attitude" of a spacecraft describes its orientation in three-dimensional space, which is crucial for various operations, such as: 1. **Pointing Sensors and Instruments**: Accurate orientation allows spacecraft to direct instruments, antennas, and other equipment towards specific targets, such as Earth, other celestial bodies, or communication satellites.

Vibrational analysis with scanning probe microscopy (SPM) refers to a set of techniques that combine the capabilities of scanning probe microscopy (such as atomic force microscopy, or AFM, and scanning tunneling microscopy, or STM) with vibrational spectroscopy techniques to study the vibrational modes and properties of materials at the nanoscale.

A Porkchop plot is a type of diagram used in astrodynamics and celestial mechanics to illustrate the relationship between two key parameters of a spacecraft trajectory, typically the delta-v (change in velocity) and the time of flight. It is often employed in mission planning for interplanetary travel, where trajectories between two bodies (like planets or moons) need to be optimized. The name "Porkchop plot" comes from the shape of the graph, which resembles a pork chop.

Jacobi's four-square theorem is an extension of Lagrange's four-square theorem, which states that every positive integer can be expressed as the sum of four squares. Jacobi's contribution to this area lies in his work on representing numbers as sums of squares and his formulation of a more explicit representation. The theorem states that the number of ways to represent a natural number \( n \) as a sum of four squares can be expressed through a specific counting function.

Legendre's three-square theorem is a result in number theory that describes the conditions under which a positive integer can be expressed as the sum of three squares.

Ramanujan's ternary quadratic form refers to a specific type of quadratic form that is expressed in three variables. One of the most notable forms studied by Srinivasa Ramanujan is given by the equation: \[ x^2 + y^2 + z^2 - xyz \] This particular form is significant in number theory and has connections to various mathematical problems, including partitions and representations of numbers as sums of squares.