Re: Dollar Plus

[ambrus]

The story of this obfuscation is this. When martin posted the obfuscation ASCII arithmetic, I praised it in the chatterbox, but mentioned that it would be even more amazing if one could have a similar obfuscation that

worked over the GF(128) field.

martin replied with this obfu the day after, which indeed does what I asked for.

Again, the characters long string literal gives the coefficients of a polynomial. This time, however, the values are over GF(128), represented in the obvious way, with the bit i of the character adding g**i to the value where g is a generator of the field. The first map loop generates the first 257 powers of g, writing them to @+. Then this table is inverted to %+ which functions as a discrete logarithm table. This allows one to compute the product of two values $x, $y as simply $+[$+{$x}+$+{$y}] (except when one of the values is zero for which an extra test $;eq$/ is needed at one place). The polynomial is again evaluated at a points in a geometric series.

Of course, some obfuscations have multiple layers, so one can't easily be sure one does what it looks like. Thus, I verified that my thinking is right by trying to construct a new polynomial.

$;^=$;;$:='+';${::}{$:}=$_,for{},[];$==65;@+=map{$=<<=1;
$=^=131,if+128&$=;chr$=}0..1<<8;@+{@+}=(0..126)x$=;print
map{$:=$+[$+{$:}+$+{z}];$/=$;;$/=$;eq$/?$_:$+[$+{$/}+$+{
$:}]^$_,for@_;$/}@_=split//,"gi!EVpr/'Vts\6X0Kw\tZj'TF".
"\36\5\e?S\b/1! P84&p{\\0FY[\aW%\ck";