'Permutation Argument in Halo 2: Sin7Y Tech Review (15)' by Sin7Y_Labs
Sin7Y is a tech team that explores layer 2, cross-chain, ZK, and privacy computing. #WHAT IS HAPPENING IN BLOCKCHAIN#Halo2 uses permutation argument technology to allow copy constraint on any number of columns;
Define: cycle => represents the cyclic mapping relationship between elements, namely: map[a]=b, map[b]=c, map[c]=a, which can be extended to an arbitrary-sized cycle.If we don’t have any copy constraint now, we can treat the four X values as an independent permutation cycle, namely ; now, we have added the first copy constraint, f =. Obviously, cycle and cycle are not affected, and cycle and cycle will be combined into a big cycle.
As shown in the figure: there are three columns of data, corresponding to the values of three polynomials V3, V5, V7, when {X=0…2k-1}. It can be found that we have performed copy constraint on the values between different polynomials . Next, we will use the permutation argument to prove the corresponding X to the values that we set to be equivalent, is valid.
Similar to the lookup argument, we need to introduce some random numbers to achieve zero knowledge. If the total number of rows is 2k, the number of valid rows is u, and the number of invalid rows is t, then u + t +1=2k must be satisfied.qlast, the value of row u is 1, and others are 0 )⋅I0=0According to the formula of polynomial Zp, Z=1 . It is worth noting that this constraint constrains Z within the range of {0,1}, but the probability of being 0 is very small.
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