'Lookup Argument in Halo2 - Sin7Y Tech Review (14)' by Sin7Y_Labs sin7y blockchain
)∙l_0=0As is known, with d+1 points, a polynomial, of which the order is less than d+1, can be exclusively confirmed. Therefore, if the order of the polynomial is not enough, just with more queries than orders of the polynomial on different points, the verifier can get all data of the polynomial, losing the features of zero-knowledge.
If the order is greater than 1, then the verifier knows the values of the two points and any information about the secret cannot be revealed; In detail, for the table with a size of 2^k, if the size of A and S is less than 2^k, some random values need to be filled in it. But it must be noted that the filled random values, which don’t meet the requirements of the Lookup argument theory, need to be selected using the selector.
a. For example, constrain R on each row, which means that the R can be regarded as some sets of S, and then verify ϵ R.
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