%reverseHash = reverse %hash;
%hash = reverse %reverseHash;
##</code><code>##

my %reverseHash;
while(($key, $value)=each %hash)
{
   $processedValue = someFunc($value);
   $reverseHash{$processedValue} = $key;
}

my @keys = values %reverseHash;

my %newHash;
@newHash{@keys} = @hash{@keys};
##</code><code>##

use Data::Dumper;
my %hash = (
  a => [1, 2],
  b => [2, 3],
  c => [1, 2]
);

my %reverseHash = map { Dumper($hash{$_}) => $_ } keys %hash;
%hash = map { $_ => $hash{$_} } values %reverseHash;
print Dumper \%hash;