Depends on #149 .
Actually, for our applications, in which we compare only small numbers (usually max 64 bits in length), we can do better by defining the comparison directly for the UInt gadgets: to prove an inequality of the from x >= y, where x and y are UInt gadgets, we can follow an approach similar to what we did for the ThresholdSignatureCircuit (enforcing number_of_valid_signatures >= threshold) https://github.com/HorizenOfficial/zendoo-sc-cryptolib/blob/development/doc/GenericThresholdCircuit.pdf, e.g. enforcing that pack(x_bits) - pack(y_bits) == pack(alloc(x_val-y_val).to_bits_with_length_restriction[..64])
(We can do this with 1 LC of the form 2^0(x_b0 - y_b0) + ... + 2^n-1(x_bn-1 - y_bn-1) = 2^0 diff_0 + ... + 2^n-1 * diff_n-1.
We can also integrate Add and Mul gadgets for UInt (we already have AddMany), and let them return an "overflow" bit that, if desired, we can enforce it to be 0. This will make operations and comparison doable without using any Field gadget, thus completely controllable and secure.
Depends on #149 .
Actually, for our applications, in which we compare only small numbers (usually max 64 bits in length), we can do better by defining the comparison directly for the UInt gadgets: to prove an inequality of the from x >= y, where x and y are UInt gadgets, we can follow an approach similar to what we did for the ThresholdSignatureCircuit (enforcing number_of_valid_signatures >= threshold) https://github.com/HorizenOfficial/zendoo-sc-cryptolib/blob/development/doc/GenericThresholdCircuit.pdf, e.g. enforcing that pack(x_bits) - pack(y_bits) == pack(alloc(x_val-y_val).to_bits_with_length_restriction[..64])
(We can do this with 1 LC of the form 2^0(x_b0 - y_b0) + ... + 2^n-1(x_bn-1 - y_bn-1) = 2^0 diff_0 + ... + 2^n-1 * diff_n-1.
We can also integrate Add and Mul gadgets for UInt (we already have AddMany), and let them return an "overflow" bit that, if desired, we can enforce it to be 0. This will make operations and comparison doable without using any Field gadget, thus completely controllable and secure.