Chapter 3 Cryptography 97
Security Considerations
= (r-1)(r)(md)
= (1)(md) mod n
Crypto-C offers both blinding and non-blinding RSA private operations through
separate algorithm methods. It currently offers no blinding technique in Diffie-
Hellman or DSA operations.
Crypto-C uses MD5 random number generation to produce the random value r. The
seed is the following digest:
MD5(p || padP || MD5(q || padQ || m))
where p and q are the two primes, padP and padQ are paddings of zeros to make sure
the length is a multiple of 64 bytes, and the symbol || means concatenation. An
attacker will not know what r is without knowing what the seed is, and will not know
what the seed is without knowing what p and q are. An attacker w ho knows p and q is
not going to implement a timing attack to determine the private key, because
knowledge of p and q is equivalent to knowledge of the private key already.
Choosing Key Sizes
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, that bit number might not
describe the entire key.
For instance, 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,” that is, bits that are known, out of the 64, you really only
get 56 secret bits. Hence, a DES key, while consisting of 64 bits of data, is only 56
cryptographic bits large.
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. The security of an RSA key pair is tie d up in how big the modulus is; hence,
the measurement used is the bit size of the modulus. The actual keys themselves will
contain more information than the modulus, so the “physical” size will be much
larger.
In choosing a key size, if larger keys offer greater security, why not simply always
choose the largest possible key? Larger RSA, Diffie-Hellman, DSA, and elliptic curve
keys can slow down cryptographic operations.
For the RC2, RC4, and RC5 ciphers, larger keys generally do not significantly degrade
performance. However, larger keys do require more management.