On the correlation of binary sequences Original Research Article

In a series of papers Mauduit and Sárközy (partly with further coauthors) studied finite pseudorandom binary sequences. In particular, one of the most important applications of pseudorandomness is cryptography. If, e.g., we want to use a binary sequence image (after transforming it into a bit sequence) as a key stream in the standard Vernam cipher [A. Menezes, P. van Oorschot, R. Vanstone, Handbook of Applied Cryptography, CRC Press, Boca Raton, 1997], then image must possess certain pseudorandom properties. Does image need to possess both small well-distribution measure and, for any fixed small k, small correlation measure of order k? In other words, if image is large, resp. image is large for some fixed small k, then can the enemy utilize this fact to break the code? The most natural line of attack is the exhaustive search: the attacker may try all the binary sequences image with large image, resp. large image, as a potential key stream. Clearly, this attack is really threatening only if the number of sequences image with