RSA Security 5.2.2 manual DES Keys, Public Key Size

System Considerations In Crypto-C

Key Size

In cryptography, security is measured in key size: the bigger the key, the greater the security. Key size, in turn, is measured in bits. However, a bit number does not necessarily describe the entire key.

DES Keys

A DES key is 56 bits. However, that size refers to its cryptographic size, not its physical size. To build a DES key, you need 64 bits, but because eight of those bits are “parity bits,” which are known, you really only get 56 secret bits. Therefore, a DES key, while consisting of 64 bits of data, is only 56 cryptographic bits in length.

RSA Keys

An RSA key-pair measurement describes the modulus length. When cryptographers talk about a “768-bit RSA key pair,” what they really mean is that the modulus is 768 bits long. Because the security of an RSA key pair depends on how big the modulus is, the measurement used is the bit-size of the modulus. However, the actual keys themselves contain more information than the modulus, so the physical size is much larger.

Public Key Size

A public key consists of a modulus and a public exponent. To store that public key requires space for both of those components; so for a 768-bit public key, you need more than 768 bits of storage space.

Many people who use the RSA algorithm use F4 as the public exponent. F4 is one of a sequence of prime numbers with a special binary representation, which is 10.....01.

F4 is short for Fermat 4, first described by the 17th-century mathematician Pierre de Fermat. Fermat believed that there are infinite prime numbers of the form 2^(2^n) + 1. Now it is believed that n = 4 is the last prime number in the sequence.

Because of their special representation, using these numbers speeds up the public key operations of RSA encryption and RSA signature verification. F4 has been analyzed by RSA Labs and others, and has been found to be secure.

F4 = 01 00 01 in hexadecimal notation (65,537 in decimal), and it is 17 bits long. If you use F4, you need 785 bits of space to store a 768-bit public key and its public exponent. Of course, storage space comes only in bytes, so you actually need 99 bytes of space.

In addition, when you access the public key, you need to know where the modulus

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