Bound for linear complexity of quadratic functions in Fp

Information security is of capital importance, and several cryptographic techniques have been developed to perform the security services required, not only data confidentiality. Taking into account the high speed of the current broadband, the only cryptographic techniques one can use are those based on symmetric systems, and more precisely, those based on stream ciphers. Pseudorandom sequences are the basis of these cryptosystems, and many different generators have been defined. This paper deals with quadratic functions in finite fields, frequently used in cryptography, as a pseudorandom number generation. The importance of this kind of function is not limited to pseudorandom sequence generation, but to public-key cryptosystems. We focus on an important parameter regarding the randomness of the sequences generated: linear complexity as an unpredictability measurement