(aka Dossy)
Hi. I run several wikis using Wikit, especially the AOLserver Wiki [L1 ].
I can be reached at mailto:[email protected] . I blog at http://dossy.org/ .
I've got 4+ years of Tcl, specifically in Vignette StoryServer R4.x and V/5 through 5.6.
Located in Northern New Jersey and looking for short term contract/consulting work, preferably telecommute. See http://panoptic.com/ ...
I'm willing to consider a full-time position given the right offer, though.
LV Are you the one who wrote http://panoptic.com/cfx_tcl/ ?
Dossy Yes, that would be me. Why, did you give it a whack? Think it might be useful if further developed?
(The following should get put somewhere in Category Cryptography, I think.)
In struggling with implementing DSA signature verification, I discovered that math::bignum::powm is slow. Using the algorithm found here [L2 ] for modular exponentiation (i.e., x = a^b mod y), it yielded a faster implementation:
proc _modexp_bignum {m e n} {
set p [fromstr 1]
set zero [fromstr 0]
set one [fromstr 1]
set two [fromstr 2]
while {[gt $e $zero]} {
if {[eq [mod $e $two] $one]} {
set p [mod [mul $p $m] $n]
}
set m [mod [mul $m $m] $n]
set e [div $e $two]
}
return $p
}However, this is still quite slow for large values. So, I converted the inner-workings to use mpexpr and the speedup is tremendous:
proc _modexp_mpexpr {m e n} {
foreach v {m e n} {
set $v [mpexpr [tostr [set $v]]]
}
set p [mpexpr 1]
while {[mpexpr $e > 0]} {
if {[mpexpr $e % 2 == 1]} {
set p [mpexpr $p * $m % $n]
}
set m [mpexpr $m * $m % $n]
set e [mpexpr $e / 2]
}
return [fromstr $p]
}Here's my script that I used to benchmark performance:
package require math::bignum
package require Mpexpr
set g [math::bignum::fromstr 0x626d027839ea0a13413163a55b4cb500299d5522956cefcb3bff10f399ce2c2e71cb9de5fa24babf58e5b79521925c9cc42e9f6f464b088cc572af53e6d78802]
set u1 [math::bignum::fromstr 0xbf655bd046f0b35ec791b004804afcbb8ef7d69d]
set p [math::bignum::fromstr 0x8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adac32ab7aac49693dfbf83724c2ec0736ee31c80291]
# contains ::dsa namespace with _modexp_bignum and _modexp_mpexpr inside.
source dsa.tcl
set start [clock seconds]
puts "math::bignum::powm [time {math::bignum::powm $g $u1 $p} 5]"
puts "dsa::_modexp_bignum [time {dsa::_modexp_bignum $g $u1 $p} 5]"
puts "dsa::_modexp_mpexpr [time {dsa::_modexp_mpexpr $g $u1 $p} 5]"
set end [clock seconds]
puts "Total elapsed: [expr {$end - $start}] seconds."Here's the output:
math::bignum::powm 55341757 microseconds per iteration
dsa::_modexp_bignum 56942386 microseconds per iteration
dsa::_modexp_mpexpr 311979 microseconds per iteration
Total elapsed: 563 seconds.As the timings show, the math::bignum::powm and _modexp_bignum are comparable, but the _modexp_mpexpr trashes them both.