Error Free Perfect Secrecy Systems

Shannon's fundamental bound for perfect secrecy says that the entropy of the secret message cannot be larger than the entropy of the secret key initially shared by the sender and the legitimate receiver. Massey gave an information theoretic proof of this result, however this proof does not require independence of the key and ciphertext. By further assuming independence, we obtain a tighter lower bound, namely that the key entropy is not less than the logarithm of the message sample size in any cipher achieving perfect secrecy, even if the source distribution is fixed. The same bound also applies to the entropy of the ciphertext. The bounds still hold if the secret message has been compressed before encryption. This paper also illustrates that the lower bound only gives the minimum size of the pre-shared secret key. When a cipher system is used multiple times, this is no longer a reasonable measure for the portion of key consumed in each round. Instead, this paper proposes and justifies a new measure for key consumption rate. The existence of a fundamental tradeoff between the expected key consumption and the number of channel uses for conveying a ciphertext is shown. Optimal and nearly optimal secure codes are designed.Comment: Submitted to the IEEE Trans. Info. Theor

Long Range Dependence and Structural Breaks in the Gold Markets

The price of gold and its determining factors have been studied extensively in the literature. However, there is a lack of research on structural break in the long memory of the gold markets. This paper examines the long memory properties of gold prices. In particular, it attempts to test the stability of the long range dependence of gold returns and volatility. The results suggest that long memory exists in gold returns and volatility, and that the volatility of daily gold futures returns can be characterized by a hyperbolic decaying long memory process. Three episodes of structural breaks are found