Editing Dc (computer program) (section)

===Diffie–Hellman key exchange===

A more complex example of dc use embedded in a [[Perl]] script performs a [[Diffie–Hellman key exchange]]. This was popular as a [[signature block]] among [[cypherpunk]]s during the [[ITAR]] debates, where the short script could be run with only Perl and dc, ubiquitous programs on Unix-like operating systems:<ref>{{cite web
|url=http://www.cypherspace.org/adam/rsa/perl-dh.html
|title=Diffie–Hellman in 2 lines of Perl
|access-date=5 Jan 2009
|author=Adam Back
}}</ref>

<syntaxhighlight lang="perl">
#!/usr/bin/env perl -- -export-a-crypto-system-sig Diffie-Hellman-2-lines
($g, $e, $m) = @ARGV, $m || die "$0 gen exp mod\n";
print `echo "16dio1[d2%Sa2/d0<X+d*La1=z\U$m%0]SX$e"[$g*]\EszlXx+p | dc`
</syntaxhighlight>

A commented version is slightly easier to understand and shows how to use loops, conditionals, and the <code>q</code> command to return from a macro. With the GNU version of dc, the <code>|</code> command can be used to do arbitrary precision modular exponentiation without needing to write the X function.

<syntaxhighlight lang="perl">
#!/usr/bin/env perl

my ($g, $e, $m) = map { "\U$_" } @ARGV;
die "$0 gen exp mod\n" unless $m;

print `echo $g $e $m | dc -e '
# Hex input and output
16dio
# Read m, e and g from stdin on one line
?SmSeSg

# Function z: return g * top of stack
[lg*]sz

# Function Q: remove the top of the stack and return 1
[sb1q]sQ

# Function X(e): recursively compute g^e % m
# It is the same as Sm^Lm%, but handles arbitrarily large exponents.
# Stack at entry: e
# Stack at exit: g^e % m
# Since e may be very large, this uses the property that g^e % m == 
#     if( e == 0 )
#         return 1
#     x = (g^(e/2)) ^ 2
#     if( e % 2 == 1 )
#         x *= g
#     return x %
[
    d 0=Q   # return 1 if e==0 (otherwise, stack: e)
    d 2% Sa # Store e%2 in a (stack: e)
    2/      # compute e/2
    lXx     # call X(e/2)
    d*      # compute X(e/2)^2
    La1=z   # multiply by g if e%2==1
    lm %    # compute (g^e) % m
] SX

le          # Load e from the register
lXx         # compute g^e % m
p           # Print the result
'`;
</syntaxhighlight>