Compression and encryption of data using irrational numbers

Abstract

An irrational number is used as a pattern generator for encrypting and / or compressing data. The number may be transmitted and shared as an easily stored and / or transmitted expression of the irrational number which can be used to generate a rational approximation with a arbitrary number of non-repetitive digits. The digits can then be used for encryption and / or as patterns for compression.

Description

[0001] APPLICATION FOR PATENT

[0002] Inventor(s): Gal ROTEM

[0003] Title: COMPRESSION AND ENCRYPTION OF DATA USING

[0004] IRRATIONAL NUMBERS

[0005] RELATED APPLICATION / S

[0006] This application claims the benefit of priority from Israel Patent Application no. 310639, filed 4 Feb. 2024.

[0007] FIELD AND BACKGROUND OF THE INVENTION

[0008] The present invention, in some embodiments thereof, relates to a system and method for data compression and / or data encryption and, more particularly, but not exclusively, to an encryption that is resistant to deciphering using quantum computers.

[0009] Two components that may be considered pivotal to information processing are bitwise operations and information compression. Each potentially plays a key role in enhancing computational efficiency and data manageability. Bitwise operations, include AND, OR, XOR, NOT, and bit shifts. Bitwise operations are often fundamental to the inner workings of computer algorithms. These operations facilitate direct manipulation of data at a granular level, which could contribute to fast and efficient processing. While bitwise operations are frequently used in applications ranging from simple arithmetic calculations to complex graphics rendering and encryption algorithms, their significance may vary depending on the specific context.

[0010] Information compression has seen a wide range of developments with algorithms designed for both lossless and lossy compression. Lossless techniques, such as Huffman coding and Lempel-Ziv-Welch (LZW) compression, are typically used in scenarios where data integrity is critical, as they allow for the original data to be reconstructed from the compressed version. On the other hand, lossy compression, as seen in formats like JPEG and MP3, may be more suited to applications like multimedia transmission, where some data loss could be acceptable in exchange for significantly reduced file sizes.

[0011] SUMMARY OF THE INVENTION

[0012] According to an aspect of some embodiments of the invention, there is provided a method of encoding electronic data including: receiving an input of data; supplying an irrational number; choosing selected digits from a rational approximation of the irrational number; and transforming the data using the input data using the selected digits to produce transformed data.

[0013] According to some embodiments of the invention, where the transformed data is encrypted data and further includes: transmitting the encrypted data from a first party to a second party; and providing the second party with information on how to decrypt the data.

[0014] According to some embodiments of the invention, the providing includes an exact expression of the irrational number.

[0015] According to some embodiments of the invention, the providing includes a definition of the selected digits of the irrational number.

[0016] According to some embodiments of the invention, the providing includes a content dependent parameter.

[0017] According to some embodiments of the invention, the providing is via a channel different from the transmitting.

[0018] According to some embodiments of the invention, where the transformed data is encrypted data and further includes: storing the encrypted data from a first party to a second party; and providing encryption parameters with information on how to decrypt the data.

[0019] According to some embodiments of the invention, the providing includes an exact expression of the irrational number.

[0020] According to some embodiments of the invention, the providing includes a definition of the selected digits of the irrational number. According to some embodiments of the invention, the providing includes a content dependent parameter.

[0021] According to some embodiments of the invention, the providing includes storing the information on different media from the encrypted data.

[0022] According to some embodiments of the invention, the irrational number has an exact expression that is a combination of a rational number and a function.

[0023] According to some embodiments of the invention, the irrational number is a square root of a rational number which is not a perfect square.

[0024] According to some embodiments of the invention, the data is text.

[0025] According to some embodiments of the invention, the rational approximation is accurate to at least 10A6 significant figures in a decimal representation.

[0026] According to some embodiments of the invention, where the transformed data is compressed data and further includes: storing the compressed data; and storing an encryption parameter with information on how to decrypt the data.

[0027] According to some embodiments of the invention, where the transformed data is compressed data and further includes: finding patterns in the selected digits; and representing the patterns in the transformed data with a pointer.

