Cryptography MIX

This is just a compilation of texts from wikipedia.
I'll extend this text little bit more later.

1. Symmetric-key algorithm
   
   1. Triple DES
   2. Serpent
   3. Blowfish
   4. Twofish
2. Asymmetric key algorithms
   
   1. Diffie–Hellman key exchange
   2. Digital Signature Algorithm (DSA)
   3. ElGamal encryption
   4. Cramer–Shoup cryptosystem
   5. Elliptic curve cryptography (ECC)
3. Cryptographic hash function
   
   1. SHA hash functions
   2. MD5 (Message-Digest algorithm 5)
4. Key size Brute force

Symmetric-key algorithm

Are a class of algorithms for cryptography that use trivially related, often identical, cryptographic keys for both decryption and encryption.

Symmetric-key algorithms can be divided into stream ciphers and block ciphers. Stream ciphers encrypt the bytes of the message one at a time, and block ciphers take a number of bytes and encrypt them as a single unit.

AES(Rijndael)

Standard adopted by the U.S. government
128, 192 and 256 bit. wiki

A related-key attack can break 256-bit AES with a complexity of 2¹¹⁹, which is faster than brute force but is still infeasible. 192-bit AES can also be defeated in a similar manner, but at a complexity of 2¹⁷⁶. 128-bit AES is not affected by this attack. A chosen-plaintext attack can break 8 rounds of 192-bit and 256-bit AES, and 7 rounds of 128-bit AES, although the workload is impractical at 2¹²⁸ - 2¹¹⁹. (Ferguson et al., 2000). wiki

DES
56 bits
Old. DES is now considered to be insecure for many applications.

Triple DES
168 bits (three 56-bit DES keys)
Triple DES provides a relatively simple method of increasing the key size of DES to protect against brute force attacks, without requiring a completely new block cipher algorithm. wiki

Serpent
128, 192 or 256 bits
The Serpent cipher has not been patented. It is completely in the public domain and can be freely used by anyone.
The XSL attack, if effective, would weaken Serpent (though not as much as it would weaken Rijndael, which became AES). However, many cryptanalysts believe that once implementation considerations are taken into account the XSL attack would be more expensive than a brute force attack.
The 32 rounds make Serpent have a higher security margin than Rijndael; however, Rijndael with 10 rounds is faster and easier to implement for small blocks. Hence, Rijndael was selected as the winner in the AES competition.
wiki

Blowfish
Variable key length from 32 up to 448 bits.
recommends using the more recent Twofish algorithm instead.
wiki

Twofish
128, 192 or 256 bits
On most software platforms Twofish is slightly slower than Rijndael (the chosen algorithm for Advanced Encryption Standard) for 128-bit keys, but somewhat faster for 256-bit keys.
The Twofish cipher has not been patented and the reference implementation has been placed in the public domain.

Advanced Encryption Standard process
The Advanced Encryption Standard (AES), the block cipher ratified as a standard by National Institute of Standards and Technology of the United States.
Rijndael: 86 positive, 10 negative
Serpent : 59 positive, 7 negative
Twofish : 31 positive, 21 negative
RC6 : 23 positive, 37 negative
MARS : 13 positive, 83 negative
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Asymmetric key algorithms

Diffie–Hellman key exchange
In practice, Diffie–Hellman is not used in this way, with RSA being the dominant public key algorithm. This is largely for historical and commercial reasons, namely that RSA created a Certificate Authority that became Verisign. Diffie–Hellman cannot be used to sign certificates, although the ElGamal and DSA signature algorithms are related to it.
wiki

Digital Signature Algorithm (DSA)
United States Federal Governmentstandard or FIPS for digital signatures.DSA is covered by U.S. Patent 5,231,668, filed July 26, 1991, and attributed to David W. Kravitz, a former NSA employee. This patent was given to "The United States of America as represented by the Secretary of Commerce, Washington, D.C." and the NIST has made this patent available worldwide.wiki

ElGamal encryption
ElGamal encryption is used in the free GNU Privacy Guard software, recent versions of PGP, and other cryptosystems.
wiki

RSA (Rivest, Shamir and Adleman)
It is the first algorithm known to be suitable for signing as well as encryption, and was one of the first great advances in public key cryptography. RSA is widely used in electronic commerce protocols, and is believed to be secure given sufficiently long keys and the use of up-to-date implementations.
wiki

Cramer–Shoup cryptosystem
It is an extension of the Elgamal cryptosystem. In contrast to Elgamal, which is extremely malleable, Cramer–Shoup adds additional elements to ensure non-malleability even against a resourceful attacker. This non-malleability is achieved through the use of a collision-resistant hash function and additional computations, resulting in a ciphertext which is twice as large as in Elgamal.
wiki

