is known as the absolute indicator. If all autocorrelation coefficients are 0 (i.e. the derivatives are balanced) for a certain number of bits then the function is said to satisfy the propagation criterion to that order; if they are all zero then the function is a bent function. The autocorrelation coefficients play a key role in differential cryptanalysis. The Walsh coefficients of a Boolean function and its autocorrelation coefficients are related by the equivalent of the Wiener–Khinchin theorem, which states that the autocorrelation and the power spectrum are a Walsh transform pair. These concepts can be extended naturally to vectorial Boolean functions by considering their output bits (coordinates) individually, or more thoroughly, by looking at the set of all linear functions of output bits, known as its components. The set of Walsh transforms of the components is known as a Linear Approximation Table (LAT) or correlation matrix; it describes the correlation between different linear combinations of input and output bits. The set of autocorrelation coefficients of the components is the autocorrelation table, related by a Walsh transform of the components to the more widely used Difference Distribution Table (DDT) which lists the correlations between differences in input and output bits (see also: S-box). Real polynomial form On the unit hypercube Any Boolean function can be uniquely extended (interpolated) to the real domain by a multilinear polynomial in , constructed by summing the truth table values multiplied by indicator polynomials:For example, the extension of the binary XOR function iswhich equalsSome other examples are negation (), AND () and OR (). When all operands are independent (share no variables) a function's polynomial form can be found by repeatedly applying the polynomials of the operators in a Boolean formula. When the coefficients are calculated modulo 2 one obtains the algebraic normal form (Zhegalkin polynomial). Direct expressions for the coefficients of the polynomial can be derived by taking an appropriate derivative:this generalizes as the Möbius inversion of the partially ordered set of bit vectors:where denotes the weight of the bit vector . Taken modulo 2, this is the Boolean Möbius transform, giving the algebraic normal form coefficients:In both cases, the sum is taken over all bit-vectors a covered by m, i.e. the "one" bits of a form a subset of the one bits of m. When the domain is restricted to the n-dimensional hypercube , the polynomial gives the probability of a positive outcome