Encryption Algorithms

Encryption algorithm, or cipher, is a mathematical function used in the encryption and decryption process – series of steps that mathematically transforms plaintext or other readable information into unintelligible ciphertext. A cryptographic algorithm works in combination with a key (a number, word, or phrase) to encrypt and decrypt data. To encrypt, the algorithm mathematically combines the information to be protected with a supplied key. The result of this combination is the encrypted data. To decrypt, the algorithm performs a calculation combining the encrypted data with a supplied key. The result of this combination is the decrypted data. If either the key or the data is modified, the algorithm produces a different result. The goal of every encryption algorithm is to make it as difficult as possible to decrypt the generated ciphertext without using the key.

Each algorithm uses a string of bits known as a “key” to perform the calculations. The larger the key (the more bits), the greater the number of potential patterns can be created, thus making it harder to break the code and descramble the contents. Most encryption algorithms use the block cipher method, which codes fixed blocks of input that are typically from 64 to 128 bits in length. Some use the stream method, which works with the continuous stream of input.

Some cryptographic methods rely on the secrecy of the encryption algorithms; such algorithms are only of historical interest and are not adequate for real-world needs. Instead of the secrecy of the method itself, all modern algorithms base their security on the usage of a key; a message can be decrypted only if the key used for decryption matches the key used for encryption.

Types of encryption algorithms

There are two kinds of key-based encryption algorithms, symmetric encryption algorithms (secret key algorithms) and asymmetric encryption algorithms (or public key algorithms). The difference is that symmetric encryption algorithms use the same key for encryption and decryption (or the decryption key is easily derived from the encryption key), whereas asymmetric encryption algorithms use a different key for encryption and decryption, and the decryption key cannot be derived from the encryption key.

Symmetric encryption algorithms

Symmetric encryption algorithms can be divided into stream ciphers and block ciphers. Stream ciphers encrypt a single bit of plaintext at a time, whereas block ciphers take a number of bits (typically 64 bits in modern ciphers), and encrypt them as a single unit.

Some examples of popular symmetric encryption algorithms:
– AES/Rijndael
– Blowfish
– RC2
– RC4
– RC6
– Serpent
– Triple DES
– Twofish

AES encryption algorithm
AES stands for Advanced Encryption Standard. AES is a symmetric key encryption technique which will replace the commonly used Data Encryption Standard (DES). It was the result of a worldwide call for submissions of encryption algorithms issued by the US Government’s National Institute of Standards and Technology (NIST) in 1997 and completed in 2000.
In response to the growing feasibility of attacks against DES, NIST launched a call for proposals for an official successor that meets 21st century security needs. This successor is called the Advanced Encryption Standard (AES).
Five algorithms were selected into the second round, from which Rijndael was selected to be the final standard. NIST gave as its reasons for selecting Rijndael that it performs very well in hardware and software across a wide range of environments in all possible modes. It has excellent key setup time and has low memory requirements, in addition its operations are easy to defend against power and timing attacks. NIST stated that all five finalists had adequate security and that there was nothing wrong with the other four ciphers.
The winning algorithm, Rijndael, was developed by two Belgian cryptologists, Vincent Rijmen and Joan Daemen.
AES provides strong encryption and was selected by NIST as a Federal Information Processing Standard in November 2001 (FIPS-197).
Rijndael follows the tradition of square ciphers. AES algorithm uses three key sizes: a 128-, 192-, or 256-bit encryption key. Each encryption key size causes the algorithm to behave slightly differently, so the increasing key sizes not only offer a larger number of bits with which you can scramble the data, but also increase the complexity of the cipher algorithm.

Blowfish encryption algorithm
Blowfish is a symmetric encryption algorithm designed in 1993 by Bruce Schneier as an alternative to existing encryption algorithms.
Blowfish has a 64-bit block size and a variable key length – from 32 bits to 448 bits. It is a 16-round Feistel cipher and uses large key-dependent S-boxes. While doing key scheduling, it generates large pseudo-random lookup tables by doing several encryptions. The tables depend on the user supplied key in a very complex way. This approach has been proven to be highly resistant against many attacks such as differential and linear cryptanalysis. Unfortunately, this also means that it is not the algorithm of choice for environments where a large memory space is not available. Blowfish is similar in structure to CAST-128, which uses fixed S-boxes.

