Abstract: N-state switching tables are transformed by a Lab-transform into a Lab-transformed n-state switching table. Memory devices, processors and combinational circuits with inputs and an output are characterized by the Lab-transformed n-state switching table and perform switching operations between physical states in accordance with a Lab-transformed n-state switching table. The devices characterized by Lab-transformed n-state switching tables are applied in cryptographic devices. The cryptographic devices perform standard cryptographic operations that are modified in accordance with a Lab-transform.

Abstract: Methods and apparatus to create and display panoramic images on a mobile device are disclosed. Such a mobile device can be a mobile phone. Apparatus is provided to control the position of a lens in relation to a reference lens. Methods and apparatus are provided to generate multiple images that are combined into a panoramic image. A panoramic image may be a static image. It may also be a video image. A controller provides correct camera settings for different conditions. An image processor creates a panoramic image from the correct settings provided by the controller. A panoramic camera is applied in a computer gaming system.

Abstract: A first and a second device both have access to a series of data representing configurations of hash functions. The first device selects a first configuration and implements a hashing function from the selected configuration. A hash value is generated and transmitted to the second device. The second device has hashing configurations stored on a memory. A processor in the second device selects the first hashing configuration to implement the hash function from the first configuration and generates a hash value. The hash values generated on the first device and generated on the second device are compared to determine an action. The first configuration is disabled and a new configuration is retrieved. At least 4 and more preferably at least 5 different n-state functions with n>2 are used in a hash function.

Abstract: A digital image is obtained from a camera in a smartphone and is processed by a processor on the smartphone to modify a part but not all of the pixels in a frame of the digital image, which is a digital video image, which is modified by image processing in accordance with a modification mask and reversible modification instructions, and is transmitted to a second smartphone with a display screen to display the modified image. Image processing data are transmitted to the second smartphone to enable restoring the original digital video image from the partially reversibly modified image and to be displayed in unmodified form on the display screen.

Abstract: A sequence generator implemented on a processor that generates a sequence of signals applies a feedback shift register with feedback. A feedback loop connects at least a first and a second shift register element to last shift register element to a first shift register element of the shift register and includes at least one two-input n-state switching functions that is characterized by non-associative switching functions or switching tables. The sequence generator may be part of a scrambler, an autonomous sequence generator, a hash code generator, a communication device, and a data storage device.

Abstract: Methods and apparatus for coding and decoding n-state symbols with n?2 and n>2 and n>3 and n>4 are provided with at least one implementation of a switching function based on an addition and a multiplication over an alternate finite field GF(n) wherein a zero element in not 0. Encoders and decoders implementing a single n-state truth table of an addition over an alternate finite field modified in accordance with at least one inverter defined by a multiplication over the alternate finite field are also provided. Coders include scramblers, Feedback Shift Register (FSR) based encoders, sequence generator based encoders, block coders, streaming cipher encoders, transposition encoders, hopping rule encoders, Feistel network based encoders, check symbol based encoders, Hamming coder, error correcting encoders, encipherment encoders, Elliptic Curve Coding encoders and all corresponding decoders, CRC coders and hash function generators. Systems applying encoders and decoders also are provided.

Abstract: Maximum length properties of n-state sequences of n-state symbols with n=2 or n>2 are tested. Checkwords are generated from p consecutive n-state symbols in a sequence of n-state symbols which may overlap by (p?1) n-state symbols. If a sequence has np?1 n-state symbols in which 2 consecutive checkwords overlap in (p?1) n-state symbols and each checkword formed in the extended sequence is unique, then the sequence is a maximum length n-state sequence. An n-state feedback shift register based sequence generator with p n-state register elements is tested on the content of the shift register for np?1 cycles. If the shift register content is not repeated the sequence is maximum length. Generation of a sequence is stopped when the content repeats. Non-reversible n-state inverters and non-reversible n-state logic functions are applied to generate n-state sequences.

Abstract: Shift register based circuits include non-binary polynomial calculation circuits, coder circuits, scramblers, descramblers and sequence generators that apply non-binary two-input/single output switching functions wherein at least one input contains a non-binary inverter or multiplier. A combination of a two-input/single output non-binary switching device with at least one non-binary inverter at an input is advantageously reduced to a single device that implements a single non-binary switching function. The reduced single device may be an electronic memory that stores the truth table of the single non-binary switching function.

Abstract: Methods, apparatus and systems for error correction of n-valued symbols in (p,k) codewords including Reed Solomon codes of p n-valued symbols with n>2 and k information symbols have been disclosed. Coders and decoders using a Linear Feedback Shift Registers (LFSR) are applied. An LFSR can be in Fibonacci or Galois configuration. Errors can be corrected by execution of an n-valued expression in a deterministic way. Error correcting methods using Galois arithmetic are disclosed. Methods using Cramer's rule are also disclosed. Deterministic error correction methods based on known symbols in error are provided, making first determining error magnitudes not necessary. An error location methods using up and down state tracking is provided. Methods and apparatus executing the methods with binary circuits are also disclosed. Systems using the error correcting methods, including communication systems and data storage systems are also provided.

Abstract: Methods, apparatus and systems for error correction of n-valued symbols in codewords of p n-valued symbols with n>2 and for n=2 and k information symbols have been disclosed. Coders and decoders using a Linear Feedback Shift Registers (LFSR) are applied to generate codewords and detect the presence of errors. An LFSR can be in Fibonacci or Galois configuration. Errors can be corrected by execution of an n-valued expression in a deterministic non-iterative way. Deterministic error correction methods based on known symbols in error are provided. Corrected codewords can be identified by comparison with received codewords in error. N-valued LFSR based pseudo-noise generators and methods to determine if an LFSR is appropriate for generating error correcting codes are also disclosed. Methods and apparatus applying error free assumed windows and error assumed windows are disclosed. Systems using the error correcting methods, including communication systems and data storage systems are also provided.

