Abstract: A cryptographic system (CS) is provided. The CS (800) comprises a data stream receiving means (DSRM), a generator (702), a mixed radix converter (MRC) and an encryptor (908). The DSRM (902) is configured to receive a data stream (DS). The generator is configured to selectively generate a random number sequence (RNS) utilizing a punctured ring structure. The MRC (704) is coupled to the generator and configured to perform a mixed radix conversion to convert the RNS from a first number base to a second number base. The encryptor is coupled to the DSRM and MRC. The encryptor is configured to generate an altered data stream by combining the RNS in the second number base with the DS. The punctured ring structure and the MRC are configured in combination to produce an RNS in the second number base which contains a priori defined statistical artifacts after the mixed radix conversion.

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: Methods for code-division multiplex communications. The method involve generating orthogonal or statistically orthogonal chaotic spreading codes (CSC1, . . . , CSCK) having different static offsets using a set of polynomial equations (f0(x(nT)), . . . , fN-1(x(nT)) and/or f0[x((n+v)T+t)], . . . , fN-1[x((n+v)T+t)]). The methods also involve forming spread spectrum communications signals respectively using the orthogonal or statistically orthogonal chaotic spreading codes. The methods further involve concurrently transmitting the spread spectrum communications signals over a common RF frequency band. The spreading codes are generated using different initial values for a variable “x” of a polynomial equation f(x(nT)) and/or different acc-dec values for a variable “v” of a polynomial equation f[x((n+v)T+t)]. The static offsets are defined by the different initial values for a variable “x” and/or different acc-dec values for a variable “v”.

Abstract: Systems (100) and methods (700) for processing a data signal in a communications system. The methods involve generating a first chaotic sequence at a transmitter (102). The methods also involve performing first basis function algorithms using the first chaotic sequence to generate first statistically orthogonal chaotic sequences. At least one sequence is selected from the first statistically orthogonal chaotic sequences for combining with a first data signal. The selected sequence is combined with a second data signal to obtain a modulated chaotic communication signal. The modulated chaotic communication signal is transmitted to a receiver (104). At the receiver, the received modulated chaotic communication signal is processed to obtain data therefrom. Notably, the signal processing generally involves performing a deterministic process (e.g., a Hidden Markov Model deterministic process).

Abstract: Systems (600) and methods (500) for Pulse Rotation Modulation. The methods involve: generating First Segments (“FSs”) of a Numerical Sequence (“NS”) based on a First Data Symbol Sequence (“FDSS”); and encoding FDSS within NS. The encoding is achieved by: (a) shifting positions of numbers contained in each FS “X” positions to the right or left; and (b) moving a last “X” numbers of the FSs to a beginning of a respective segment thereof or moving a first “X” numbers of the FSs to an end of the respective segment. X” is defined as an integer value represented by a respective portion of FDSS. Thereafter, the NS having FDSS encoded therein can be used to spread a Second Data Signal (“SDS”) over a wide intermediate frequency band. SDS has second data symbols, that are different then FDSS, phase and/or amplitude encoded therein.

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: Ad-hoc wireless network which operates in accordance with a time division multiple access (TDMA) channel scheme. The network includes a plurality of nodes configured for wireless ad-hoc network communications using at least a first tier waveform and a second tier waveform.

Abstract: A cryptographic system (1000) is provided. The cryptographic system includes a data stream receiving means (DSRM), a number generator (NG), a mixed radix accumulator (MRA) and an encryptor. The DSRM (1002) receives a data stream (DS). The NG (702) generates a first number sequence (FNS) contained within a Galois Field GF[M]. The MRA (750) is configured to perform a first modification to a first number (FN) in FNS. The first modification involves summing the FN with a result of a modulo P operation performed on a second number in FNS that proceeds FN. The MRA is also configured to perform a second modification to FN utilizing a modulo P operation. The MRA is further configured to repeat the first and second modification for numbers in FNS to generate a second number sequence (SNS). The encryptor (1004) is configured to generate a modified data stream by combining SNS and DS.

