cryptanalysis

Cryptanalysis is the study of analyzing cryptographic systems to understand hidden information and to recover plaintext or keys without access to the original secret key. It combines mathematical theory, algorithmic analysis, and experimental methods to assess or defeat the security of ciphers, protocols, and implementations.

Historically, cryptanalysis evolved from breaking simple substitution and transposition ciphers to addressing complex modern schemes. The field gained prominence during World War II with efforts to break Enigma, where a combination of mathematics, engineering, and intelligence led to significant advances in breaking encrypted communications.

Techniques used in cryptanalysis range from classical methods to advanced mathematical attacks. Classical approaches include frequency analysis and pattern recognition that exploit weaknesses in the structure of ciphers. Modern cryptanalysis employs algebraic and number-theoretic techniques to attack public-key systems, as well as differential and linear cryptanalysis for block and stream ciphers. Side-channel analyses examine leakage from implementations, such as timing or power consumption. Attacks are often categorized by the information an attacker can obtain, such as known-plaintext, chosen-plaintext, or chosen-ciphertext attacks.

In contemporary practice, cryptanalysis informs the design and evaluation of secure algorithms. Security proofs, empirical testing, and consideration of evolving computational capabilities guide claims of resilience. Notable achievements include practical breaks of DES via differential cryptanalysis, and the discovery of weaknesses in hash functions such as MD5 and SHA-1. The field continues to evolve as new cryptographic primitives are proposed and new attack techniques are developed.