Abstract: A digital image is obtained from a camera in a smartphone and is processed by a processor on the smartphone to modify a part but not all of the pixels in a frame of the digital image, which is a digital video image, which is modified by image processing in accordance with a modification mask and reversible modification instructions, and is transmitted to a second smartphone with a display screen to display the modified image. Image processing data are transmitted to the second smartphone to enable restoring the original digital video image from the partially reversibly modified image and to be displayed in unmodified form on the display screen.

Abstract: A system includes a first device to select and transmit a first code by a transmitter to a remote device; the remote device implements a sequence detector based on the first code; the transmitter in the first device generates a first sequence based on the first code; the sequence detector in the remote device detects the first sequence and activates the mechanism based on the detection; the first device may be a smartphone or a smart watch.

Abstract: Methods and apparatus to create and display screen stereoscopic and panoramic images are disclosed. Methods and apparatus are provided to generate multiple images that are combined into a stereoscopic or a panoramic image. A controller provides correct camera settings for different conditions. A controller rotationally aligns images of lens/sensor units that are rotationally misaligned. A compact controllable platform holds and rotates a camera. A remote computing device with a camera and a digital compass tracks an object causing the camera in the platform to track the object.

Abstract: A sequence generator implemented on a receiver is synchronized with a sequence generator at a transmitter. The receiver receives k n-state symbols, with k>1 and n>1 wherein each of the k n-state symbols is associated with a generating state of the sequence generator at the transmitter. A processor in the receiver evaluates an n-state expression that generates an n-state symbol that is associated with a synchronized state of the receiver. Coefficients related to the n-state expression are stored on a memory and are retrieved by the processor. The synchronized state in one embodiment is part of a code hop. The sequence generator in the receiver may be part of a descrambler, of a communication device, of a data storage device and/or of an opening mechanism.

Abstract: Methods and apparatus reducing the number of multipliers in Galois Field arithmetic are disclosed. Methods and apparatus for implementing n-valued Linear Feedback Shift Register (LFSR) based applications with a reduced number of multipliers are also disclosed. N-valued LFSRs with reduced numbers of multipliers in Fibonacci and in Galois configuration are demonstrated. Multiplier reduction methods are extended to n-valued functions with more than 2 inputs. Methods to create multiplier reduced multi-input n-valued function truth tables are disclosed. Methods and apparatus to implement these truth tables with a limited number of n-valued inverters are also disclosed. Scrambler/descrambler combinations with adders and multipliers over GF(2p) are provided. Communication, data storage and digital rights management systems using multiplier reduction methods and apparatus or the disclosed scrambler/descrambler combination are also provided.

Abstract: Methods for storing on a storage or memory medium, and retrieving, and displaying of multiple images in a registered manner, the images have been recorded concurrently. The images may comprise at least 2 video programs. A camera system for recording multiple concurrent images is also disclosed. Lenses and corresponding image sensors are calibrated to have calibrated and associated settings for recording multiple images that are substantially registered images. A registered image may be displayed on a single display. It may also be displayed on multiple displays. A camera for recording and displaying registered multiple images may be part of a mobile phone.

Abstract: A sequence generator implemented on a receiver is synchronized with a sequence generator at a transmitter. The receiver receives k n-state symbols, with k>1 and n>1 wherein each of the k n-state symbols is associated with a generating state of the sequence generator at the transmitter. A processor in the receiver evaluates an n-state expression that generates an n-state symbol that is associated with a synchronized state of the receiver. Coefficients related to the n-state expression are stored on a memory and are retrieved by the processor. The synchronized state in one embodiment is part of a code hop. The sequence generator in the receiver may be part of a descrambler, of a communication device, of a data storage device and/or of an opening mechanism.

Abstract: Methods and apparatus to create and display panoramic images on a mobile device are disclosed. Such a mobile device can be a mobile phone. Apparatus is provided to control the position of a lens in relation to a reference lens. Methods and apparatus are provided to generate multiple images that are combined into a panoramic image. A panoramic image may be a static image. It may also be a video image. A controller provides correct camera settings for different conditions. An image processor creates a panoramic image from the correct settings provided by the controller. A panoramic camera is applied in a computer gaming system.

Abstract: Methods and apparatus track an object with a first camera causing a second camera to also track the object. The object is a moving object. Geospatial coordinates, including an elevation or altitude of a camera are determined on the camera. A pose of the camera, including a pitch angle and an azimuth angle are also determined. Azimuth is determined by a digital compass. A camera pose including pitch is determined by accelerometers and/or gyroscopes. Cameras are communicatively connected allowing to display an image recorded by one camera being displayed on a second camera. At least one camera is on a movable platform with actuators. Actuators are controlled to minimize a difference between a first image of the object and a second image of the object. Cameras are part of a wearable headframe.

Abstract: Methods and apparatus create a corruption mask from a sequence that is generated by an n-state sequence generator with n>2. A digital media stream containing n-state symbols is corrupted in accordance with the corruption mask. The corruption takes place by applying a one argument or a two argument n-state logic function. The corruption rate of the digital media stream is preferably less than 100% allowing it to be reviewed. Data related to the corruption mask and the corruption mask are transmitted to a processor based receiver, allowing the receiver to decorrupt the corrupted digital media stream and to display it in its uncorrupted state.