Results 1  10
of
19
Propagation Characteristics of Boolean Functions
, 1990
"... The relation between the WalshHadamard transform and the autocorrelation function of Boolean functions is used to study propagation characteristics of these functions. The Strict Avalanche Criterion and the Perfect Nonlinearity Criterion are generalized in a Propagation Criterion of degree k. New p ..."
Abstract

Cited by 82 (3 self)
 Add to MetaCart
The relation between the WalshHadamard transform and the autocorrelation function of Boolean functions is used to study propagation characteristics of these functions. The Strict Avalanche Criterion and the Perfect Nonlinearity Criterion are generalized in a Propagation Criterion of degree k. New properties and constructions for Boolean bent functions are given and also the extension of the definition to odd values of n is discussed. New properties of functions satisfying higher order SAC are derived. Finally a general framework is established to classify functions according to their propagation characteristics if a number of bits is kept constant.
An Approximate Distribution for the Maximum Order Complexity
, 1995
"... In this paper we give an approximate probability distribution for the maximum order complexity of a random binary sequence. This enables the development of statistical tests based on maximum order complexity for the testing of a binary sequence generator. These tests are analogous to those based on ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
(Show Context)
In this paper we give an approximate probability distribution for the maximum order complexity of a random binary sequence. This enables the development of statistical tests based on maximum order complexity for the testing of a binary sequence generator. These tests are analogous to those based on linear complexity. Key Words. Binary Sequence, Stream Cipher, Feddback Shift Register, Maximum Order Complexity This author acknowledges the support of the Nuffield Foundation 1 1 Introduction The linear complexity is a wellknown tool for assessing the cryptographic strength of a binary sequence. For a given sequence, it measures the length of the shortest linear feedback shift register (LFSR) that can generate the sequence. The linear complexity is easily calculated using the Berlekamp Massey algorithm [5], which also gives a corresponding LFSR. A sequence with a low linear complexity can therefore easily be simulated, and so a sequence with a large linear complexity is clearly nec...
A scalable method for constructing Galois NLFSRs with period 2 n − 1 using crossjoin pairs
 IEEE Trans. on Inform. Theory
"... Abstract. This paper presents a method for constructing nstage Galois NLFSRs with period 2 n − 1 from nstage maximum length LFSRs. We introduce nonlinearity into state cycles by adding a nonlinear Boolean function to the feedback polynomial of the LFSR. Each assignment of variables for which this ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
(Show Context)
Abstract. This paper presents a method for constructing nstage Galois NLFSRs with period 2 n − 1 from nstage maximum length LFSRs. We introduce nonlinearity into state cycles by adding a nonlinear Boolean function to the feedback polynomial of the LFSR. Each assignment of variables for which this function evaluates to 1 acts as a crossing point for the LFSR state cycle. By adding a copy of the same function to a later stage of the register, we cancel the effect of nonlinearity and join the state cycles back. The presented method requires no extra time steps and it has a smaller area overhead compared to the previous approaches based on crossjoin pairs. It is feasible for large n. However, it has a number of limitations. One is that the resulting NLFSRs can have at most ⌊n/2⌋1 stages with a nonlinear update. Another is that feedback functions depend only on state variables which are updated linearly. The latter implies that sequences generated by the presented method can also be generated using a nonlinear filter generator. 1
Suffix Trees and String Complexity
 Advances in Cryptology: Proc. of EUROCRYPT, LNCS 658
, 1992
"... Let s = (s 1 ; s 2 ; : : : ; s n ) be a sequence of characters where s i 2 Z p for 1 i n. One measure of the complexity of the sequence s is the length of the shortest feedback shift register that will generate s, which is known as the maximum order complexity of s [17, 18]. We provide a proof th ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Let s = (s 1 ; s 2 ; : : : ; s n ) be a sequence of characters where s i 2 Z p for 1 i n. One measure of the complexity of the sequence s is the length of the shortest feedback shift register that will generate s, which is known as the maximum order complexity of s [17, 18]. We provide a proof that the expected length of the shortest feedback register to generate a sequence of length n is less than 2 log p n+ o(1), and also give several other statistics of interest for distinguishing random strings. The proof is based on relating the maximum order complexity to a data structure known as a suffix tree. 1 Introduction A common form of stream cipher are the socalled running key ciphers [4, 9] which are deterministic approximations to the one time pad. A running key cipher generates an ultimately periodic sequence s = (s 1 ; s 2 ; : : : ; s n ), s i 2 Z p ; 1 i n, for a given seed or key K. Encryption is performed as with the one time pad, using s as the key stream, but perfect secu...