[0028] According to some embodiments of the invention, the method further includes using an artificial intelligence routine to perform the finding.

[0029] According to some embodiments of the invention, the method further includes generating an index of the patters.

[0030] According to some embodiments of the invention, the finding includes searching for nonconsecutive patterns.

[0031] According to an aspect of some embodiments of the invention, there is provided a system for encrypting data including: an irrational key; and an encoder for encrypting the data to encrypted data based on the irrational key.

[0032] According to some embodiments of the invention, the system further includes: a first communication channel for transmitting the encrypted data; and a second communication channel for transmitting the irrational key.

[0033] According to an aspect of some embodiments of the invention, there is provided a system for compressing data including: an irrational key; and an encoder for compressing the data to compressed data based on the irrational key. According to some embodiments of the invention, the system further includes: an index of patterns in at least one of the irrational key and a rational approximation of the irrational key.

[0034] According to some embodiments of the invention, the system further includes: a computer readable memory storing at least one of the irrational can and a rational approximation of the irrational key.

[0035] According to some embodiments of the invention, the system further includes: an artificial intelligence routine configured for generating the index.

[0036] According to some embodiments of the invention, the encoder includes a processor.

[0037] Unless otherwise defined, all technical and / or scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the invention pertains. Although methods and materials similar or equivalent to those described herein can be used in the practice or testing of embodiments of the invention, exemplary methods and / or materials are described below. In case of conflict, the patent specification, including definitions, will control. In addition, the materials, methods, and examples are illustrative only and are not intended to be necessarily limiting.

[0038] As will be appreciated by one skilled in the art, some embodiments of the present invention may be embodied as a system, method or computer program product. Accordingly, some embodiments of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a “circuit,” “module” or “system.” Furthermore, some embodiments of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon. Implementation of the method and / or system of some embodiments of the invention can involve performing and / or completing selected tasks manually, automatically, or a combination thereof. Moreover, according to actual instrumentation and equipment of some embodiments of the method and / or system of the invention, several selected tasks could be implemented by hardware, by software or by firmware and / or by a combination thereof, e.g., using an operating system.

[0039] For example, hardware for performing selected tasks according to some embodiments of the invention could be implemented as a chip or a circuit. As software, selected tasks according to some embodiments of the invention could be implemented as a plurality of software instructions being executed by a computer using any suitable operating system. In an exemplary embodiment of the invention, one or more tasks according to some exemplary embodiments of method and / or system as described herein are performed by a data processor, such as a computing platform for executing a plurality of instructions. Optionally, the data processor includes a volatile memory for storing instructions and / or data and / or a non-volatile storage, for example, a magnetic hard-disk and / or removable media, for storing instructions and / or data. Optionally, a network connection is provided as well. A display and / or a user input device such as a keyboard or mouse are optionally provided as well.

[0040] Any combination of one or more computer readable medium(s) may be utilized for some embodiments of the invention. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.

[0041] A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.

[0042] Program code embodied on a computer readable medium and / or data used thereby may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

[0043] Computer program code for carrying out operations for some embodiments of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) and / or a mesh network (meshnet, emesh) and / or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider).

[0044] Some embodiments of the present invention may be described below with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0045] These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function / act specified in the flowchart and / or block diagram block or blocks.

[0046] The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0047] Some of the methods described herein are generally designed only for use by a computer, and may not be feasible or practical for performing purely manually, by a human expert. A human expert who wanted to manually perform similar tasks might be expected to use completely different methods, e.g., making use of expert knowledge and / or the pattern recognition capabilities of the human brain, which would be vastly more efficient than manually going through the steps of the methods described herein.

[0048] Data and / or program code may be accessed and / or shared over a network, for example the Internet. For example, data may be shared and / or accessed using a social network. A processor may include remote processing capabilities for example available over a network (e.g. the Internet). For example, resources may be accessed via cloud computing. The term “cloud computing” refers to the use of computational resources that are available remotely over a public network, such as the internet, and that may be provided for example at a low cost and / or on an hourly basis. Any virtual or physical computer that is in electronic communication with such a public network could potentially be available as a computational resource. To provide computational resources via the cloud network on a secure basis, computers that access the cloud network may employ standard security encryption protocols such as SSL and PGP, which are well known in the industry.

