Re: google + bit of time == ecc curve that is better

In article <fd958ce4-0e2d-4e4a-9ba0-430de58cbc0d@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Tom St Denis <tom@xxxxxxx> wrote:
... The modulus in HEX is

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF13

Which is 2^192 - 237, meaning that reduction modulo this is

x == (x >> 192) + 237 * (x mod 2^192)

I think you have the '+' and '*' back to front.

Also, there is the possibility that x, after
multiplication, is too big, that is, the reduction
above still gives an answer bigger than 2^192. So
you have to do that reduction twice, or
conditionally (which opens up side channel
attacks). Then there is still the funky case where
reduction results in a number that's bigger than P
but smaller than 2^192.

I refer you to Figure 6.12 in that excellent book
"BigNum Math". ;-)

Greg.
--
Greg Rose
232B EC8F 44C6 C853 D68F E107 E6BF CD2F 1081 A37C
Qualcomm Australia: http://www.qualcomm.com.au
.

Relevant Pages

  • Re: [PATCH] x86: introduce and use percpu_inc()
    ... Signed-off-by: Jan Beulich ... byte reduction (the immediate operand of the add); ... wasn't even used) is certainly a bigger win ...
    (Linux-Kernel)
  • Re: Paul knew marriage was "doomed!"
    ... Hey, thanks for the link. ... Her boobs certainly DO look bigger than I ever imagined. ... she had a reduction. ...
    (rec.music.beatles)
  • Re: Equivalent modal logics
    ... so you're wanting a reduction that preserves some intuitive notion ... > of meaning. ... But the reduction in question guarantees you nothing of the ... Now that I realize there are only 6 inequivalent modalities ...
    (sci.logic)