Abstract: Algebraic immunity is a new cryptographic criterion proposed to against algebraic attacks. In order to resist algebraic attacks,Boolean functions used in many stream ciphers should have optimum algebraic immunity. This paper presented a construction of Boolean function in odd variables with optimum algebraic immunity. It's a recursive construction. Given any odd number, we can construct Boolean function with optimum algebraic immunity in the same number of variables.

Key words: Cryptography, Stream cipher, Algebraic attacks, Boolean function