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