[0049] BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

[0050] Some embodiments of the invention are herein described, by way of example only, with reference to the accompanying drawings. With specific reference now to the drawings in detail, it is stressed that the particulars shown are by way of example and for purposes of illustrative discussion of embodiments of the invention. In this regard, the description taken with the drawings makes apparent to those skilled in the art how embodiments of the invention may be practiced.

[0051] In the drawings:

[0052] Fig. 1 is a flow chart overview of an encryption decryption process in accordance with an embodiment of the current invention;

[0053] Fig. 2 is a flow chart illustrating deriving content dependent parameters for a transformation based on irrational numbers, in accordance with some embodiments of the current invention;

[0054] Fig. 3 is a flow chart illustrating an example of deriving content dependent parameters for a transformation based on irrational numbers, in accordance with some embodiments of the current invention;

[0055] Figs. 4A and 4B are a flow charts illustrating a Polarity-Gate base method for Data Compression in accordance with some embodiments of the disclosed current invention;

[0056] Fig. 4C is a flow chart illustration of decoding of data in accordance with an embodiment of the current invention;

[0057] Fig. 5 is a flow chart illustrating a method of communication, in accordance with some exemplary embodiments of the current invention;

[0058] Fig. 6 is a flow chart illustrating Generating a hash value from input data. Using Polarity-Gate in accordance with some embodiments of the current invention;

[0059] Fig. 7 is a schematic illustration of a Polarity-Gate System in accordance with some exemplary embodiments of the current invention; and Fig. 8 is a block diagram illustration of a Polarity-Gate System in accordance with some exemplary embodiments of the current invention.

[0060] DESCRIPTION OF SPECIFIC EMBODIMENTS OF THE INVENTION

[0061] Overview

[0062] The present invention, in some embodiments thereof, relates to a system and method for data compression and / or data encryption and, more particularly, but not exclusively, to an encryption that is resistant to deciphering using quantum computers.

[0063] The term computing device refers herein to a device that includes a processing unit. Examples for such device are a personal computer, a laptop, a server, a wearable device, a tablet, a cellular device and IOT or any CPU, Ram, and VO device.

[0064] The term Polarity-Gate refers to a module that is used for data transfer and transformation by converting an irrational number to binary code. For example, a Polarity-Gate may use an operation on the irrational number such as "Mod2" operation. In some embodiments, the generated binary code may use for several applications.

[0065] The term Polarity-Gate Data Transfer refers to any usage of the Polarity-Gate for transferring data between computing devices. For example, the transfer operation may include sending data between two communication devices. For example, both devices may use the same irrational number as a Polarity-Gate generator and / or may bitwise polarize (change the bit value according to a predefined rule) while sending the data from point to point.

[0066] The term Polarity-Gate Data Transformation refers to the usage of the Polarity-Gate as a tool for data processing. For example, the Polarity-Gate Data Transformation may be used for data compression, pattern indexing and / or random data generator.

[0067] The term Polarity-Gate Unique-ID refers to an identifier of a subject that is generated by the polarity gate. Optionally, the Polarity-Gate Unique-ID is used as an Identity provider. For example, the Unique-ID may be generated from hardware of the device owner (e.g., Motherboard Serial Number). Alternatively or additionally, the Polarity-Gate Unique-ID may use a biometric input of a user and / or any other features that bind the Polarity-Gate to a digital input source.

[0068] One technical problem in Data transformation is minimizing the size of the Data without losing information, (aka: Loss Less compression).

[0069] One technical solution is the use of polarity-gate for data compression.

