Abstract: Methods for code-division multiplex communications. The methods involve generating orthogonal or statistically orthogonal chaotic spreading codes (CSC1, . . . , CSCK) using different sets of polynomial equations (f0(x(nT)), . . . , fN-1(x(nT))), different constant values (C0, C1, . . . , CN-1) for the polynomial equations, or different sets of relatively prime numbers (p0, p1, . . . , pN-1) as modulus (m0, m1, . . . , mN-1) in solving the polynomial equations. The methods also involve forming spread spectrum communications signals using the orthogonal or statistically orthogonal chaotic spreading codes, respectively. The method further involve concurrently transmitting the spread spectrum communications signals over a common RF frequency band.

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: 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 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: 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 (30°) 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 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 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 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: 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: 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 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: 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].

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 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 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 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 for encrypting data is provided. The method includes formatting data represented in a weighted number system into data blocks. The method also includes converting the data blocks into a residue number system representation. The method further includes generating a first error generating sequence and inducing errors int he data blocks after converting the data blocks into a residue number system representation. It should be understood that the errors are induced in the data blocks by using the first error generating sequence. After inducing errors into the data blocks, the data of the data blocks is formatted into a form to be sorted or transmitted. The method also includes generating a second error generating sequence synchronized with and identical to the first error generating sequence and correcting the errors in the data blocks using an operation which is an arithmetic of a process used in inducing errors.

Abstract: A method is provided for extending a sequence repetition period of a random number generator in systems based on the availability of random sequences. The method includes performing RNS arithmetic operations to express a random number in a sequence as RNS residue values. Each generated random number has a value between zero and n!?1. The method also includes converting each of the RNS residue values to a relatively prime base number system so that each of the RNS residue values includes at least one digit. The method further includes generating an arbitrary permutation ordering of output sequence numbers using a select combination of digits associated with each of the RNS residue values. The arbitrary permutation ordering is applied to a cyclic structure having n elements. Each of the n elements has an associated output sequence number.