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Cryptography, or cryptology (from Ancient Greek: κρυπτός, romanized: kryptós "hidden, secret"; and γράφειν graphein, "to write", or -λογία-logia, "study", respectively [1]), is the practice and study of techniques for secure communication in the presence of adversarial behavior. [2]
In this theory, the class P consists of all decision problems (defined below) solvable on a deterministic sequential machine in a duration polynomial in the size of the input; the class NP consists of all decision problems whose positive solutions are verifiable in polynomial time given the right information, or equivalently, whose solution can ...
Historically, various forms of encryption have been used to aid in cryptography. Early encryption techniques were often used in military messaging. Since then, new techniques have emerged and become commonplace in all areas of modern computing. [1] Modern encryption schemes use the concepts of public-key [2] and symmetric-key. [1]
Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key . [ 1 ] [ 2 ] Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions .
The following outline is provided as an overview of and topical guide to cryptography: Cryptography (or cryptology) – practice and study of hiding information. Modern cryptography intersects the disciplines of mathematics, computer science, and engineering. Applications of cryptography include ATM cards, computer passwords, and electronic ...
Although the original paper of Rivest, Shamir, and Adleman used Fermat's little theorem to explain why RSA works, it is common to find proofs that rely instead on Euler's theorem. We want to show that m ed ≡ m (mod n ) , where n = pq is a product of two different prime numbers, and e and d are positive integers satisfying ed ≡ 1 (mod φ ( n
It is commonly accepted that this paper was the starting point for development of modern cryptography. Shannon was inspired during the war to address "[t]he problems of cryptography [because] secrecy systems furnish an interesting application of communication theory". Shannon identified the two main goals of cryptography: secrecy and authenticity.
Illustration of the concept behind Diffie–Hellman key exchange. Diffie–Hellman key exchange establishes a shared secret between two parties that can be used for secret communication for exchanging data over a public network. An analogy illustrates the concept of public key exchange by using colors instead of very large numbers: