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Symmetric and Asymmetric Encryption Algorithms, Research Paper Example

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Research Paper

Encryption algorithms are very important to many applications, both in computer science as well as in other fields.  For an application designer, understanding the different types of encryption algorithms and different encryption algorithms is very important.  The biggest distinction within encryption algorithms is whether or not an algorithm is symmetric.  Symmetric algorithms, such as AES, use the same private key (also called the secret key) at both the sending and receiving sides.  On the other hand, asymmetric algorithms (usually known as public key cryptography) such as ECC and RSA use a public key and private key; the private key is only known the receiver, while everyone has access to the public key.  The public key is used to encrypt a message and the private key, only held by the owner, is used to decrypt the message.  The design of asymmetric algorithms do not allow anyone with a public key to decrypt other messages.  In this paper, we shall examine 3 encryption algorithms: AES (the Advanced Encryption Standard, a symmetric algorithm), ECC (Elliptic Curve Cryptographic, an asymmetric algorithm), and RSA (name after its discoverers, Ron Rivest, Adi Shamir and Leonard Adleman, an asymmetric algorithm).

AES, or the Advanced Encryption Standard, is a popular symmetric encryption algorithm.  AES was designed to supersede the now obsolete DES (Data Encryption Standard).  AES is based on the Rijndael cipher (named after its 2 designers, Vincent Rijmen and Joan Daemen).  AES allows for key sizes of 128, 192, or 256 bits and uses 128 bit blocks.  The number of rounds are based on the key size.  For 128-bit keys, 10 rounds are used.  For 192-bit keys, 12 rounds are used, and for 256-bit keys, 14 rounds are used.  The AES algorithm ses 4 steps.  First, a step called “KeyExpansion” uses Rijndael’s key schedule to derive the round keys from the cipher key.  Next, the “InitialRound” occurs, using the AddRoundKey operation, where each byte of the state is operated on by a bitwise xor with the round key.  Next, the rounds begin, in the order of SubBytes (a non-linear substitution that replaces all bytes with another using a constant table), ShiftRows (where each row is shifted left cyclically a number of times based on how many preceding rows), MixColumns (each column of the state is multiplied by a constant invertible matrix), and finally AddRoundKey.  These four steps are repeated for each round.  The final step consists of 3 steps: SubBytes, ShiftRows, and AddRoundKey.  All known attacks on AES are currently computationally infeasible.  For 128-bit AES, the best attack has a computation complexity of .  For 192-bit and 256-bit AES, the best attacks have computation complexities if  and , respectively.

Next, we discuss RSA.  RSA is the most popular algorithm in practice, and it is usually combined with AES in SSL/TLS.  The security of RSA is based on the difficulty of factoring extremely large semi-prime numbers.   RSA allows for any key size technically, but use of powers of 2 is conventional in computer science.  The minimum recommended size is 1024-bits, and the largest in practical use is 4096-bit, but RSA keys may be larger or smaller.  RSA only uses 1 round.  The largest RSA key to be broken yet is a 768-bit key.  There are no known attacks on a well-implemented RSA toolkit.

Finally, we discuss ECC, or elliptic curve cryptography.  The advantage of ECC is that ECC is much more secure than RSA of the same key size; a 256-bit ECC key is approximately equivalent to a 3072-bit RSA key.  ECC is based on the equation .  The variables a and b are part of the public key.  The security of ECC is based on the difficulty of computing the discrete logarithm of an elliptic curve with respect to a known base point.  Theoretically, elliptic curve cryptography has a computation complexity of , where n is the key size.

Works Cited

Koblitz, N. (1987). Elliptic curve cryptosystems. Mathematics of Computation, 48(177), 203–209.

RSA Laboratories. (2003, January). What is the AES? Retrieved from RSA: http://www.rsa.com/rsalabs/node.asp?id=2235

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