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If you want to know about the history of cryptography, I would recommend The Code Book by Simon Singh and The Codebreakers by David Kahn. Introduction to Modern Cryptography by Jonathan Katz and Yehuda Lindell is a good book to know about provable security.
Theory of cryptography refers to the study of cryptographic algorithms and protocols in a formal framework. The two main goals of the study are definitions and proofs of security.
Heres how math is used in cryptography: Key generation: Cryptographic systems rely on keys to encode and decode information. These keys are generated using complex mathematical algorithms that leverage number theory and computational problems.
Cryptography is the process of hiding or coding information so that only the person a message was intended for can read it. The art of cryptography has been used to code messages for thousands of years and continues to be used in bank cards, computer passwords, and ecommerce.
Cryptographic principles are the fundamental concepts and techniques that are used in the field of cryptography to secure communication and protect data. These principles include confidentiality, integrity, authentication, non-repudiation, and key management.
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Data integrity, authenticity, and non-repudiation. Encrypted data does not mean the data can not be manipulated (for example, repeated, deleted, or even altered).

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