Since then Blowfish has been analyzed considerably, and is gaining acceptance as a strong encryption algorithm.
Blowfish was designed in 1993 by Bruce Schneier as a fast, free alternative to existing encryption algorithms. Since then it has been analyzed considerably, and it is slowly gaining acceptance as a strong encryption algorithm. Blowfish is unpatented and license-free, and is available free for all uses.

The only known attacks against Blowfish are based on its weak key classes.

CAST stands for Carlisle Adams and Stafford Tavares, the inventors of CAST. CAST is a popular 64-bit block cipher which belongs to the class of encryption algorithms known as Feistel ciphers.
CAST-128 is a DES-like Substitution-Permutation Network (SPN) cryptosystem. It has the Feistel structure and utilizes eight fixed S-boxes. CAST-128 supports variable key lenghts between 40 and 128 bits.
CAST-128 is resistant to both linear and differential cryptanalysis. Currently, there is no known way of breaking CAST short of brute force. CAST is now the default cipher in PGP.

Data Encryption Standard (DES)
Digital Encryption Standard (DES) is a symmetric block cipher with 64-bit block size that uses using a 56-bit key.

In 1977 the Data Encryption Standard (DES), a symmetric algorithm, was adopted in the United States as a federal standard.

DES encrypts and decrypts data in 64-bit blocks, using a 56-bit key. It takes a 64-bit block of plaintext as input and outputs a 64-bit block of ciphertext. Since it always operates on blocks of equal size and it uses both permutations and substitutions in the algorithm. DES has 16 rounds, meaning the main algorithm is repeated 16 times to produce the ciphertext. It has been found that the number of rounds is exponentially proportional to the amount of time required to find a key using a brute-force attack. So as the number of rounds increases, the security of the algorithm increases exponentially.

For many years, DES-enciphered data were safe because few organizations possessed the computing power to crack it. But in July 1998 a team of cryptographers cracked a DES-enciphered message in 3 days, and in 1999 a network of 10,000 desktop PCs cracked a DES-enciphered message in less than a day. DES was clearly no longer invulnerable and since then Triple DES (3DES) has emerged as a stronger method.

Triple DES encrypts data three times and uses a different key for at least one of the three passes giving it a cumulative key size of 112-168 bits. That should produce an expected strength of something like 112 bits, which is more than enough to defeat brute force attacks. Triple DES is much stronger than (single) DES, however, it is rather slow compared to some new block ciphers. However, cryptographers have determined that triple DES is unsatisfactory as a long-term solution, and in 1997, the National Institute of Standards and Technology (NIST) solicited proposals for a cipher to replace DES entirely, the Advanced Encryption Standard (AES).

IDEA encryption algorithm
IDEA stands for International Data Encryption Algorithm. IDEA is a symmetric encryption algorithm that was developed by Dr. X. Lai and Prof. J. Massey to replace the DES standard. Unlike DES though it uses a 128 bit key. This key length makes it impossible to break by simply trying every key. It has been one of the best publicly known algorithms for some time. It has been around now for several years, and no practical attacks on it have been published despite of numerous attempts to analyze it.
IDEA is resistant to both linear and differential analysis.

RC2 is a variable-key-length cipher. It was invented by Ron Rivest for RSA Data Security, Inc. Its details have not been published.

RC4 was developed by Ron Rivest in 1987. It is a variable-key-size stream cipher. It is a cipher with a key size of up to 2048 bits (256 bytes). The algorithm is very fast. Its security is unknown, but breaking it does not seem trivial either. Because of its speed, it may have uses in certain applications. It accepts keys of arbitrary length. RC4 is essentially a pseudo random number generator, and the output of the generator is exclusive-ored with the data stream. For this reason, it is very important that the same RC4 key never be used to encrypt two different data streams.

RC6 is a symmetric key block cipher derived from RC5. It was designed by Ron Rivest, Matt Robshaw, Ray Sidney, and Yiqun Lisa Yin to meet the requirements of the Advanced Encryption Standard (AES) competition. RC6 encryption algorithm was selected among the other finalists to become the new federal Advanced Encryption Standard (AES).

