Abstract: A method for generating an accelerated and/or decelerated chaotic sequence. The method involves selecting a plurality of polynomial equations constructed from an acc-dec variable v. The method also involves selecting a value for the acc-dec variable v for advancing or stepping back a chaotic sequence generation by at least one cycle at a given time. The method further involves using residue number system (RNS) arithmetic operations to respectively determine solutions for the polynomial equations using the acc-dec variable v. The solutions iteratively computed and expressed as RNS residue values. The method involves determining a series of digits in a weighted number system based on the RNS residue values.

Abstract: A cryptographic system (CS) comprised of generators (502), (504), (510), an encryption device (ED), and a decryption device (DD). The generator (502) generates a data sequence (DS) including payload data. The generator (504) generates an encryption sequence (ES) including random numbers. The ED (506) is configured to perform a CGFC arithmetic process. As such, the ED is comprised of a mapping device (MD) and an encryptor. The MD is configured to map the DS and ES from Galois field GF[pk] to Galois extension field GF[pk+1]. The encryptor is configured to generate an encrypted data sequence (EDS) by combining the DS and ES utilizing a Galois field multiplication operation in Galois extension field GF[pk+1]. The generator (510) is configured to generate a decryption sequence (DS). The DD (508) is configured to generate a decrypted data sequence by performing an inverse of the CGFC arithmetic process utilizing the EDS and DS.

Abstract: Systems (400, 500, 600) and methods (300) for generating a chaotic amplitude modulated signal absent of cyclostationary features by preserving a constant variance. The methods involve: generating a PAM signal including pulse amplitude modulation having a periodically changing amplitude; generating a first part of a constant power envelope signal (FPCPES) by dividing the PAM signal by a square root of a magnitude of the PAM signal; generating a second part of the constant power envelope signal (SPCPES) having a magnitude equal to a square root of one minus the magnitude of the PAM signal; and generating first and second spreading sequences (FSS and SSS). The methods also involve combining the FPCPES with the FSS to generate a first product signal (FPS) and combining the SPCPES with the SSS to generate a second product signal (SPS). A constant power envelope signal is generated using the FPS and SPS.

Abstract: A method is provided for correlating samples of a received signal and samples of an internally generated/stored sample sequence (“IGSSS”). The method involves performing a first iteration of a first-resolution correlation state. The first-resolution correlation state involves: selecting a first N sets of samples from the received signal; selecting a first set of samples from the IGSSS; and concurrently comparing each of the N sets of samples with the first set of samples to determine if a correlation exists between the same. If it is determined that a correlation does not exist between one of the N sets of samples and the first set of samples, then a second iteration of the first-resolution correlation state is performed. If it is determined that a correlation exists between one of the N sets of samples and the first set of samples, then a first iteration of a second-resolution correlation state is performed.

Abstract: A method is provided for coherently demodulating a chaotic sequence spread spectrum signal at a receiver (104). The method includes receiving a chaotic sequence spread spectrum signal including a plurality of information symbols. The method also includes generating a first string of discrete time chaotic samples. The first string of discrete time chaotic samples is identical to a second string of discrete time chaotic samples generated at a transmitter. The method further includes processing the chaotic sequence spread spectrum signal at the receiver to identify a time offset and a frequency offset relative to the first string of discrete time chaotic samples. Each of the discrete time chaotic samples of the first string of discrete time chaotic samples has a shorter sample time interval than the duration of the information symbols.

Abstract: A method is provided for combining two or more input sequences in a communications system to increase a repetition period of the input sequences in a resource-efficient manner. The method includes a receiving step, a mapping step, and a generating step. The receiving step involves receiving a first number sequence and a second number sequence, each expressed in a Galois field GF[pk]. The mapping step involves mapping the first and second number sequences to a Galois extension field GF[pk+1]. The generating step involves generating an output sequence by combining the first number sequence with the second number sequence utilizing a Galois field multiplication operation in the Galois extension field GF[pk+1]. p is a prime number. k is an integer. pk+1 defines a finite field size of the Galois extension field GF[pk+1].

Abstract: A method is provided for generating a coherent chaotic sequence spread spectrum communications system. The method includes phase modulating a carrier with information symbols. The method also includes generating a string of discrete time chaotic samples. The method further includes modulating the carrier in a chaotic manner using the string of discrete time chaotic samples. Each of the discrete time chaotic samples has a shorter sample time interval than the duration of the information symbols. The generating step includes selecting a plurality of polynomial equations. The generating step also includes using residue number system (RNS) arithmetic operations to respectively determine solutions for the polynomial equations. The solutions are iteratively computed and expressed as RNS residue values. The generating step further includes determining a series of digits in the weighted number system based on the RNS residue values.

