References 1 THOMPSON, G. H. B., and HENSHALL, G. D. : 'Nonradiative carrier loss and temperature sensitivity of threshold in 1-27 jim (GaIn)(AsP)/InP DH lasers', Electron. Lett., 1980,16, pp. 42-44 2 YANO, M., IMAI, H., and TAKUSAGAWA, M. : 'Analysis of threshold temperature characteristics for InGaAsP/InP double heterojunction lasers', J. Appl. Phys., 1981, 52, pp. 3172-3175 3 OOMURA, E., MUROTANI, T., HIGUCHI, H., NAMIZAKI, H., a n d SUSAKI, w.: 'Low threshold InGaAsP/InP buried crescent laser with double current confinement structure', IEEE J. Quantum Electron., 1981, QE-17, pp. 646-650 4 ISHIKAWA, H., IMAI, H., TANAHASHI, T., NISHITANI, Y., a n d TAKUSAGAWA, M.: 'V-grooved substrate buried heterostructure I n G a A s P - /InP laser', Electron. Lett., 1981,17, pp. 465-466 5 MITO, I., KITAMURA, M., KAEDE, K., ODAGIRI, Y., SEKI, M., SUGIMOTO, M., and KOBAYASHI, K.: 'InGaAsP planar buried heterostructure laser diode (PBH-LD) with very low threshold current', ibid., 1982, 18, pp. 2-3 6 ADAMS, A. R., ASADA, M., SUEMATSU, Y., and ARAI, s.i T h e tem- perature dependence of the efficiency and threshold current of In^^Ga^As^P^y lasers related to intervalence band absorption', Jpn. J. Appl. Phys., 1980,19, pp. L621-L624 0013-5194/82/160703-03$1.50/0 AUTOCORRELATION FUNCTION PARAMETERS USED TO INDICATE INCIPIENT BLOCKAGE IN A PNEUMATIC TRANSPORT SYSTEM Indexing terms: Measurement, Pneumatic transport, Stochastic processes A study of autocorrelation properties in pneumatic transport systems has been performed. The autocorrelation height at zero time delay and the time delay at which the autocorrelation function becomes zero have been considered. Introduction: T h e use of pneumatic conveying for transporting solids in pipelines is fairly well established. Conveyors have been built involving many hundreds of metres of vertical lift and horizontal pipeline runs. Both positive and negative pressure systems have been used, negative pressure systems having the advantage of higher plant safety and cleanliness since all leaks are inwards. Positive pressure systems, on the other hand, allow a higher solids-mass flow rate since higher differential pressures can be established across the system. Indeed, dense phase conveying (solids/air-mass flow-rate ratios of > 20) can only be carried out under positive pressure. The work described here concerns itself with light phase conveying (solids/air-mass flow-rate ratio < 10). In this type of conveyor the types of solids conveyed range from submicron cement powder to 75 mm pieces of coal. Solids velocities range from 5 m/s to 50 m/s, and solids mass flow rates can be up to several hundreds of tons per hour. Little if any automatic control of these conveyors has been implemented to date. In light phase conveying, degradation of solids and pipeline wear are natural consequences of high-velocity pipeline transport. Also, the energy consumed per ton of solids transported increases with increasing velocity (and also with decreasing solids-mass flow rate). Fig. 1 shows a 3-D plot of air-mass flow-rate against solids-mass flowrate against electrical energy consumed by the compressor per kilogram of solids transported. As one would expect, the specific energy consumption shows a strong dependency on the solids-mass flow rate. There is also a minimum in specific energy consumption, though less well pronounced, associated with the air-mass flow rate for fixed solids-mass flow rate. Ideally, a pneumatic conveyor should be run at as low a velocity and as high a solids-mass flowrate as possible, thus minimising the aforementioned factors. However, at lower velocities the risk of blocking the conveyor increases since for a given solids-mass flow rate more solids reside in the conveyor than at higher velocities. Clearly, in order to use the conveyor at the most economic operating point, it is necessary to minimise the risk of blockage and ensure that if the conveyor's operating conditions shift such that it is likely to block then some indication of this is made or corrective action taken. The crosscorrelation of two signals from transducers axially spaced along a pipe will yield information on the velocity of solids in the pipe,1 but this is not wholly indicative of incipient pipeline blockage. Experiments have been performed using the autocorrelation (ACF) function of the signal from one sensor, and this seems to give much better indication of operation in the region close to blockage of the pipe. Experimental work: The experimental set-up at Bradford is a negative-pressure pneumatic conveyor. The pipes, of 76 mm ID aluminium, are in sections, facilitating the alteration of the plant layout. A MINC-11 computer is used to monitor plant performance, log measured data, and effect independent control over the air- and solids-mass flow rates (see Fig. 2). The sensors used in the correlation work are ring sensors comprising a 2 mm-thick ring set flush to the pipe wall in PTFE insulator. The charge induced in the ring is converted to a voltage signal by a charge amplifier. The correlator used is a Hewlett Packard 5420A digital signal analyser, this also being controlled by the MINC-11 computer. The solids used for these experiments were 3 mm PVC cubes. The MINC-11 was programmed to set the solids-mass flow rate to five equally spaced values in the range 0-12-0-67 kg/s. For each of these values the air-mass flow rate was set to ten equally spaced values in the range 0-1-0-22 kg/s. At each of these 50 operating points the correlator took and averaged a set of 50 autocorrelations each taken with 40 ms data time. ^air-mass flow rate.kg/s Fig. 2 Schematic diagram of plant Two parameters of the auto-correlation functions were measured: 28 (a) the correlation height at zero time delay (b) the time delay at which the ACF first became zero. solids mass flow rate. kg/s Fig. 1 Graph of air-mass flow rate against solids-mass flow rate against energy consumption per kilogram of solids conveyed ELECTRONICS LETTERS 5th August 1982 Vol.18 No. 16 These parameters were plotted as two 3-D graphs: solids-mass flow rate against air-mass flow rate against correlation parameter (see Figs. 3 and 4). 