Abstract: A method (300) for generating a sine and cosine of an input angle (Ø102). The method involves decomposing Ø102 to an octant or quadrant, a coarse angle (A), and a fine angle (B), determining cos(A), and determining sin(A). The method also involves decomposing cos(A) and sin(A) to a most significant word (MSW) and a least significant word (LSW). The method further involves computing an approximation of 1?cos(B), an approximation of sin(B), and a plurality of products (P1, . . . , P4) using the MSWs and approximations. The method involves computing approximations of cos(Ø?102) and sin(Ø?102) using the values for cos(A), sin(A), and P1, . . . , P4. The method involves scaling the approximations of cos(Ø?102) and sin(Ø?102) to a desired resolution.

Abstract: A cryptographic system (CS) is provided. The CS (500) is comprised of a data stream receiving device (DSRD), a chaotic sequence generator (CSG) and an encryptor. The DSRD (602) is configured to receive an input data stream. The CSG (300) includes a computing means (3020, . . . , 302N?1) and a mapping means (304). The computing means is configured to use RNS arithmetic operations to respectively determine solutions for polynomial equations. The solutions are iteratively computed and expressed as RNS residue values. The mapping means is configured to determine a series of digits in the weighted number system based on the RNS residue values. The encryptor is coupled to the DSRD and CSG. The encryptor is configured to generate a modified data stream by incorporating or combining the series of digits with the input data stream.

Abstract: Method and system for identifying neighbor nodes in an ad-hoc wireless network including two or more nodes. The method involves generating a beacon signal at a first node of the network for alerting other nodes in the network of the presence of the first node. A digitally generated first spreading sequence is also generated at the first node. Thereafter, the beacon signal is modulated with the first spreading sequence to produce a spread spectrum signal which is then transmitted. The spreading sequence is selected to be a chaotic sequence.

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 improving a signal-to-noise ratio in a received signal. The method involves receiving a spread spectrum signal (SSS) with a power level below a noise floor of a receiver. The SSS is generated by modulating a data signal using a spreading sequence (SS) comprised of a random number sequence (RNS). The SS can be generated using a chaos generator or any other deterministic means. The method also involves comparing a magnitude of each number of the RNS which was used to generate the SSS to an adaptable threshold value. The adaptable threshold value is selected based on a minimum magnitude of each number necessary to produce samples having a predetermined signal-to-noise ratio. Notably, samples of the received SSS are excluded from a receiver processing based on a result of the comparison. Similarly, each number of a random number sequence is excluded from the receiver processing based on the comparison.

Abstract: Systems (100) and methods (700) for processing a data signal in a communications system. The methods involve generating a first chaotic sequence at a transmitter (102). The methods also involve performing first basis function algorithms using the first chaotic sequence to generate first statistically orthogonal chaotic sequences. At least one sequence is selected from the first statistically orthogonal chaotic sequences for combining with a first data signal. The selected sequence is combined with a second data signal to obtain a modulated chaotic communication signal. The modulated chaotic communication signal is transmitted to a receiver (104). At the receiver, the received modulated chaotic communication signal is processed to obtain data therefrom. Notably, the signal processing generally involves performing a deterministic process (e.g., a Hidden Markov Model deterministic process).

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 cryptographic system (CS) is provided. The CS (500) is comprised of a data stream receiving means (DSRM), a ring generator (RG) and an encryptor. The DSRM (602) provides a data stream (DS). The RG (400) includes a computing (404-408), converting (404-408) and permutation (410) means. The computing means is configured to perform RNS arithmetic operations to express a random number in a random number sequence as RNS residue values (RNSRV). The converting means is configured to convert each RNSRV to a relatively prime number system so that each RNSRV includes at least one digit. The permutation means is configured to generate an arbitrary permutation ordering of output sequence numbers (OSNs) using a select combination of digits associated with each RNSRV. The arbitrary permutation ordering is determined using a cyclic structure. The encryptor is configured to generate a modified data stream by combining the OSNs and DS.

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].