Mathematic Crytopraphy

Cryptography (from Greek κρύπτω, "to conceal, to obscure", and γράφω, "to etch, to inscribe, to write down") is, traditionally, the study of means of converting information from its normal, comprehensible form into an incomprehensible format, rendering it unreadable without secret knowledge — the art of encryption. Cryptography is often used to replace or in combination with steganography. In the past, cryptography helped ensure secrecy in important communications, such as those of spies, military leaders, and diplomats. In recent decades, the field of cryptography has expanded its remit in two ways. Firstly, it provides mechanisms for more than just keeping secrets: schemes like digital signatures and digital cash, for example. Secondly, cryptography has come to be in widespread use by many civilians who do not have extraordinary needs for secrecy, although typically it is transparently built into the infrastructure for computing and telecommunications, and users are not aware of it.

The Enigma machine was a portable cipher machine used to encrypt and decrypt secret messages. More precisely, Enigma was a family of related electro-mechanical rotor machines — there are a variety of different models.The Enigma was used commercially from the early 1920s on, and was also adopted by military and governmental services of a number of nations — most famously, by Nazi Germany before and during World War II. The German military model, the Wehrmacht Enigma, is the version most commonly discussed. Allied codebreakers were, in many cases, able to decrypt messages protected by the machine (see cryptanalysis of the Enigma). The intelligence gained through this source — codenamed ULTRA — was a significant aid to the Allied war effort. Some historians have suggested that the end of the European war was hastened by up to a year or more because of the decryption of German ciphers.

• New Windows malware "Gpcode.AK" appears in early June 2008, using RC4-128 and RSA-1024 ciphers to take document files hostage for ransom.
• RSA-640 was factored on November 2, 2005.
• From 14 August 2005–18 August 2005 the 25th Annual International Cryptology Conference CRYPTO 2005 took place in Santa Barbara, California, USA. At the rump session, an improved collision attack on SHA-1 was announced.
• RSA-200 was factored on 9 May 2005. At 663 bits (200 decimal digits), the number is the largest of the RSA numbers yet factored.
• The US Secret Service is reported to be using 4,000 of its computers in a distributed dictionary attack to solve passwords used to protect encryption keys [1]. They report particular success in crafting custom dictionaries based on knowledge of a suspect's personal interests.
• In Australia, the Vigenère cipher is being used to communicate with an extortionist via the advertisements in a newspaper 

Did you know...

...that the Pigpen cipher was used by the Freemasons for correspondence and record keeping?
...that Polish mathematician Marian Rejewski (pictured) deduced the wiring of the German Enigma machine in 1932 using theorems about permutations?

...that acoustic cryptanalysis is a type of attack that exploits sound in order to compromise a system?
...that one scheme to defeat spam involves proving that the sender has performed a small amount of computation: a proof-of-work system?