tailieunhanh - Báo cáo vật lý: "ON COUNTING CERTAIN PERMUTATIONS USED FOR SPEECH SCRAMBLING"

Tuyển tập các báo cáo nghiên cứu khoa học trên tạp chí khoa học vật lý quốc tế đề tài: ON COUNTING CERTAIN PERMUTATIONS USED FOR SPEECH SCRAMBLING | Journal of Physical Science Vol. 17 2 131-139 2006 131 ON COUNTING CERTAIN PERMUTATIONS USED FOR SPEECH SCRAMBLING B. Jayaramakrishnan1 Rajesh Vijayaraghavan2 and V. Ravichandran3 1School of Management Circuit House Area East Jamshedpur 831 001. Jharkhand India 2Department of Computer Science Courant Institute of Mathematical Sciences New York University New York NY-10012 USA 3School of Mathematical Sciences Universiti Sains Malaysia 11800 USM Pulau Pinang Malaysia Corresponding author vravi@ Abstract The shift factor of a permutation is the average of the displacement of elements. In this paper we count the number of permutations having maximum shift factor in which adjacent elements not appearing together. Keywords speech scrambling key generation permutations derangements shift factor residual intelligibility 1. INTRODUCTION In a scrambling system the signal is encrypted by rearranging the input plain text data using permutations. When the signal is divided into portions or sub-bands the method directs the rearrangement or jumbling the order of these portions or sub-bands. This rearrangement is enabled by a key and the inverse of this key would decrypt back the original data. The scrambling works with permutation as the key element for encryption and its inverse permutation as the key for decryption. However not all of these permutations generated result in a scrambled signal with acceptably low Residual Intelligibility RI . The prime requirement of any encryption algorithm is that the RI should be minimized . after permutation one should not be in a position to decipher any details from the permuted data. The problem of key selection is therefore an important issue in the design of a scrambling system. On Counting Certain Permutations Used for Speech Scrambling 132 The following are examples of permutations that can minimize RI C1 Derangements permutations whose elements are displaced from their original position. C2 Permutations whose elements do .