Abstract
Cryptography was concerned initially with providing secrecy for written messages. Its principles apply equally well to securing data flow between computers, to digitized speech, and to encrypting facsimile and television signals. For example, most satellites routinely encrypt the data flow to and from ground stations to provide both privacy and security for their subscribers. In this chapter, we shall introduce some basic concepts and techniques in public-key cryptography based on primality testing/prime number generation, integer factorization, discrete logarithms, quadratic residuosity, and elliptic curve discrete logarithms, etc.
Cryptography relies heavily on number-theoretic tools. In particular, systems based on (assumed) hardness of problems in number theory, such as factoring and discrete log, form an important part of modern cryptography.
Motwani and Raghavan [110]
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Yan, S.Y. (2004). Number-Theoretic Cryptography. In: Primality Testing and Integer Factorization in Public-Key Cryptography. Advances in Information Security, vol 11. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3816-2_4
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DOI: https://doi.org/10.1007/978-1-4757-3816-2_4
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