Joseph J. Rushanan

Duadic codes and difference sets

This note illustrates the strong relationship between duadic codes and difference sets. Sufficient conditions are given for the code of a difference set to be embedded into a duadic code. This result generalizes some wellknown results on projective planes and is related to Wilbrinks Theorem.

EIGENVALUES AND THE SMITH NORMAL FORM

Abstract We compare the Smith normal form (SNF) over the integers of an integral nonsingular matrix with its spectrum when its eigenvalues are integers. Our results include tight bounds on the size of the largest element of the SNF when the matrix is diagonalizable with nonzero integer eigenvalues, with no assumptions on the diagonalizing matrices.

Algebraic-integer quantization an residue number system processing

The algebraic-integer number representation, in which the signal sample is represented by a set of (typically four to eight) small integers, combines with residue number system (RNS) processing to produce processors composed of simple parallel channels. The analog samples must first be quantized into the algebraic-integer representation, and the final algebraic-integer result converted back to an analog or digital form. In between these two conversions, the algebraic-integer representation must be converted into and out of two levels of RNS parallelism. The authors address these quantization and conversion problems and demonstrate their solution by implementing a 128-tap algebraic-integer filter using the moduli 17 and 31, with four parallel channels per modulus. This processor performs equivalently to an integer processor with 19 bits of dynamic range. It is concluded that the algebraic-integer representation is best suited to control the dynamic range requirements of integer processors in situations where there is a high sensitivity to quantization and roundoff errors, especially when there is a matching nonuniform input distribution.<<ETX>>

VLSI design of an algebraic-integer signal processor

A programmable 128-tap linear systolic FIR filter was implemented in VLSI with a throughput of 5 MHz. The design combines algebraic-integer quantization and residue number system (RNS) processing in order to add a second level of parallelism to integer RNS processing, generalizing the quadratic RNS concept. This 9-b processor performs equivalently to an integer processor with 20 b of dynamic range.<<ETX>>

On quadratic m-sequences

Maximal sequences generated by linear feedback shift registers (FSRs), known as m-sequences, have been well-studied in the literature. These sequences have long periods, good statistical properties and two-valued autocorrelation functions. However, m-sequences are extremely vulnerable to a known plaintext attack. In order to overcome these weaknesses, nonlinearities have been introduced. We study nonlinear feedback functions by investigating quadratic functions. The quadratic span of a periodic binary sequence is the length of the shortest quadratic FSR that generates the sequence. This paper considers the question as to whether the sequence obtained from a DeBruijn sequence by dropping the all-zero state can now have quadratic span n. Such sequences are the quadratic analog of the linear m-sequences and present an attractive extremal case to explore further the structure of nonlinear FSRs. >

Optical key distribution system using atmospheric turbulence as the randomness generating function: classical optical protocol for information assurance

Abstract. We describe an experimental laboratory system that generates and distributes random binary sequence bit streams between two optical terminals (labeled Alice and Bob). The random binary sequence is generated through probing the optical channel of a turbulent atmosphere between the two terminals with coincident laser beams. The two laser beams experience differential phase delays while propagating through the atmospheric optical channel. The differential phase delays are detected and sampled at each terminal to yield raw random bit streams. The random bit streams are processed to remove bit errors and, through privacy amplification, to yield a bit stream known only to Alice and Bob. The same chaotic physical mechanism that provides randomness also provides confidentiality. The laboratory system yielded secret key bit rates of a few bits/second. For external optical channels over longer channel lengths with atmospheric turbulence levels, secret bit rates of 10 s of bits/second are predicted.

Blind synchronization of m-sequences with even span

The problem of recovering the phase on a known binary m-sequence that is corrupted by a binary noise source is considered. This problem arises in the cryptanalysis of stream ciphers formed from a nonlinear combination of m-sequences. A synchronization procedure is developed for even span n. The procedure obtains a reliable estimate of the phase of an m-sequence of span n from unreliable estimates of the phases of a small number of shifts of a fixed m-sequence of span n/2. These latter estimates can be obtained from a variety of methods available in the literature. The procedure results in a reduction of complexity but requires observing on the order of the square root of the m-sequences period.

A coset correlation for sequences with two-valued periodic autocorrelation

Defines a new coset correlation that generalizes previous coset correlation results for m-sequences. This new correlation can be computed in terms of the coset sizes for any sequence that has a two-valued periodic autocorrelation function and that is constant on cosets. Thus the results apply to a larger family of periodic sequences than just m-sequences. >