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TimeDelay Neural Networks: Representation and Induction of Finite State Machines
 IEEE Transactions on Neural Networks
, 1997
"... In this work, we characterize and contrast the capabilities of the general class of timedelay neural networks (TDNN), with input delay neural networks (IDNN), the subclass of TDNNs with delays limited to the inputs. Each class of networks is capable of representing the same set of languages, those ..."
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Cited by 15 (6 self)
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In this work, we characterize and contrast the capabilities of the general class of timedelay neural networks (TDNN), with input delay neural networks (IDNN), the subclass of TDNNs with delays limited to the inputs. Each class of networks is capable of representing the same set of languages, those embodied by the definite memory machines (DMM), a subclass of finite state machines. We demonstrate the close affinity between TDNNs and DMM languages by learning a very large DMM (2048 states) using only a few training examples. Even though both architectures are capable of representing the same class of languages, they have distinguishable learning biases. Intuition suggests that general TDNNs which include delays in hidden layers should perform well, compared to IDNNs, on problems in which the output can be expressed as a function on narrow input windows which repeat in time. On the other hand, these general TDNNs should perform poorly when the input windows are wide, or there is little r...
A New Statistical Testing for Symmetric Ciphers and Hash Functions
 Proc. Information and Communications Security 2002, volume 2513 of LNCS
, 2002
"... This paper presents a new, powerful statistical testing of symmetric ciphers and hash functions which allowed us to detect biases in both of these systems where previously known tests failed. We first give a complete characterization of the Algebraic Normal Form (ANF) of random Boolean functions by ..."
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Cited by 11 (1 self)
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This paper presents a new, powerful statistical testing of symmetric ciphers and hash functions which allowed us to detect biases in both of these systems where previously known tests failed. We first give a complete characterization of the Algebraic Normal Form (ANF) of random Boolean functions by means of the M obius transform. Then we built a new testing based on the comparison between the structure of the different Boolean functions Algebraic Normal Forms characterizing symmetric ciphers and hash functions and those of purely random Boolean functions. Detailed testing results on several cryptosystems are presented. As a main result we show that AES, DES Snow and Lili128 fail all or part of the tests and thus present strong biases.
A Study on the Construction and Analysis of Substitution Boxes for Symmetric Cryptosystems
, 1990
"... S(ubstitution)boxes are quite important components of modern symmetric cryptosystems (in particular, block ciphers) in the sense that Sboxes bring nonlinearity to block ciphers and strengthen their cryptographic security. An Sbox is said to satisfy the strict avalanche criterion (SAC), if and onl ..."
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Cited by 3 (1 self)
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S(ubstitution)boxes are quite important components of modern symmetric cryptosystems (in particular, block ciphers) in the sense that Sboxes bring nonlinearity to block ciphers and strengthen their cryptographic security. An Sbox is said to satisfy the strict avalanche criterion (SAC), if and only if for any single input bit of the Sbox, the inversion of it changes each output bit with probability one half. In this thesis, with the concrete proof of cryptographical properties of Sboxes satisfying the SAC, we propose a variety of provable construction methods for Sboxes satisfying the SAC. For Boolean Sboxes satisfying the SAC, we can construct and enlarge them by using concatenation, Kronecker (or direct) product, and dyadic shift. For bijective Sboxes satisfying the SAC, when an nbit input Boolean function and an nbit input bijective function satisfying the SAC are given, the combined function is proved to become an (n+1)bit bijective function satisfying the SAC as well. A...
Clockcontrolled generators
, 1999
"... A stream cipher generator can not be considered as suitable for stream ciphers applications unless its output sequences have large periods, large linear complexities and possess certain randomness properties. The use of clockcontrolled shift registers in keystream generators appears to be a good wa ..."
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Cited by 2 (0 self)
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A stream cipher generator can not be considered as suitable for stream ciphers applications unless its output sequences have large periods, large linear complexities and possess certain randomness properties. The use of clockcontrolled shift registers in keystream generators appears to be a good way of achieving sequences with these properties. In this thesis we look at clockcontrolled generators, these are built up from two registers, one controlling the clock of a second register from which the output is taken. Examples that have appeared in the literature include the stop and go generator, the binary rate multiplier, the (a, b) clockcontrolled generator, the cascade generator, and the shrinking generator. The binary rate multiplier and the (a, b) clockcontrolled generator may be seen as generalizations for the stop and go generator. Similarly we introduce generalizations of the cascade generator and the shrinking generator that allows us, by using the same initial states and feedback functions, to produce many more sequences with the same desirable properties as those
AN IMAGE SCRAMBLING ALGORITHM USING PARAMETER BASED MSEQUENCES
"... Image scrambling is a useful approach to secure the image data by scrambling the image into an unintelligible format. This paper introduces a new parameter based Msequence which can be produced by a series shift registers. In addition, a new image scrambling algorithm based on the Msequence is pre ..."