[0070] Irrational numbers possess an inherently infinite amount of information. In some embodiments, through the application of searching, strings can be indexed and / or stored within a database as a symbol (e.g., a pointer). Optionally, by running a search for pattern in the data base, during the compression phase, the binary strings are found in the data base and replaced with the original data. For example, for compressing the word "data" the word is translated into ascii code: "01100100011000010111010001100001 ", then the polarity-gate searches for the position of this ascii code in a predefined irrational number such as the root of 2, and associates in the database this position with a unique code, ("0101" for example). For example, data may be compressed, by replacing the word "Data" with the symbol 0101.

[0071] One other technical problem is generation of a true random strings. Today a lot of methods rely on Pseudo-Random generators. The pseudo random generators may reduce the strength of the randomness to the "seed" strength. In other words, the result may not be truly random.

[0072] One other technical solution to create a more true random generator may include using the polarity-gate. In some embodiments, an irrational number may be used to generate random numbers. Optionally, in communication multiple parties can agree on an irrational number e.g., an irrational square root, as a shared secret for generating a random string. Optionally, the random string may be used as a XOR of the information passing between them. For example, using this XOR the parties may "polarize" the information while sending and / or while receiving. Optionally, the shared secret is based on a transformation of an individual seed of each of the participants in a communication transformed by a transformation which makes it possible for each participant to recover the communicated data, but makes it exceedingly difficult for any participant to figure out the key of any other participant.

[0073] In some embodiments, that current invention includes a content sensitive encryption and / or decryption method that uses irrational numbers. For example, a content sensitive algorithm may determine an irrational key for encoding and / or decoding one block based on the content a previous block. One advantage of the method is that a finite and / or small block of data can be used to produce an infinite and / or very large number of digits in an irrational key. For example, taking the square root of a byte sum of a block of data (and optionally transforming the byte sum to avoid perfect squares) may produce an infinite string of digits to use as a key for the encoding and / or decoding the next block of data.

[0074] Exemplary Embodiments

[0075] Before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not necessarily limited in its application to the details of construction and the arrangement of the components and / or methods set forth in the following description and / or illustrated in the drawings and / or the Examples. The invention is capable of other embodiments or of being practiced or carried out in various ways. Corresponding or like numerals or characters indicate corresponding or like components. Unless indicated otherwise, the drawings provide exemplary embodiments or aspects of the disclosure and do not limit the scope of the disclosure.

[0076] Fig. 1 is a flow chart overview of an encryption decryption process in accordance with an embodiment of the current invention. In some embodiments, a process begins by providing 11 initial encryption parameters. Optionally, the parameters may include an expression of an irrational number. For example, the irrational number may be expressed as a transcendental number (e.g., Pi) and / or may be expressed as a rational number and a mathematical transformation thereof that results in an irrational number (e.g., the square root of 2). Additionally or alternatively, the parameters may include a skip and / or a starting point. Additionally or alternatively, the parameters may include a data transformation that can be used to encrypt and / or decrypt data dependent on the encryption parameters, (for example, the data transformation may include a polarity gate and / or a polarity gate transformation) and / or an initial block length.

[0077] For example, initial encryption parameters may include an initial block size of 5 bytes, a seed 77 for generating an irrational key (e.g., the exact representation of the irrational number is the square root of 77), a skip of two, an initial position of 4, polarity gate of modulo 2, and a polarity transform of XOR. The data to be encrypted / decrypted may include the phrase “a small light pushes away a lot of darkness”. Since the block size is 5, the first block is designated 16 as “a sma”

[0078] In the example, the first data block is “a sma”. The ASCII code for the first data block is 97, 32, 115, 109, 97 and in binary 01100001

[0079] 0110000100100000011100110110110101100001. The irrational key is sqrt(77)= 8.77496438898038083205937457728898075631677558096554229. Selecting from the irrational key starting at the starting point (the 4thdigit) and skipping according to the skip value (every second digit) gives the underlined digits of the square root of 77 which is 46388038482537572880753177558965422. Applying the polarity gate (modulo 2) gives the binary transformation key 0100100100100001001111011100010011011011110010110001. Applying the polarity transformation (XOR) to the binary data using the transformation key encrypts 26 the data to the string 001010000100000111011011000100101100101111001011000. Knowing the encryption parameters, one can reverse the transformation and gates to decrypt 26 the encrypted string and / or give back the original data. Without knowing the keys and gates, it would be very difficult to restore the data.

