The algebraic degree of a boolean function 
, denoted by deg(), is defined as the number of variables in the longest term of the algebraic normal form of . cryptographic functions must have high algebraic degrees.Using boolean functions of low degree in ciphers makes the algebraic
and differential attacks effective.
A Balanced boolean function ,is a function in which the number of zeroes equals the number of ones. In other words, the Hamming weight of , wt() = 
. Cryptographic functions must be balanced to avoid statistical dependence between the input and the output which can be used in attacks.
A Bent function, is a boolean function that has the maximum possible nonlinearity. Bent functions have an even number of variables. They do not exist for odd number of variables.
The minimum Hamming distance between a boolean function and the set of all affine boolean functions is called the nonlinearity of . Cryptographic functions must be at a sufficeintly big distance from any affine function so as to be resistant to the correlation attacks. In terms of Walsh transform ? , the nonlinearity of is 
A boolean function is said to be correlation immune of order m , if the output of the function is statistically independent of the combination of any m of its inputs. In terms of Walsh transform ? , it is correlation immune of degree m if W(
) = 0 for 1 <= wt() <= m. The combination of correlation immunity of order m and the property "Balanced" results in the property of resiliency of order m. Thus a boolean function is resilient if 
A boolean function is said to satisfy the propagation criterion of degree k,PC(k), if all its derivatives with respect to vectors 
with 1 <= wt() <=k are balanced. In the autocorrelation spectrum ? , this means that 
Boolean functions that satisfy PC(k) when at most t coordinates are fixed, are said to satisfy PC(k) of order t.
The Absolute indicator of an n-variable boolean function is defined as 
, where 
is the autocorrelation spectrum ? of with respect to .
The sum of square indicator of an n-variable boolean function is defined as SSI = 
, where is the autocorrelation spectrum ? of with respect to
The Walsh transform of a n-variable boolean function , is a real valued function defined on all the vectors that belong to GF(2)^n as
The autocorrelation function of an n-variable boolean function is a real valued function defined on all the vectors that
belong to GF(2)^n as 