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Cited by 2 (0 self)
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Image scrambling is a useful approach to secure the image data by scrambling the image into an unintelligible format. This paper introduces a new parameter based Msequence which can be produced by a series shift registers. In addition, a new image scrambling algorithm based on the Msequence is presented. The user can change the security keys, r, which indicates the number of shift operations to be implemented, or the distance parameter p, to generate many different Msequences. This makes the scrambled images difficult to decode thus providing a high level of security protection for the images. The presented algorithm can encrypt the 2D or 3D images in one step. It also shows good performance in the image attacks such as filters (data loss) and noise attacks. The algorithm can be applied in the realtime applications since it is a straightforward process and easily implemented. Keywords: Image scrambling algorithm; maximum length sequence;
1 AbsoluteType Shaft Encoding Using LFSR Sequences with Prescribed Length
"... Abstract — Maximallength binary sequences have been known for a long time. They have many interesting properties, one of them is that when taken in blocks of n consecutive positions they form 2 n − 1 different codes in a closed circular sequence. This property can be used for measuring absolute ang ..."
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Cited by 1 (1 self)
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Abstract — Maximallength binary sequences have been known for a long time. They have many interesting properties, one of them is that when taken in blocks of n consecutive positions they form 2 n − 1 different codes in a closed circular sequence. This property can be used for measuring absolute angular positions as the circle can be divided in as many parts as different codes can be retrieved. This paper describes how a closed binary sequence with arbitrary length can be effectively designed with the minimal possible blocklength, using linear feedback shift registers (LFSR). Such sequences can be used for measuring a specified exact number of angular positions, using the minimal possible number of sensors that linear methods allow. Index Terms — Linear feedback shift register, Absolute angular position sensor, Closed circular sequences, Polynomials over finite
ABSOLUTE TYPE SHAFT ENCODING USING LFSR SEQUENCES WITH PRESCRIBED LENGTH
"... Abstract. Maximallength binary sequences have been known for a long time. They have many interesting properties, one of them is that when taken in blocks of n consecutive positions they form 2 n − 1 different codes in a closed circular sequence. This property can be used for measuring absolute angu ..."
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Abstract. Maximallength binary sequences have been known for a long time. They have many interesting properties, one of them is that when taken in blocks of n consecutive positions they form 2 n − 1 different codes in a closed circular sequence. This property can be used for measuring absolute angular positions as the circle can be divided in as many parts as different codes can be retrieved. This paper describes how can a closed binary sequence with arbitrary length be effectively designed with the minimal possible blocklength, using linear feedback shift registers (LFSR). Such sequences can be used for measuring a specified exact number of angular positions, using the minimal possible number of sensors that linear methods allow. 1.
Counting TwoState TransitionTour Sequences
"... This paper develops a closedform formula, f(k), to count the number of transitiontour sequences of length k for bistable machines. It is shown that the function f(k) is related to Fibonacci numbers. Some applications of the results in this paper are in the areas of: testable sequential machine ..."
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This paper develops a closedform formula, f(k), to count the number of transitiontour sequences of length k for bistable machines. It is shown that the function f(k) is related to Fibonacci numbers. Some applications of the results in this paper are in the areas of: testable sequential machine designs, random testing of register data paths, and qualification tests for random pattern generators. Index Terms: TransitionTours, Sequential Machine Testing, Fibonacci Numbers, Checking Experiments, and Testable Synthesis. 1.0 Introduction A transitiontour sequence is a binary sequence that includes all four transitions between adjacent binary bits. For example, 01100 is a transitiontour sequence because it has all four transitions 0 1, 1 0, 1 1 and 0 0 between adjacent bits. The definition of transitiontour is consistent with the general definition of transition tours defined for finite state machines in [15]. We want to find a function, f(k), that counts the number of disti...
Commonly Used Distributions
"... umbers. (b) Return the the a smallest number as BT(a# b). 3. If a and b are less than one: (a) Generate two uniform U(0,1) random numbers u (b) Let x = u and y = u . If (x + y) ? 1, go back to the previous step. Otherwise, return x=(x + y) as BT(a# b). 4. If a and b are greater than 1: Us ..."
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umbers. (b) Return the the a smallest number as BT(a# b). 3. If a and b are less than one: (a) Generate two uniform U(0,1) random numbers u (b) Let x = u and y = u . If (x + y) ? 1, go back to the previous step. Otherwise, return x=(x + y) as BT(a# b). 4. If a and b are greater than 1: Use rejection Binomial Distribution ffl The number of successes x in a sequence of n Bernoulli trials has a binomial distribution. ffl Characteristics: p = Probability of success in a trial, 0 ! p ! 1. n = Number of trials# n must be a positive integer. 2. Range: x = 0# 1# : : : # n B B B B C C C C n;x 4. Mean: np 5. Variance: np(1 ; p) successes 1. The number of processors that are up in a multiprocessor system. 2. The number of packets that reach the destination without loss. 3. The number of bits in a packet that are not affected by noise. 4. The number of items in a batch that have certain characteristics. ffl Variance ! Mean ) Binomial Variance ? Mean ) Negative Binomial Va