705 At low solids-mass flow rates, the lines A-A' on the graphs, the variation in ACF height is small over the whole range of air-mass flow rates. Similarly the time delay for zero ACF height shows little change. However, as we progress towards high solids-mass flow rates, lines B-B' on the graph, we note that the time delays exhibit a sharp upward trend at low air velocities, with subsequent blockage of the conveyor as the air-mass flow rate is decreased. The conveyor will operate for an extended period at a point intermediate between the lower, stable-running plateau and the upper, system-blocked plateau. Acknowledgment: This work is financially supported by the Science & Engineering Research Council, who has provided grants for the equipment and research staff. C. M. BECK 11th June 1982 R. M. HENRY B. T. LOWE A. PLASKOWSKI Postgraduate School of Studies in Control Engineering University of Bradford Bradford, West Yorkshire BD7 1DP, England References 1 BECK, M. s.: 'Cross-correlation flowmeters', NRDC Bull., 1981, 52, p. 26 2 BENDAT, i. s., and PIERSOL, A. c : 'Measurement and analysis of random data' (Wiley) 3 BECK, c. M., HENRY, R. M., LOWE, B. T., and PLASKOWSKI, A.: 'Instru- mentation for minimising the operating costs of fluid transport systems'. Interflow '82 Conference, Harrogate, 1982 0013-5194/82/160705-02$ 1.50/0 solids-mass"-flow rate,kg/s Fig. 3 Graph of air-mass flow rate against solids-mass flow rate against correlation zero time-delay height Rxx{0) air-mass flow rate,kg/s B1 SHORT CYCLING IN THE KRAVITZ-REED PUBLIC KEY ENCRYPTION SYSTEM Indexing terms: Codes, Polynomials solids-mass flow rate,kg/s Fig. 4 Graph of air-mass flow rate against solids-mass flow rate against correlation time delay for zero height {Rxx( ) = 0) On the ACF height graph another interesting feature develops at high solids loadings. As the air-mass flow rate is dropped, the height of the correlation at zero time delay (equivalent to the RMS voltage of the transducer output) falls, but, at a point before system blockage occurs, the ACF rises with decreasing air-mass flow rate and then continues to fall again. This second peak in the ACF against air-mass flow rate graph, which is more pronounced at high solids loadings, is a repeatable indicator of conditions approaching blockage. It should be possible to use these two properties of the ACF as an indicator of the increased risk of system blockage with decreasing air-mass flow rate or increasing solids-mass flow rate. Measurement of the autocorrelation parameters at two points along a pipeline and subtracting them should yield information as to the operating trend of the conveyor (see Fig. 5). Stable flow should give zero difference, a trend towards blockage, say, a positive difference and the opposite for a trend away from blockage. The sharp rise in time delay for zero ACF height suggests that it may be useful in switching the control strategy of a pneumatic conveyor controller so as to prevent the system from blocking while maintaining as much as possible the constraints of minimum velocity and maximum solids-mass flow rate and their associated benefits. ACF trend in solids-mass flow rate along pipe Fig. 5 Use of autocorrelations from two points along a pipeline to indicate the trend in solids-mass flow rate along the pipe 706 The Kravitz-Reed public key encryption system, a variant of the MIT system based on Galois fields, is interesting because it offers the potential of high security with efficient implementation. In the letter we demonstrate that high security and efficient implementation are not, in reality, compatible goals with this algorithm. Efficient implementation is subject to a short cycling attack that exposes the secret key to computation. If the parameters of the algorithm are selected for high security, then the algorithm cannot be efficiently implemented. Description of algorithm: In the public key encryption system introduced by Kravitz and Reed,1 an extension of the MIT system,2 two irreducible polynomials, p(x) and q(x), having degrees n and m, are selected. An enciphering exponent e relatively prime to r = (2" — lX2m — 1) is chosen; the deciphering exponent d is the inverse of e modulo r. A message y is enciphered as E(y) = ye mod /, where f(x) = p{x)q(x). The ciphertext E{y) is decrypted using the same formula with d replacing e. Kravitz and Reed base the security of this algorithm on the supposition that one must factor the polynomial f(x) in order to discover n and m, and thus the secret key d, from the public key (e,/). However, it appears that a short cycling attack based on superenciphering any polynomial with enciphering exponent e = any power of 2 will provide the values of n and m with work factor nm. Here we note that efficient hardware implementations rest on selecting n and m to have perhaps 3 to 5 decimal digits, which would lead to shift register implementations involving several hundred to a few thousand bits. Unfortunately this selection of n and m leads to a work factor for penetration of about 103 to 105 encryption operations, which is trivial. Proper security will require that n and m be selected to have several hundred decimal digits, which will prejudice efficient implementations. Short cycling: Short cycling attacks against other public key algorithms3-4 have proved to be largely unsuccessful, possibly because the attempts may have been too limited by concentrating on the received ciphertext while trying to recover plaintext. When applied in this way the short cycling attack is generally little better than using the algorithm as a randomnumber generator. In using short cycling to attack the Kravitz-Reed algorithm, however, we ignore intercepted ciphertext, and instead concentrate on recovering n and m from knowledge of/(x) only. ELECTRONICS LETTERS 5th August 1982 Vol. 18 No. 16

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