Theodore Hope <[EMAIL PROTECTED]>:
[...]
> The fields I've marked above (n, e, d, p, q) refer to the similarly-named
> terms in the RSA FAQ description of "how RSA works" (quoted below).
> Can someone tell me what the fields "exponent1", "exponent2" and
> "coefficient" are, and how they fit in to the math calculation for
> the keys?
When doing an RSA secret-key calculation, you don't actually compute
x^d mod n. As the factors are known, a more efficient method can be
used: Compute x^d mod p and x^d mod q (with moduli of about half
the original length, which save time in the computations), and then
combine these two results using the so-called Chinese Remainder
Theorem. x^d mod p is the same as x^(d mod p-1) mod p (Fermat's
theorem: in a group with p-1 elements, x^p-1 = 1 for every x), and
similarly x^d mod q = x^(d mod q-1) mod q. This cuts the length of
the exponents by about two and saves further computing power.
These are the two extra exponents that you asked about; the
coefficient is for combining the two partial results.
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