[0080] In some embodiments, the transformation parameters of the next block are derived 31 from the previous block. For example, for each subsequent block, the seed value may be derived 31 from the decrypted data of the previous block as the square root of the letter count of the data attached to the left side as an additional most significant digit to the byte sum of the previous block. For example, the letter count is 4 and the values of the bytes of the first block “a sma” a=97 + space=32 + s=l 15 + m=109 + 1=97 = 452 may give a byte sum of 452. For example, the parameter used to as 4452 which is not a perfect square. Optionally, the seed is defined as 4452 and / / or the irrational key has an exact representation as the square root of 4452. Optionally, characteristics of the data of the first block are used as parameters for transforming the next block. The example, the block size of the next block may be based on the previous block, for example, the block size of the next block may be set to the first two digits (two most significant digits) of the seed generator, (e.g., the digits 44), may be used to determine the block size of the second block (e.g., the next block will be 44 bytes). For example, the skip may be chosen as the letter count of the previous block, (i.e., the letter count is 4) and / or the starting point the last two digits of the seed 52. In some embodiments, when the selected number for generating the seed is a perfect square then the seed may be defined as the square root of the seed generator plus 1.

[0081] The method may continue using the computations to derive parameters for the next block transformation from each previous block in turn and / or designate 36 the next block and / or encrypt / decrypt the next block in accordance with the parameters derived 31 from the previous block.

[0082] Fig. 2 is a flow chart illustrating deriving content dependent parameters for a transformation based on irrational numbers, in accordance with some embodiments of the current invention. In some embodiments, an encryption system in provided 55 input data. Optionally, the data may include content recovered during decryption and / or data intended for encryption (e.g., content dependent encryption / decryptions). For example, the word "hello" is considered as the initial content (e.g., a previous block that has been decrypted and / or encrypted). In some embodiments, the system derives 60 a seed and / or other parameters for the encryption / decry ption process of a further block based on the previous block. Optionally, the seed may be generated from the input number itself by some process that may be established between the encryptor and the decryptor (e.g., a transmitter and receiver and / or the encryption and decryption may be performed on the same actor) and / or the seed itself may be transmitted between the transmitter and the receiver. For example, the system may execute a byte sum and / or letter count operation, where each letter is assigned a numerical value and / or the seed may be a native value on a device (e.g., a processor identification number such that an actor stealing the encrypted data alone will be inhibited from decrypting the data on a different device). For example, using an encoding wherein the byte sum of “hello” is 1017, the word, "hello" yields a seed of "005 + 1017=51017," by combining the byte sum with the letter count. Alternatively or additionally, a seed may be generated using a random number generator and / or by prior agreement (for example, a seed may be agreed upon between the receiver and the transmitter and / or the seed generator may be changed periodically).

[0083] In some embodiments, the seed is converted 65 into an irrational key. Optionally, a standard function (e.g., the square root) may be used to convert the seed into an irrational square root (e.g., the exact representation of the seed square root of 51017) (alternatively other functions may be used, for example, a relatively fast computation of generating an irrational number may be chosen). For example, a check is performed to ensure that the seed is not a perfect square. Optionally when the seed is a perfect square, the system modifies the number by adding 1 to it, ensuring that it is not a perfect square and allowing for the subsequent extraction of a non-integer square root. In the example, wherein the seed 51017 is not a perfect square, the system performs the square root on the seed itself. In the example, the square root of "51017"is: 225.869431309...

[0084] In some embodiments, the irrational number is converted 70 into a transformation key. For example, the system determines the length of a Polarity-Gate, which, for this example, is set to 20. For example, a rule determines which digits from the rational approximation of the irrational number will be selected for the transformation. For example, a starting point after the decimal of the irrational key for generating the transformation key. In this embodiment, the start is defined at 10 positions after the decimal point. Optionally, a skip value is used, skipping digits in the irrational key when generating the transformation key, with this example using a frequency of every 2 digits. For example, the system extracts from the irrational key the transformation key according to the previously defined starting point and skip.