Abstract: A method is presided for masking a process used in generating a random number sequence. The method includes generating a random number sequence. This step involves selectively generating the random number sequence utilizing a ring structure which has been punctured. The method also includes performing a mixed radix conversion to convert the random number sequence from a first number base to a second number base. The method further includes puncturing the ring structure by removing at least one element therefrom to eliminate a statistical artifact in the random number sequence expressed in the second number base. The first number base and second number base are selected so that they are respectively defined by a first Galois field characteristic and a second Galois field characteristic.

Abstract: A method is provided for masking a process used in generating a number sequence. The method includes generating a first sequence of numbers contained within a Galois field GF[M]. The method also includes performing a first modification to a first number in the first sequence of numbers. The first modification includes summing the first number with a result of a modulo P operation performed on a second number of the first sequence that proceeds the first number. M is relatively prime with respect to P. The method further includes performing a second modification to the first random number. The second modification is comprised of a modulo P operation. This second modification is performed subsequent to the first modification. The method includes repeating the first and second modification for a plurality of numbers comprising the first sequence of numbers to generate a second sequence of numbers.

Abstract: A method is provided for generating a chaotic sequence. The method includes selecting a plurality of polynomial equations. The method also includes using residue number system (RNS) arithmetic operations to respectively determine solutions for the polynomial equations. The solutions are iteratively computed and expressed as RNS residue values. The method further includes determining a series of digits in a weighted number system (e.g., a binary number system) based on the RNS residue values. According to an aspect of the invention, the method includes using a Chinese Remainder Theorem process to determine a series of digits in the weighted number system based on the RNS residue values. According to another aspect of the invention, the determining step comprises identifying a number in the weighted number system that is defined by the RNS residue values.

Abstract: Systems (100) and methods for selectively controlling access to data streams communicated from a first communication device (FCD) using a timeslotted shared frequency spectrum and shared spreading codes. Protected data signals (1301, . . . , 130S) are modulated to form first modulated signals (1321, . . . , 132S). The first modulated signals are combined with first chaotic spreading codes to form digital chaotic signals. The digital chaotic signals are additively combined to form a protected data communication signal (PDCS). The PDCS (136) and a global data communication signal (GDCS) are time division multiplexed to form an output communication signal (OCS). The OCS (140) is transmitted from FCD (102) to a second communication device (SCD) over a communications channel. The SCD (106, 108, 110) is configured to recover (a) only global data from the OCS, or (b) global data and at least some protected data from the OCS.

Abstract: A receiver (104) in communications system (100) includes an antenna system (302) for receiving a composite signal comprising multi-path components associated with the multi-path images of a transmitted signal. The receiver also includes a correlation system (368) for correlating the received composite signal with a spreading sequence using different time-offset values to generate time-offset de-spread signals associated with at least a portion the multi-path images, where the spreading sequence is based on sequence of discrete-time chaotic samples. The receiver further includes receiver fingers (108a-108n) for generating synchronized de-spread signals from the time-offset de-spread signals based at least on said time-offset values. The receiver also includes a combiner (350) for combining the de-spread signals into a combined coherent de-spread signal.

Abstract: A communications system includes RF hardware (104) configured for receiving an input data signal includes a modulated carrier encoded with information symbols and modulated using a sequence of discrete time chaotic samples. The system also includes a chaotic sequence generator (340) configured for generating the sequence of discrete-time chaotic samples and a correlator (328). The correlator is configured for synchronizing the input data signal with the sequence of discrete-time chaotic samples and obtaining normalization factor values for each of the information symbols based on comparing a received symbol energy for the information symbols and a symbol energy of the discrete-time chaotic samples associated with the duration of transmission of the information symbols.

Abstract: Systems (100) and methods for selectively controlling access to multiple data streams which are communicated using a shared frequency spectrum and spreading code. The methods involve forming a global data communication signal (134) by amplitude modulating a global data signal (130) comprising global data symbols and forming a phase modulated signal (120) by phase modulating a protected data signal. The phase modulated signal represents protected data symbols. The methods also involve forming a protected data communication signal (126) by changing phase angles of the protected data symbols using a variable angle Ø determined by a random number source and combining the protected data signal with a spreading sequence (CSC). The methods further involve combining the global and protected data communication signals to form an output communication signal (140) having a spread spectrum format. The output communication signal is transmitted over a communications channel (104).

