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Titlebook: Algebra for Applications; Cryptography, Secret Arkadii Slinko Textbook 20151st edition Springer International Publishing Switzerland 2015 B

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發(fā)表于 2025-3-21 19:47:34 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
期刊全稱(chēng)Algebra for Applications
期刊簡(jiǎn)稱(chēng)Cryptography, Secret
影響因子2023Arkadii Slinko
視頻videohttp://file.papertrans.cn/153/152497/152497.mp4
發(fā)行地址Shows the incredible power of algebra and number theory in the real world.Uses GAP, a system for computational discrete algebra, to illustrate the main ideas.Suitable for beginners with a very little
學(xué)科分類(lèi)Springer Undergraduate Mathematics Series
圖書(shū)封面Titlebook: Algebra for Applications; Cryptography, Secret Arkadii Slinko Textbook 20151st edition Springer International Publishing Switzerland 2015 B
影響因子.This book examines the relationship between mathematics and data in the modern world. Indeed, modern societies are awash with data which must be manipulated in many different ways: encrypted, compressed, shared between users in a prescribed manner, protected from an unauthorised access and transmitted over unreliable channels. All of these operations can be understood only by a person with knowledge of basics in algebra and number theory..This book provides the necessary background in arithmetic, polynomials, groups, fields and elliptic curves that is sufficient to understand such real-life applications as cryptography, secret sharing, error-correcting, fingerprinting and compression of information. It is the first to cover many recent developments in these topics. Based on a lecture course given to third-year undergraduates, it is self-contained with numerous worked examples and exercises provided to test understanding. It can additionally be used for self-study..
Pindex Textbook 20151st edition
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發(fā)表于 2025-3-22 00:10:03 | 只看該作者
Cryptology,sks is linear while the naive trial and error method of factoring integers has exponential complexity. All this allow us then to explain in detail RSA cryptosystem. In the last section we also deal with testing primality and explain how the two primes needed for the RSA cryptosystem can be found. Se
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發(fā)表于 2025-3-22 02:11:55 | 只看該作者
1615-2085 t is self-contained with numerous worked examples and exercises provided to test understanding. It can additionally be used for self-study..978-3-319-21951-6Series ISSN 1615-2085 Series E-ISSN 2197-4144
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發(fā)表于 2025-3-22 05:06:10 | 只看該作者
Integers, applications to cryptography. In this chapter we familiarise the reader with the basics of Number Theory necessary to understand the RSA cryptosystem that will appear in Chap.?.. We make emphasis on the prime factorisation, the greatest common divisor, modular arithmetic, Euler’s function and Euler
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Groups, start by looking at groups of permutations from which the concept of a group took its origin. Permutations have a diverse range of applications to cryptography. We pay a special attention to orders of permutations and analysis of repeated actions. We briefly consider several topics in general group
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發(fā)表于 2025-3-22 18:14:13 | 只看該作者
Fields,r of a prime. Such fields exist and we lay the grounds for the construction of such fields in Chap.?.. In this chapter we also prove a very important result that the multiplicative group of any finite field is cyclic. This makes it possible to define “discrete logarithms”—special functions on finite
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Error-Correcting Codes, not completely reliable. Even the best telecommunication systems connecting numerous information centres in various countries have some non-zero error rate. Error-correcting codes considered in this chapter were designed to resolve this problem. After a giving an example of a non-linear code based
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