[0085] In the exemplary embodiment, the number resulting after starting at the starting point, taking digits and skipping digits is "398891202044689585022", which was extracted from the irrational key

[0086] “225.8694313093296828297122405210947476282925881590524264398051669431 302484780520381377235201925491721."

[0087] Fig. 3 is a more detailed flow chart of method and system for content based transformation based on irrational numbers, in accordance with some exemplary embodiments of the current invention.

[0088] At block 100 content is provided to be processed. For example, the word "hello" is considered as the initial content (e.g., the first block to be encrypted and / or the first block decrypted).

[0089] At block 105 The system executes a byte sum and letter count operation, where each letter is assigned a numerical seed value. In this instance (in accordance with a particular letter encoding scheme), "hello" yields "005 + 1017=51017," combining the byte sum with the letter count.

[0090] At block 110 a check is performed to ensure the resulting seed is not a perfect square. If it is, the system modifies the number by adding 1 to it, ensuring that it is not a perfect square and facilitating for the subsequent extraction of an irrational square root. The system performs the square root on the result of block 105. In the example the irrational key is the square root of "51017" = 225.869431309...

[0091] At block 115 the system determines the length of the Polarity-Gate (numbers after the decimal point of the result of the operation of block 110), which, for this example, is set to 20.

[0092] Blocks 120, 125, 130, 135 illustrate a process of encoding the data from the irrational number.

[0093] At block 120 The system decides the starting point after the decimal for encoding the data from the irrational number. For example, in communication the starting point may be agreed to between a transmitter and a receiver of the data. For example, this may be a shared secret between the actors. In this embodiment, the start is defined at 10 positions after the decimal point.

[0094] At block 125 the system determines the skips (e.g., when extracting digits from the irrational key some digits are extracted and others skipped) with this example using a frequency of every 2 digits. Alternatively or additionally, that after a skip multiple digits may be extracted and / or the skips and extractions may have different lengths (e.g., an increasing series etc.). For example, in communication the skips and extractions may be agreed to between a transmitter and a receiver of the data. For example, this may be a shared secret between the actors.

[0095] At block 130 The system extracts the selected digits from the irrational key. For example, according to the previously defined starting point and jump frequency. In the exemplary embodiment, the digits "398891202044689585022," are extracted from "225.8694313093296828297122405210947476282925881590524264398051669431 302484780520381377235201925491721."

[0096] At block 135 the system converts the result of extracted digits into a binary transformation key according to predefined rules. For example, each digit from the result of block 130 is converted to 1 for odd number and to 0 for even number.

[0097] For example: the result of 130 is: " 398891202044689585022", which for the Polarity Gate of "hello" results in the binary string " 110011000000001101000." For example, in communication rules may be agreed to between a transmitter and a receiver of the data. For example, this may be a shared secret between the actors. At block 135 the system performs modulo 2 on the string. In the exemplary embodiment, the transformation key is the polarity gate of "hello" e.g., the binary string " 110011000000001101000."

[0098] Fig. 4A is a flow chart illustrating a Polarity-Gate base method of building a database and / or index for Data Compression in accordance with some embodiments of the disclosed current invention. at Block 200 - Irrational Number Expression.

[0099] In some embodiments, a numerical sequence is created. For example, the list may in numbers ranging from 1 to 1 billion excluding perfect squares. Optionally, the sequence may include non-integer numbers. In the example, exclusion of perfect squares is to facilitate the production of non-repeating, non-terminating decimals upon extraction of square roots. Optionally, each irrational number may be truncated to an agreed to number of digits. In some embodiments, this creates a massive data base of patterns that can be generated and / or communicated without transmitted or storing massive quantities of data. In some embodiments, the database may include a vast number of digits of a single irrational number. Optionally, the irrational numbers may be expressed in any way that is convenient to specify and generate. For example, an irrational number may be expressed with an exact expression. For example, the exact expression may include a rational seed and a transformation that results in an irrational number and / or the irrational number may be expressed as a transcendental number (e.g., Pi, e etc.)

