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- 关键词：Finite pseudorandom binary sequences
- 刊名：Journal of Molecular Catalysis A: Chemical
- 出版年：2008
- 出版时间：1 May 2008
- 年：2008
- 卷：286
- 期：1-2
- 页码：vii-xii
- 全文大小：531 K
文摘
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 EN![]()
{-1,+1}N (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 EN must possess certain pseudorandom properties. Does EN need to possess both small well-distribution measure and, for any fixed small k, small correlation measure of order k? In other words, if W(EN) is large, resp. Ck(EN) 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 EN![]()
{-1,+1}N with large W(EN), resp. large Ck(EN), as a potential key stream. Clearly, this attack is really threatening only if the number of sequences EN![]()
{-1,+1}N with
- (i) large W(EN), resp.