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add SafeLessThan template to comparators with range checks over inputs #86

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add SafeLessThan template to comparators with range checks over inputs #86

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112d0bd
add `SafeLessThan` template to comparators
enricobottazzi Jan 17, 2023
4309a3c
use `LessThan` component inside `SafeLessThan` to save compatibility
enricobottazzi Jan 18, 2023
fb185d7
Restrict `Num2Bits` component instantiation to n bits instead of 252
enricobottazzi Jan 18, 2023
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17 changes: 17 additions & 0 deletions circuits/comparators.circom
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Original file line number Diff line number Diff line change
Expand Up @@ -98,6 +98,23 @@ template LessThan(n) {
out <== 1-n2b.out[n];
}

// Do Range checks on the inputs to avoid overflow
template SafeLessThan(n) {
assert(n <= 252);
signal input in[2];
signal output out;

component aInRange = Num2Bits(252);
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We can save some constraints by restricting to n bits instead. It will always be safe since n <= 252 anyway. Also, that way we can interpret SafeLessThan(n) as meaning "safely compare two n-bit numbers." This makes it easier to understand why in[0]+ (1<<n) - in[1] should be an n+1 bit number.

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Thanks for the comment. Good point. Added to the PR.

aInRange.in <== in[0];
component bInRange = Num2Bits(252);
bInRange.in <== in[1];

component n2b = Num2Bits(n+1);

n2b.in <== in[0]+ (1<<n) - in[1];

out <== 1-n2b.out[n];
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Perhaps we could use a normal LessThan component here to avoid code reuse. It makes it clearer what the difference between LessThan and SafeLessThan is, and if LessThan changes in the future we don't risk two difference implementations.

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Agree, applied change in this commit

}


// N is the number of bits the input have.
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