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At a broad level it should be noted that competition comes not just from other garment suppliers, but also from other products and services that compete for consumers discretionary income. High prices for garments may encourage consumers to spend more money on other consumer durables such as high-de nition televisions or on leisure activities such as holidays. The unattractiveness of the prices of garments in relation to other competing products and services should be kept in mind. The relative sales and trends of various sectors of industry, plus the in ation rates by sector, are indicators of how well or otherwise this inter-sector competition is being met. The more homogeneous the product the greater the price competition. The fashion industry tries to encourage non-price competition by the branding and creation of unique designs and images for ranges. At the designer level of the market, such garments are in limited supply through exclusive outlets and, the creators hope, for limited periods. The ability of competitors to produce similar products is restricted by some legislative protection of the design. Consumer con dence in garment quality and the ability to purchase an up-todate design immediately enable higher prices to be charged. For other products such as socks the latitude to command exclusivity or any special design point that can be re ected in a higher price is more restricted.

Protocol description Setup: Suppose a set of n users P = {U1 , U2 , , Un } wish to agree upon a secret key Let US be a subset of users Quite often, we identify a user with its instance during the execution of a protocol In case US is a singleton set, we will identify US with the instance it contains Each user set US has a representative Rep(US) and for the sake of concreted ness we take Rep(US) = Uj , where j = min{k : Ukk US} We use the notation A[1, , n] for an array of n elements A1 , , An and write A[i] or Ai to denote the ith element of array A[ ] Let G1 = P , G2 (groups of prime order q) and e(, ) be as described in Section 1353.

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An ADC assigns a digital code for each pixel depending on the amplitude of the signal (0 4095 ADUs for a 12 bit system). Pixel values are stored in a frame buffer in the computer. The process repeats until all 1000 rows of pixels of the parallel register are emptied. For a 1 megapixel CCD chip processed at 2 bytes/pixel, 2 Mbytes are stored in the computer; the image is displayed in an 8 bit (256 gray-level) format on the monitor. The CCD chip is cleared (reread without digitization) to remove residual electrons prior to the next exposure. The total time for readout and display is 0.5 s for a 1 Mpixel camera operating at 5 MHz. Considering the large number of operations, it is remarkable that greater than a million pixels can be transferred across the chip, assigned a gray-scale value ranging from 0 to 4095, and stored in a frame buffer in the computer in less than a second! The accuracy of transfer of electron packets over thousands of pixels is also nearly error-free. The quantitative nature of a digital CCD image is shown in Figure 14-7. Another important feature in the camera head is the elements associated with cooling. As described below, CCD images are degraded by electron noises, the most serious of which are due to heat and the electronic readout of the camera. Thermal noise refers to the generation of electrons from the kinetic vibrations of silicon atoms in the CCD substrate. Thermal electrons cannot be distinguished from photoelectrons and thus contribute noise to the image. Cooling is essential for all scientific-grade CCD cameras, the

We choose a hash function H : G2 Zq The public parameters are params = (G1 , G2 , e, q, P, H) Each user Ui P chooses si Zq at random which it uses as its ephemeral key These keys are session speci c and determine the nal common key for the users in a session Key agreement: Let p = n/3 and r = n mod 3 The set of users participating in a session is partitioned into three user sets US1 , US2 , US3 with respective cardinalities being p, p, p if r = 0; p, p, p + 1 if r = 1; and p, p + 1, p + 1 if r = 2 This top-down recursive procedure is invoked for further partitioning to obtain a ternary tree structure (cf Section 1311).

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