Cryptographic techniques are analyzed so as to find methods to
break codes used to secure information. Examples include frequency analysis
for breaking mono-alphabetic substitution ciphers, index of coincidence
analysis for breaking polyalphabetic substitution ciphers, the breaking of
the Enigma cipher in World War II through mathematical and optical
techniques combined with knowledge of keys and key usage, exhaustive attacks
on the DES encryption standard, code-listeners for breaking many analog
speech encoding systems, and improved factoring for breaking cryptosystems
based on modular arithmetic.
Complexity: Cryptanalysis is a widely studies
mathematical area and typically involves a great deal of expertise and
computing power against modern cryptographic systems. Cryptanalysis of
improperly designed systems and of systems more invented before the 1940s is
almost universally accomplished by relatively simple automation.