[0100] At Block 205 - Square Root Extraction and Storage

[0101] In some embodiments, the system converts the seeds to irrational numbers (e.g., irrational keys), (e.g., computes the square root of each non-perfect square number generated in Block 200). Optionally, each irrational number is calculated and / or truncated to prespecified decimal length, potentially up to a trillion digits. For example, the results extensive sequences are cataloged in a database.

[0102] At Block 210 - Binary Conversion e.g., via Modulo Operation

[0103] In some embodiments, a binary transformation is applied to the sequence results from Block 205. For example, transformation may be by implementing a modulo 2 operations. This process, optionally, outputs a binary string for each number, e.g., with odd results yielding T and even results producing 'O'.

[0104] At Block 215 - Sequential Pattern Search

[0105] In some embodiments, the system initiates a search for meaningful sequences within the extensive binary strings produced in Block 210. For example, this may involve identifying and cataloging patterns and / or repetitions.

[0106] At Block 220 - Detect Further Patterns

[0107] In some embodiments, further hidden patters are identified. Optionally, machine learning algorithms may be used to analyze the binary sequences. For example, the analysis may be performed using various "skips," or intervals, to detect patterns that may not be immediately apparent.

[0108] At Block 225 - Creation of a "Smart Index"

[0109] The result of the machine learning analysis from Block 220 is used to construct a 'Smart Index,' which will facilitate rapid searching and referencing of the data patterns recognized.

[0110] Fig. 4B is a flow chart illustrating a Polarity-Gate base method of Data Compression in accordance with some embodiments of the disclosed current invention.

[0111] At Block 230

[0112] In some embodiments, a method for compressing text, includes employs a smart index of patterns and / or sequences identified in a database based on irrational numbers to reduce the size of the data. Optionally, the data may include text and / or other data. In some embodiments, the data may have been previously compressed with an existing algorithm.

[0113] At Block 235 - Conversion to Binary Format The input data from Block 230 is optionally converted into a binary file. For example, a text file may be compressed into a binary file according to known methods. Alternatively or additionally, some data may be provided

[0114] At Block 240 - Database Sequence Matching

[0115] The system searches the database for sequences that match or correlate with the patterns in the binary data from Block 235. These matching patterns may be used in the compression or encryption process.

[0116] At Block 245 - Pointer-Based File Rewriting

[0117] The compressed file is rewritten as a binary encoded filing. For example, long strings of data may be replaced using a system of pointers, which likely refers to a method of data representation that uses addresses or indexes to facilitate data retrieval or compression processes.

[0118] At Block 250 - save the result.

[0119] The result of the compressed file is rewritten to disk.

[0120] Fig. 4C is a flow chart illustration of decoding of data in accordance with an embodiment of the current invention. In some embodiments, data is provided 285 in a coded format (e.g., compressed and / or encrypted, for example as described by other embodiments herein). For example, the coded data may be transferred from another computer (e.g., over a network) and / or retrieved from storage. Additionally or alternatively, coding parameters are supplied 290. For example, the parameters may be supplied over a safe media (e.g., an internal data source [e.g., an internal number of the characterizing system], a physical media [e.g., a data card], a safe channel, a temporary source [e.g., a clock time] and / or a data dependent extraction (e.g., extracting a number from a previous block to code / decode a subsequent block) etc.). Parameters may include seeds for an irrational number and / or a transform and / or extraction rules (e.g., starting points and / or skips and / or block sizes and / or numbers of digits used from an irrational number) and / or databases and / or transforms. Optionally, the coded data is decoded 295. For example, decoding may include deriving irrational keys (e.g., from seeds and / or transforms) and / or transform keys and / or applying transform keys to the data etc.