Elliptic curve cryptography (ECC)
At least one ECC scheme (ECMQV) and some implementation techniques are covered by patents.
128-bit security one needs a curve over F(q), where q 2^256. This can be contrasted with finite-field cryptography (e.g., DSA) which requires 3072-bit public keys and 256-bit private keys, and integer factorization cryptography (e.g., RSA) which requires 3072-bit public and private keys.
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Cryptographic hash function

SHA hash functions

Algorithm	Output size (bits)	Collisions found
SHA-0	160	yes
SHA-1	160	None
SHA-2	256/224	None
SHA-2	512/384	None

wiki

MD5 (Message-Digest algorithm 5)

U. S. Department of Homeland Security said MD5 "should be considered cryptographically broken and unsuitable for further use,"and most U.S. government applications will be required to move to the SHA-2 family of hash functions by 2010.

is a widely used cryptographic hash function with a 128-bit hash value. As an Internet standard (RFC 1321),Recently, a number of projects have created MD5 rainbow tables which are easily accessible online, and can be used to reverse many MD5 hashes into strings that collide with the original input, usually for the purposes of password cracking. However, if passwords are combined with a salt before the MD5 digest is generated, rainbow tables become much less useful.
The use of MD5 in some websites' URLs means that Google can also sometimes function as a limited tool for reverse lookup of MD5 hashes. This technique is also rendered ineffective by the use of a salt.
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Comparison of cryptographic hash functions

Key size
The security of an algorithm cannot exceed its key length (since any algorithm can be cracked by brute force), but it can be smaller.
A key should therefore be large enough that a brute force attack (possible against any encryption algorithm) is infeasible – i.e, would take too long to execute. Shannon's work on information theory showed that to achieve so called perfect secrecy, it is necessary for the key length to be at least as large as the message to be transmitted and only used once (this algorithm is called the One-time pad).

As each of these is of a different level of cryptographic complexity, it is usual to have different key sizes for the same level of security, depending upon the algorithm used. For example, the security available with a 1024-bit key using asymmetric RSA is considered approximately equal in security to an 80-bit key in a symmetric algorithm (Source: RSA Security).
With a key of length n bits, there are 2ⁿ possible keys.

This number grows very rapidly as n increases. Moore's law suggests that computing power doubles roughly every 18 to 24 months, but even this doubling effect leaves the larger symmetric key lengths currently considered acceptably well out of reach. The large number of operations (2¹²⁸) required to try all possible 128-bit keys is widely considered to be out of reach for conventional digital computing techniques for the foreseeable future.

The Advanced Encryption Standard published in 2001 uses a key size of (at minimum) 128 bits. It also can use keys up to 256 bits (a specification requirement for submissions to the AES contest).
128 bits is currently thought, by many observers, to be sufficient for the foreseeable future for symmetric algorithms of AES's quality. The U.S. Government requires 192 or 256-bit AES keys for highly sensitive data.

As of 2003 RSA Security claims that 1024-bit RSA keys are equivalent in strength to 80-bit symmetric keys, 2048-bit RSA keys to 112-bit symmetric keys and 3072-bit RSA keys to 128-bit symmetric keys. RSA claims that 1024-bit keys are likely to become crackable some time between 2006 and 2010 and that 2048-bit keys are sufficient until 2030. An RSA key length of 3072 bits should be used if security is required beyond 2030. NIST key management guidelines further suggest that 15360-bit RSA keys are equivalent in strength to 256-bit symmetric keys.

One of the asymmetric algorithm types, elliptic curve cryptography, or ECC, appears to be secure with shorter keys than those needed by other asymmetric key algorithms.
NIST guidelines state that ECC keys should be twice the length of equivalent strength symmetric key algorithms. So, for example, a 224-bit ECC key would have roughly the same strength as a 112-bit symmetric key. These estimates assume no major breakthroughs in solving the underlying mathematical problems that ECC is based on. A message encrypted with an elliptic key algorithm using a 109-bit long key has been broken by brute force.

The amount of time required to break a 128-bit key is also daunting. Each of the 2¹²⁸ (340,282,366,920,938,463,463,374,607,431,768,211,456) possibilities must be checked. A device that could check a billion billion keys (10¹⁸) per second would still require about 10¹³ years to exhaust the key space.
This is a thousand times longer than the age of the universe, which is about 13,000,000,000 (1.3×10¹⁰) years.

AES permits the use of 256-bit keys. Breaking a symmetric 256-bit key by brute force requires 2¹²⁸ times more computational power than a 128-bit key. A device that could check a billion billion (10¹⁸) AES keys per second would require about 3×10⁵¹ years to exhaust the 256-bit key space.

An underlying assumption of this analysis is that the complete keyspace is used to generate keys, something that relies on an effective random number generator.
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