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Special-purpose and future architectures
Published in Joseph D. Dumas, Computer Architecture, 2016
Although at first blush, number factorization sounds like a rather academic exercise in itself, it has important applications, especially in the field of cryptography. The difficulty of using conventional computers to factor large integers is what makes present crypto systems, such as RSA, extremely hard to crack. (The RSA algorithm, named for its inventors Rivest, Shamir, and Adelman, is the most widely used public key encryption method, and the principal technology behind secure transactions on the Internet.) A person, organization, or government with access to a powerful quantum computer could use Shor’s (or some other) factoring algorithm to break into any encrypted message and recover the supposedly secure information; thus, today’s encryption methods could be made obsolete. Conversely, quantum computers could potentially be used to implement new codes that would encode information with far stronger encryption than is possible with even the fastest supercomputers of today and thus be essentially impossible to crack.
Spin Wave Logic Devices
Published in Evgeny Y. Tsymbal, Igor Žutić, Spintronics Handbook: Spin Transport and Magnetism, Second Edition, 2019
Alexander Khitun, llya Krivorotov
The use of the output signal phase in addition to its amplitude provides additional information that can be used for solving complex problems such as prime factorization. Prime factorization is the process of finding the set of prime numbers that multiply together to give the original integer N. The most naive approach to this problem is sequentially checking all possible products of all numbers from 2 to √N, where the number of operations increases exponentially with the increase of the input state N. Even the most efficient digital prime factoring algorithms (e.g., Fermat’s factoring algorithm [49]) take an enormous number of operations to find the primes of sufficiently large N. This explains the extensive use of prime encoding in information security [50]. Quantum computing has emerged as a promising computational paradigm in part due to its ability to solve prime factorization problem more efficiently than with conventional digital computers. P. Shor has developed a polynomial-time quantum algorithm for the factoring problem, and its computational complexity has been proved to be O((log N)2 (log log N)(log log log N)), which provides a fundamental advantage over any type of digital-type computing [51]. Although the fundamental advantage of quantum computing is undisputable, its practical realization is associated with multiple technological challenges required for quantum entanglement implementation. The prime factorization problem can be also solved by using classical wave interference. This approach has been intensively studied in optics [52]. Here, we present an example of solving the prime factorization problem by using a magnonic holographic device.
Key Generation
Published in Vinay Rishiwal, Sudeep Tanwar, Rashmi Chaudhry, Blockchain for 6G-Enabled Network-Based Applications, 2023
Surendra Kumar, Narander Kumar
ECC needs fewer significant keys than non-ECC cryptography to afford the same security. Elliptic curves are appropriate for encoding, digital marks, and other tasks. They are also used in some integer factorization techniques that have relevance in cryptography. Public key cryptography is based on tortuous mathematics. Early public key systems are protected, assuming that it is hard to factor a big integer composed of two or more huge prime factors.
A Grouping Strategy Based on Prime Factorization for Capacitor Voltage Balancing of the Modular Multilevel Converter
Published in Electric Power Components and Systems, 2018
Chengyong Zhao, Ye Wang, Maolan Peng, Zhipeng He, Chunyi Guo
According to the number theory, a positive integer can be written as a list of prime factors with their exponents multiplying [20]. The process of determining these factors is referred to as prime factorization. Inspired by the prime factorization method, N SMs in each arm can be divided as prime factorization pattern. Accordingly, where m1…mn and mn+1 are prime factors of N and some of them may be identical, since the prime factors are all listed without any exponent.
Visual Cryptography Secret Share Creation Techniques with Multiple Image Encryption and Decryption Using Elliptic Curve Cryptography
Published in IETE Journal of Research, 2022
Elliptic Curve Cryptography can be used for quicker and lesser more professional cryptography keys. The ECC can archive the same level of the safety measures 164-bit key that other systems need 1024-bit key. They are also used in several numeral factorization algorithms based on Elliptic Curve Cryptography.