Cryptography

Cryptography derived from Greek kryptos "hidden" and graphy "write" is the study of message secrecy. In modern times, cryptography is considered to be a branch of both mathematics and computer science, and is affiliated closely with information security, computer security, and engineering. Cryptography is used in applications like the security of ATM cards, computer passwords, and electronic commerce etc.

Earlier,cryptography was concerned solely with message confidentiality i.e., encryption — conversion of messages from a comprehensible form into an incomprehensible one, and back again at the other end, rendering it unreadable by interceptors or eavesdroppers without secret knowledge , the key needed for decryption of that message. In recent decades, the field has expanded beyond confidentiality concerns to include techniques for message integrity checking, sender/receiver identity authentication, digital signatures, interactive proofs, and secure computation.

The modern cryptography can be divided into several areas of study. The main ones are listed here:

Symmetric Cryptography

With secret key cryptography, a single key is used for both encryption and decryption sender uses the key or some set of rules to encrypt the plain text and sends the cipher text to the receiver. The receiver applies the same key or rule set to decrypt the message and recover the plain text. Because a single key is used for both functions, secret key cryptography is also called symmetric encryption.

With this form of cryptography, it is obvious that the key must be known to both the sender and the receiver this,is the secret. The biggest difficulty with this approach, of course, is the distribution of the key.

Secret key cryptography schemes are generally categorized as being either stream ciphers or block ciphers. Stream ciphers operate on a single bit byte or computer word at a time and implement some form of feedback mechanism so that the key is constantly changing. A block cipher is so-called because the scheme encrypts one block of data at a time using the same key on each block. In general, the same plain text block will always encrypt to the same cipher text when using the same key in a block cipher whereas the same plain text will encrypt to different cipher text in a stream cipher.

Public-Key Cryptography

Public-key cryptography has been said to be the most significant new development in cryptography in the last 300-400 years. Modern PKC was first described publicly by Stanford University professor Martin Hellman and graduate student Whitfield Diffie in 1976. Their paper described a two-key crypto system in which two parties could engage in a secure communication over a non-secure communications channel without having to share a secret key.

PKC depends upon the existence of so-called one-way functions, or mathematical functions that are easy to computer whereas their inverse function is relatively difficult to compute. Let me give you two simple examples:

Multiplication vs. factorization: Suppose I tell you that I have two numbers, 9 and 16, and that I want to calculate the product; it should take almost no time to calculate the product, 144. Suppose instead that I tell you that I have a number, 144, and I need you tell me which pair of integers I multiplied together to obtain that number. You will eventually come up with the solution but whereas calculating the product took milliseconds, factoring will take longer because you first need to find the 8 pair of integer factors and then determine which one is the correct pair.

Exponentiation vs. logarithms: Suppose I tell you that I want to take the number 3 to the 6th power; again, it is easy to calculate 36=729. But if I tell you that I have the number 729 and want you to tell me the two integers that I used, x and y so that logx 729 = y, it will take you longer to find all possible solutions and select the pair that I used.

Thus multiple implementations are present such as RSA, DSA etc..

Hash Functions

Hash functions, also called message digests and one-way encryption, are algorithms that, in some sense, use no key.Instead, a fixed-length hash value is computed based upon the plaintext that makes it impossible for either the contents or length of the plaintext to be recovered. Hash algorithms are typically used to provide a digital fingerprint of a file's contents, often used to ensure that the file has not been altered by an intruder or virus. Hash functions are also commonly employed by many operating systems to encrypt passwords. Hash functions, then, provide a measure of the integrity of a file.

Hash algorithms that are in common use today include:

Message Digest (MD) algorithms: A series of byte-oriented algorithms that produce a 128-bit hash value from an arbitrary-length message.

MD2 (RFC 1319): Designed for systems with limited memory, such as smart cards.

MD4 (RFC 1320): Developed by Rivest, similar to MD2 but designed specifically for fast processing in software.

MD5 (RFC 1321): Also developed by Rivest after potential weaknesses were reported in MD4; this scheme is similar to MD4 but is slower because more manipulation is made to the original data. MD5 has been implemented in a large number of products although several weaknesses in the algorithm were demonstrated by German cryptographer Hans Dobbertin in 1996.

Secure Hash Algorithm (SHA): Algorithm for NIST's Secure Hash Standard (SHS). SHA-1 produces a 160-bit hash value and was originally published as FIPS 180-1 and RFC 3174. FIPS 180-2 describes five algorithms in the SHS: SHA-1 plus SHA-224, SHA-256, SHA-384, and SHA-512 which can produce hash values that are 224, 256, 384, or 512 bits in length, respectively. SHA-224, -256, -384, and -52 are also described in RFC 4634.