AsymptoticallyTight Bounds on the Number of Cycles in Generalized de BruijnGood Graphs
 DISCRETE APPLIED MATHEMATICS
, 1992
"... The number of cycles of length k that can be generated by qary nstage feedback shiftregisters is studied. This problem is equivalent to finding the number of cycles of length k in the natural generalization, from binary to qary digits, of the socalled de BruijnGood graphs [2, 7]. The number o ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
The number of cycles of length k that can be generated by qary nstage feedback shiftregisters is studied. This problem is equivalent to finding the number of cycles of length k in the natural generalization, from binary to qary digits, of the socalled de BruijnGood graphs [2, 7]. The number of cycles of length k in the qary graph G (q) n of order n is denoted by fi (q) (n; k). Known results about fi (2) (n; k) are summarized and extensive new numerical data is presented. Lower and upper bounds on fi (q) (n; k) are derived showing that, for large k, virtually all qary cycles of length k are contained in G (q) n for n ? 2 log q k, but virtually none of these cycles is contained in G (q) n for n ! 2 log q k \Gamma 2 log q log q k. More precisely, if (q) k denotes the total number of qary length k cycles, then for any function f(k) that grows without bounds as k ! 1 (e.g. f(k) = log q log q log q k), the bounds obtained on fi (q) (n; k) are asymptotically t...
An equivalence preserving transformation from the Fibonacci to the Galois NLFSRs.” http://arxiv.org/abs/0801.4079
"... Abstract. Conventional NonLinear Feedback Shift Registers (NLFSRs) use the Fibonacci configuration in which the value of the first bit is updated according to some nonlinear feedback function of previous values of other bits, and each remaining bit repeats the value of its previous bit. We show ho ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
Abstract. Conventional NonLinear Feedback Shift Registers (NLFSRs) use the Fibonacci configuration in which the value of the first bit is updated according to some nonlinear feedback function of previous values of other bits, and each remaining bit repeats the value of its previous bit. We show how to transform the feedback function of a Fibonacci NLFSR into several smaller feedback functions of individual bits. Such a transformation reduces the propagation time, thus increasing the speed of pseudorandom sequence generation. The practical significance of the presented technique is that is makes possible increasing the keystream generation speed of any Fibonacci NLFSRbased stream cipher with no penalty in area.
A Method for Generating Full Cycles by a Composition of NLFSRs
"... Abstract. NonLinear Feedback Shift Registers (NLFSR) are a generalization of Linear Feedback Shift Registers (LFSRs) in which a current state is a nonlinear function of the previous state. The interest in NLFSRs is motivated by their ability to generate pseudorandom sequences which are usually har ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. NonLinear Feedback Shift Registers (NLFSR) are a generalization of Linear Feedback Shift Registers (LFSRs) in which a current state is a nonlinear function of the previous state. The interest in NLFSRs is motivated by their ability to generate pseudorandom sequences which are usually hard to break with existing cryptanalytic methods. However, it is still not known how to construct large nstage NLFSRs which generate full cycles of 2 n possible states. This paper presents a method for generating full cycles by a composition of NLFSRs. First, we show that an n ∗ kstage register with period O(2 2n) can be constructed from k nstage NLFSRs by adding to their feedback functions a logic block of size O(n ∗ k). This logic block implements Boolean functions representing the set of pairs of states whose successors have to be exchanged in order to join cycles. Then, we show how to join all cycles into one by using one more logic block of size O(n ∗ k 2) and an extra time step. The presented method is feasible for generating very large full cycles. 1