Extract numbers from a key

[Peter Lebbing]

On 04/08/11 20:30, Peter Lebbing wrote:
> Perhaps the better question is: *why* does it work? Why are the operations
> equivalent?

Hmmmm. Per the Handbook of Applied Cryptography 5th ed[1], section 8.5,
computation of d can also be done modulo lambda, with
lambda = lcm(p-1,q-1) = (p-1)(q-1)/gcd(p-1,q-1)

So that answers your question. I'd hazard it's safe :).

I also found the answer to my own question in section 8.3. It does not matter if
the message and p or q are not co-prime, the equivalency still holds.

Which goes to show, when you have a question about cryptography, it's a good
idea to consult the HAC first :).

Peter.

[1] http://www.cacr.math.uwaterloo.ca/hac/
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