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Unformatted text preview: Public Key Cryptography in Practice c circlecopyrt Eli Biham  August 18, 2010 370 Public Key Cryptography in Practice (13) How Cryptography is Used in Applications The main drawback of public key cryptography is the inherent slow speed of the public key schemes. There are only a few schemes which are relatively faster, but they require use of huge keys, and are thus impractical. Therefore, public key schemes are not used directly for encryption. Instead, public key schemes are used in conjunction with secret key schemes where encryption is performed by the secret key schemes (e.g., TripleDES) and the agreement on the keys is performed by public key distribution schemes (e.g., using RSA or DiffieHellman). This is similar to the case described in the public key signature schemes, where the signer does not sign the original message, but rather signs a short result of a fast hash function. Similarly, public key distribution schemes can be used in order to distribute MAC keys where message authentication is required. c circlecopyrt Eli Biham  August 18, 2010 371 Public Key Cryptography in Practice (13) Recommended Key Sizes In secret key schemes the trend changes from keys of 56–64 to keys of 128 bits. Keys of 128 bits are large enough to thwart any practical attack, as long as the cipher does not have weakness due to its design. Paranoids can use even longer keys, which are supported by various ciphers. The situation is different in public key schemes, where considerably longer keys are required, as the keys are not uniformly selected from all the possible keys with the same length. Therefore, the number of keys is (slightly) smaller than the number of values of the same length as the keys. However, the main reason that requires longer keys is the information inherited in the key due to the properties of the cipher. c circlecopyrt Eli Biham  August 18, 2010 372 Public Key Cryptography in Practice (13) Recommended Key Sizes (cont.) In RSA, the public key is a product of two primes. The best known factoring algorithms are the quadratic sieve and the number field sieve whose complexities are about Complexity(QS) = e c √ ln n ln ln n ; Complexity(NFS) = e c (ln n ) 1 / 3 (ln ln n ) 2 / 3 Due to the different constant factors (and other smaller terms) the quadratic sieve is faster when factoring up to about 129 decimal digits. The quadratic sieve algorithm was used to factor the number RSA129, proposed by the designers of RSA in 1978 as an example of a number whose factoring will take about 40...
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This note was uploaded on 04/14/2011 for the course CS 236506 taught by Professor Yanivcarmeli during the Spring '11 term at Technion.
 Spring '11
 YanivCarmeli

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