Abstract: A system for chaotic sequence spread spectrum communications includes a transmitter (402) for transmitting information symbols using a chaotic sequence of chips generated at the transmitter, the information symbols having a duration of transmission based on a threshold symbol energy value and the chips. The system also includes a receiver (404) for extracting the information symbols from the transmitted signal using a chaotic sequence of chips generated at the receiver and the threshold symbol energy value. In the system, the chips generated at the transmitter and the receiver are identical and synchronized in time, where the duration of transmission of the information symbols in the carrier is a total duration of a selected number of the chips used for transmitting, and where the number of the chips is selected for the information symbols to provide a total chip energy greater than or equal to the threshold symbol energy value.

Abstract: A spread spectrum communication system includes a channel encoder configured for modulating a carrier signal with data to form an information signal. A spreading sequence generator is configured for generating a spreading sequence having a phase angle dependent upon a chaotic sequence and contiguously distributed over a predetermined range. The chaotic sequence also has a magnitude which is selectively dependent upon the pseudo-random number or chaotic sequence. The invention also includes a multiplier configured for forming a spread spectrum signal by multiplying the information signal by the spreading sequence. The spreading sequence generator is responsive to a magnitude control signal for controlling the selective dependency of said magnitude. The magnitude can be constant to form a constant amplitude zero autocorrelation signal. Alternatively, the magnitude can be allowed to vary in selectively controlled chaotic or pseudo-random manner to vary a peak to average power ratio.

Abstract: A cryptographic system (500) that includes a data stream receiving device (502) configured for receiving a modified data stream representing data entries encrypted using a chaotic sequence of digits. The system also includes user processing device (503, 505) configured for receiving user access information specifying an initial value for the chaotic sequence of digits and data field location information associated with selected ones of the data entries. The system further includes a synchronized pair of chaotic sequence generators (300) coupled to the user processing devices configured for generating encryption and decryption sequences based on the initial value and the data field location information. The system additionally includes an encryption device (504) and a decryption device (506) coupled to the chaotic sequence generators and the data stream receiving device, the decrypter configured for generating an output data stream from the modified data stream by applying the decryption sequences.

Abstract: Systems (100) and methods (400) for selectively controlling access to multiple data streams which are communicated using a shared frequency spectrum and shared spreading codes. The methods involve generating a first product signal (FPS) by spreading first symbols of a first amplitude modulated (AM) signal using a first spreading code (SC). The methods also involve generating a second product signal (SPS) by spreading second symbols of a complimentary AM signal using a second SC. The FPS (124) and SPS 126 are combined to form a protected data communication signal (PDCS) including first data recoverable by a receiver (106). A global data communication signal (GDCS) is combined with PDCS (128) to form an output signal (140) having a spread spectrum format. The GDCS is generated using a digital modulation process and includes second data recoverable by a plurality of receivers (106, 108).

Abstract: The invention concerns a chaotic communications system, method and apparatus having a transmitter configured to spread an input data signal over a wide intermediate frequency band, by digitally generating a first chaotic sequence of values to form a spreading code. The spreading code is then used to form a digital IF chaotic spread spectrum signal having a uniform sampling interval. The duration of the sampling interval is then selectively varied in accordance with a first pseudo-random sequence, thereby introducing a known dither in the digital IF chaotic spread spectrum signal. After introducing the known dither, the digital IF chaotic spread spectrum signal is converted to an analog RF spread spectrum signal at a conversion rate that exceeds the sampling interval of the chaotic spread spectrum signal. A corresponding receiver recovers the input data from the spread transmitted signal. This spreading may utilize a chaotic sequence employing discrete time chaos dithering.

Abstract: Embodiments of the present invention provide a system and method for further reducing cyclostationarity and correspondingly energy density in a chaotic spread spectrum data communication channel, by digitally generating a first chaotic sequence of values to form a spreading code. The spreading code is then used to form a digital IF spread spectrum signal having a uniform sampling interval. The digital IF spread spectrum signal is converted to a sampled analog IF spread spectrum signal at a conversion rate substantially equal to the uniform sampling interval. The duration of the sampling interval is then selectively varied in accordance with a first pseudo-random sequence, thereby introducing a known dither in the analog IF spread spectrum signal. After introducing the known dither, the analog IF spread spectrum signal is upconverted to an analog RF spread spectrum signal. The first pseudo-random sequences may be designed to be a chaotic sequence.