in reply to Reverse download protocols [solved]

There's the 20-questions game of: client trying to guess a server-chosen integer. The server responds with one of higher, lower or yes to any guess from the client. The best strategy for such a game is to always guess halfway between the current possible range. This is because you are essentially doing a binary search and want to eliminate the biggest possible range with your every question, slowly zooming-in to the correct answer.

The output of a hashing algorithm can be labelled as a unique non-negative integer (or be converted to one). SHA1 has 160 bits of output. Giving the possible guesses to be in the range 0 to 2^160 = 0 to 1461501637330902918203684832716283019655932542976. The best guess would be 2^160/2. If the server answers with try lower, then your next guess should be 2^160/4.

Bonus points for how many guesses guessing a SHA1 hash needs, given that the server is ever so helpful in giving us 2 bits of information each time. But from what I gather from this post's little 20-questions game, the server does give hints (e.g. Then the server answers yes/no, or gives some hint.)

Here is something to play with, if indeed your problem falls in this category (it certainly did keep me entertained for a while):

# by bliako on 30/08/2021 # for use bigint qw/hex/; use Digest::SHA1 qw/sha1 sha1_hex/; my $digest_hex = sha1_hex('blah blah blah'); my $answer = hex($digest_hex); print "$0 : starting with this number: $answer.\n"; my $min = 0; my $max = 2**160; my $num_guesses = 0; my ($guess, $diff); while( ++$num_guesses ){ $guess = $min + ($max - $min) / 2.0; $diff = $guess - $answer; print "entering at guess number $num_guesses, current range:\n mi +n: $min\n max: $max\n answer: $answer\n guess: $guess\n diff: $di +ff\n"; if( $guess < $answer ){ print "your guess ($guess) needs to go higher ...\n"; $min = int($guess); } elsif( $guess > $answer ){ print "your guess ($guess) needs to go lower ...\n"; $max = int($guess); } else { print "bingo in $num_guesses guesses! the answer was: $digest_ +hex and your guess was ".bigint_to_hex($guess)." ($guess).\n"; last; } } sub bigint_to_hex { # graduitously ripped off from Ben Aveling's answer in # +-a-big-number-in-perl # because sprintf("%x", bigint) does not work sadly... my $inp = shift; my $out = ""; while($inp){ my $chunk=$inp & 0xf; $inp >>= 4; $out = sprintf("%x",$chunk).$out; } return $out; }
entering at guess number XXX, current range: min: 216530321997656745029789011476757518019484653536 max: 216530321997656745029789011476757518019484653568 answer: 216530321997656745029789011476757518019484653552 guess: 216530321997656745029789011476757518019484653552 diff: 0 bingo in XXX guesses! the answer was: 25ed8e31b995bb927966616df2a42b97 +9a2717f0 and your guess was 25ed8e31b995bb927966616df2a42b979a2717f0 +(216530321997656745029789011476757518019484653552).

EDIT: this is interesting reading

bw, bliako

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Re^2: Reverse download protocols
by tomasz (Acolyte) on Aug 30, 2021 at 19:07 UTC
    Thanks a lot for your positive reply. I will give you feedback later on. I need to analyse your thoughts. It may take a while... It's not exactly what I asked about, but closely related. Thanks again!
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