SEED is a block cipher developed by the Korea Information Security Agency since 1998. Both the block and key size of SEED are 128 bits and it has a Feistel Network structure which is iterated 16 times. It has been designed to resist differential and linear cryptanalysis as well as related key attacks. SEED uses two 8×8 S-boxes and mixes the XOR operation with modular addition. SEED has been adopted as an ISO/IEC standard (ISO/IEC 18033-3), an IETF RFC, RFC 4269 as well as an industrial association standard of Korea (TTAS.KO-12.0004/0025).

Serpent is a very fast and reasonably secure block cipher developed by Ross Anderson, Eli Biham and Lars Knudsen. Serpent can work with different combinations of key lengths. Serpent was also selected among other five finalists to become the new federal Advanced Encryption Standard (AES).

Tiny Encryption Algorithm is a very fast and moderately secure cipher produced by David Wheeler and Roger Needham of Cambridge Computer Laboratory. There is a known weakness in the key schedule, so it is not recommended if utmost security is required. TEA is provided in 16 and 32 round versions. The more rounds (iterations), the more secure, but slower.

Triple DES
Triple DES is a variation of Data Encryption Standard (DES). It uses a 64-bit key consisting of 56 effective key bits and 8 parity bits. The size of the block for Triple-DES is 8 bytes. Triple-DES encrypts the data in 8-byte chunks. The idea behind Triple DES is to improve the security of DES by applying DES encryption three times using three different keys. Triple DES algorithm is very secure (major banks use it to protect valuable transactions), but it is also very slow.

Twofish is a symmetric block cipher. Twofish has a block size of 128 bits and accepts keys of any length up to 256 bits.Twofish has key dependent S-boxes like Blowfish.
Twofish encryption algorithm was designed by Bruce Schneier, John Kelsey, Chris Hall, Niels Ferguson, David Wagner and Doug Whiting. The National Institute of Standards and Technology (NIST) investigated Twofish as one of the candidates for the replacement of the DES encryption algorithm.


Asymmetric encryption algorithms

Asymmetric encryption algorithms (public key algorithms) use different keys for encryption and decryption, and the decryption key cannot (practically) be derived from the encryption key. Public key methods are important because they can be used for transmitting encryption keys or other data securely even when the parties have no opportunity to agree on a secret key in private.

Types of Asymmetric encryption algorithms (public key algorithms):
– RSA encryption algorithm
– Diffie-Hellman
– Digital Signature Algorithm
– ElGamal

RSA encryption algorithm
Rivest-Shamir-Adleman is the most commonly used public key encryption algorithm. It can be used both for encryption and for digital signatures. The security of RSA is generally considered equivalent to factoring, although this has not been proved.
RSA computation occurs with integers modulo n = p * q, for two large secret primes p, q. To encrypt a message m, it is exponentiated with a small public exponent e. For decryption, the recipient of the ciphertext c = me (mod n) computes the multiplicative reverse d = e-1 (mod (p-1)*(q-1)) (we require that e is selected suitably for it to exist) and obtains cd = m e * d = m (mod n). The private key consists of n, p, q, e, d (where p and q can be omitted); the public key contains only n and e. The problem for the attacker is that computing the reverse d of e is assumed to be no easier than factorizing n.
The key size should be greater than 1024 bits for a reasonable level of security. Keys of size, say, 2048 bits should allow security for decades.
There are actually multiple incarnations of this algorithm; RC5 is one of the most common in use, and RC6 was a finalist algorithm for AES.

Diffie-Hellman is the first public key encryption algorithm, invented in 1976, using discrete logarithms in a finite field. Allows two users to exchange a secret key over an insecure medium without any prior secrets.

Diffie-Hellman (DH) is a widely used key exchange algorithm. In many cryptographical protocols, two parties wish to begin communicating. However, let’s assume they do not initially possess any common secret and thus cannot use secret key cryptosystems. The key exchange by Diffie-Hellman protocol remedies this situation by allowing the construction of a common secret key over an insecure communication channel. It is based on a problem related to discrete logarithms, namely the Diffie-Hellman problem. This problem is considered hard, and it is in some instances as hard as the discrete logarithm problem.
The Diffie-Hellman protocol is generally considered to be secure when an appropriate mathematical group is used. In particular, the generator element used in the exponentiations should have a large period (i.e. order). Usually, Diffie-Hellman is not implemented on hardware.

