System Considerations In Crypto-C
130 RSA BSAFE Crypto-C Developer’s Guide
ends and the public exponent begins. It would be a good idea to put identifying
marks on the data to make it easier to parse. BER/DER encoding standardizes such
identifying marks as an industry standard so that people using different software
packages can still trade information. Hence, with Crypto-C, the user has the option of
storing a 768-bit public key simply as a modulus and public exponent (99 bytes), or in
its DER-encoded format, which requires 126 bytes.
Private Key Size
At its most basic form, the private key consists of a modulus and a private exponent.
The modulus for the private key is the same as the modulus for the public key. The
private exponent is the truly private part of the private key. The private value is
usually the same size as the modulus, or 1 bit smaller. Therefore, to store a 768-bit
private key, one needs at least 1536 bits (192 bytes) of storage space.
To perform private key operations, you require only the modulus and private
exponent. However, the computations can be much faster if you have access to more
information.
Recall that, in RSA encryption, the modulus is actually the product of two prime
numbers. The private exponent is derived from the two primes and the public
exponent. Given only the modulus and the public exponent, an attacker cannot
deduce the private exponent.
When computing the key pair, you can find two suitable primes, multiply them
together to get the modulus, use the primes to determine the private exponent, and
then throw the primes away. Or you can use the primes to compute two prime
exponents and a Chinese Remainder Theorem (CRT) coefficient, and save all this
information. Then, when executing private key operations with the extra information,
you can use the Chinese Remainder Theorem to make the appropriate computations
much more quickly.
So when saving a 768-bit private key, you actually need to save the following:
•The modulus: 96 bytes
•The public exponent — it is small and there are advantages to having it saved
with the private key: 3 bytes
•The private exponent: 96 bytes
•Two p rim es : 2 × 48 bytes
•Two prime exponents: 2 × 48 bytes
•A CRT coefficient: 48 bytes
•The identifying marks for DER encoding