mirror of
https://github.com/logos-storage/logos-storage-proofs-circuits.git
synced 2026-01-02 13:33:07 +00:00
76 lines
2.4 KiB
Plaintext
76 lines
2.4 KiB
Plaintext
pragma circom 2.0.0;
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include "binary_compare.circom";
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include "misc.circom";
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//------------------------------------------------------------------------------
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//
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// extract the lowest `n` bits from a field element.
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//
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// NOTE: this is rather nontrivial, as everything is computed modulo `r`,
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// so naive bit decomposition does not work (there are multiple solutions).
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//
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// TODO: optimize this
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//
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template ExtractLowerBits(n) {
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signal input inp;
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signal output out[n];
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// we may have 2 solutions for this
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component tb = ToBits(254); // note: 2^253 < r < 2^254
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tb.inp <== inp;
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// bits of field prime `r`, least significant bit first
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var primeBits[254] = [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0,0,1,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0,0,0,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0,0,0,0,1,1];
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// enforce that the binary representation is < r
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component le = BinaryCompare(254);
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le.A <== tb.out;
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le.B <== primeBits;
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le.out === -1; // enforce `A < B`, that is, `bits < prime`
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// extract the lowest `n` bits
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for(var i=0; i<n; i++) {
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tb.out[i] ==> out[i];
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}
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}
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//------------------------------------------------------------------------------
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//
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// a version of the above specialized to the test field `p = 65537`
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//
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// this is used only for testing using the `r1cs-solver` tool
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//
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template ExtractLowerBits_testfield65537(n) {
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signal input inp;
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signal output out[n];
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// we may have up to 4 solutions for this
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component tb = ToBits(18); // note: 2^16 < r < 2^18
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tb.inp <== inp;
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// bits of field prime `r`, least significant bit first
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var primeBits[18] = [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0];
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// enforce that the binary representation is < r
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component le = BinaryCompare(18);
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le.A <== tb.out;
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le.B <== primeBits;
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le.out === -1; // enforce `A < B`, that is, `bits < prime`
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// extract the lowest `n` bits
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for(var i=0; i<n; i++) {
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tb.out[i] ==> out[i];
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}
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}
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//------------------------------------------------------------------------------
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