Digital Signature Algorithm
Digital Signature Algorithm (DSA) is a United States Federal Government standard or FIPS for digital signatures. It was proposed by the National Institute of Standards and Technology (NIST) in August 1991 for use in their Digital Signature Algorithm (DSA), specified in FIPS 186 [1], adopted in 1993. A minor revision was issued in 1996 as FIPS 186-1 [2], and the standard was expanded further in 2000 as FIPS 186-2 [3]. Digital Signature Algorithm (DSA) is similar to the one used by ElGamal signature algorithm. It is fairly efficient though not as efficient as RSA for signature verification. The standard defines DSS to use the SHA-1 hash function exclusively to compute message digests.
The main problem with DSA is the fixed subgroup size (the order of the generator element), which limits the security to around only 80 bits. Hardware attacks can be menacing to some implementations of DSS. However, it is widely used and accepted as a good algorithm.

The ElGamal is a public key cipher – an asymmetric key encryption algorithm for public-key cryptography which is based on the Diffie-Hellman key agreement. ElGamal is the predecessor of DSA.

Elliptic Curve DSA (ECDSA) is a variant of the Digital Signature Algorithm (DSA) which operates on elliptic curve groups. As with Elliptic Curve Cryptography in general, the bit size of the public key believed to be needed for ECDSA is about twice the size of the security level, in bits.

XTR is an encryption algorithm for public-key encryption. XTR is a novel method that makes use of traces to represent and calculate powers of elements of a subgroup of a finite field. It is based on the primitive underlying the very first public key cryptosystem, the Diffie-Hellman key agreement protocol.
From a security point of view, XTR security relies on the difficulty of solving discrete logarithm related problems in the multiplicative group of a finite field. Some advantages of XTR are its fast key generation (much faster than RSA), small key sizes (much smaller than RSA, comparable with ECC for current security settings), and speed (overall comparable with ECC for current security settings).

Differences between symmetric and asymmetric encryption algorithms

Symmetric encryption algorithms encrypt and decrypt with the same key. Main advantages of symmetric encryption algorithms are its security and high speed. Asymmetric encryption algorithms encrypt and decrypt with different keys. Data is encrypted with a public key, and decrypted with a private key. Asymmetric encryption algorithms (also known as public-key algorithms) need at least a 3,000-bit key to achieve the same level of security of a 128-bit symmetric algorithm. Asymmetric algorithms are incredibly slow and it is impractical to use them to encrypt large amounts of data. Generally, symmetric encryption algorithms are much faster to execute on a computer than asymmetric ones. In practice they are often used together, so that a public-key algorithm is used to encrypt a randomly generated encryption key, and the random key is used to encrypt the actual message using a symmetric algorithm. This is sometimes called hybrid encryption.

Strength of Encryption Algorithms

Strong encryption algorithms should always be designed so that they are as difficult to break as possible. In theory, any encryption algorithm with a key can be broken by trying all possible keys in sequence. If using brute force to try all keys is the only option, the required computing power increases exponentially with the length of the key. A 32-bit key takes 232 (about 109) steps. This is something anyone can do on his/her home computer. An encryption algorithm with 56-bit keys, such as DES, requires a substantial effort, but using massive distributed systems requires only hours of computing. In 1999, a brute-force search using a specially designed supercomputer and a worldwide network of nearly 100,000 PCs on the Internet, found a DES key in 22 hours and 15 minutes. It is currently believed that keys with at least 128 bits (as in AES, for example) will be sufficient against brute-force attacks into the foreseeable future.
However, key length is not the only relevant issue. Many encryption algorithms can be broken without trying all possible keys. In general, it is very difficult to design ciphers that could not be broken more effectively using other methods.
The keys used in public-key encryption algorithms are usually much longer than those used in symmetric encryption algorithms. This is caused by the extra structure that is available to the cryptanalyst. There the problem is not that of guessing the right key, but deriving the matching private key from the public key. In the case of RSA encryption algorithm, this could be done by factoring a large integer that has two large prime factors. In the case of some other cryptosystems, it is equivalent to computing the discrete logarithm modulo a large integer (which is believed to be roughly comparable to factoring when the moduli is a large prime number).