[0121] Fig. 5 is a flow chart illustrating a method of communication, in accordance with some exemplary embodiments of the current invention. In some embodiments, a Polarity-Gate method may be used to secure communication between two users through a server. Optionally, the secure communication is based on a shared secret derived from an irrational number. In some embodiments, the secure communication protocol creates of temporary shared secrets.

[0122] Blocks 310, 320 and 330 illustrate a method for secure communication between two users (e.g., user A and user B) in accordance with an embodiment of the current invention. For example, the method may employ a temporary shared secret. For example, a server may be provided 300 with unique identifiers (UIDs) for registered users. Optionally, a user’s UID is based on unique parameters of the user. Optionally, the UID may include parameters processed through a Polarity-Gate.

[0123] At Block 310, the Server manages the UIDs. The server maintains a database of all registered users. Each user is assigned a unique identifier (UID) upon registration. The UID is facilitates identifying users within the system and / or may be used to establish and / or secure communication sessions.

[0124] Blocks 320, 330 and 340 illustrate opening of communication in accordance with an embodiment of the current invention. Optionally, User A initiates a secure conversation with user B by requesting 310 from the server to establish a secure link to user B. This request signifies User A's intention to communicate securely with User B.

[0125] In some embodiments, the server processes 320 the request for communication. For example, upon receiving the connection request from user A, the server retrieves the UIDs associated with both user A and user B. For example, these UIDs may include a very large secret irrational key which is stored as a seed (e.g., a transcendental number and / or a rational number with a transform). The server is optionally responsible for maintaining the integrity and privacy of the UID and handling requests securely. In some embodiments, the server generates 330 a unique shared secret. For example, the shared secret may be created using a polarity transform. Optionally, the server generates unique hashes both user A and / or user B using their UID. These hashes are created for a communication session, facilitating each session having a clear and secure starting point.

[0126] In some embodiments, the server creates 340 a temporary shared secret. Optionally, the shared secret may combine elements from the hash of User A's and / or the hash of User B. Additionally or alternatively, the shared secret may include additional parameters specific to the conversation, for example, IP sockets etc. This shared secret is used to encrypt and decrypt the communication, making it secure and private. For example, the shared secret may include a polarity transform and / or a binary key and / or an irrational key.

[0127] In some embodiments, the server transmits 350 information to user A and / or user B. Opitonally, the shared secret may be transmitted to user A and / or user B using the user’s respective UID (e.g., for example using the UID may be used as a polarity transform to encrypt the shared secret when sending it to the user). For example, the shared data may include an irrational key. Optionally, the irrational key be transferred as a seed. For example, the seed may include rational number, a transcendental number and / or a transform and / or other parameters (e.g., as described in embodiments of secure communication illustrated herein). Optionally, the transmitted information facilitates each user extracting the shared secret on their side.

[0128] In some embodiments, data is encrypted and decrypted 360 by User A and / or User B using the shared secret. For example, user A prepares the data for transmission by encrypting it with the shared secret and / or User B, upon receiving the data, decrypts it using the same shared secret. For example, the shared key may include a polarity gate and / or the data may be encrypted and / or decrypted using Xor. The encryption and / or decryption inhibits entities who do not have the shared secret from reading the messages transmitted 370 between user A and user B.

[0129] Fig. 6 is a flow chart illustrating Generating a hash value from input data. Using Polarity-Gate in accordance with some embodiments of the current invention.

[0130] In some embodiments data is provided 400. For example, the data may include text, a string, a document, or any other data type. In some embodiments, preprocessing 405 is used to prepare the data for hashing. For example, when the data includes text, may be preprocessed 405 by normalizing the text, removing unnecessary spaces. In some embodiments, data may be broken the data into manageable blocks.

[0131] In some embodiments, numerical values may be defined 410. The values may be defined in a content dependent manner and / or based on a secret that may be shared and / or may be kept locally. In some embodiments, the data may include text. Optionally, the processed text is converted to numeric values. For example, conversion may include a calculation of a byte sum of a text segments. The byte sum may provide part of a numerical representation of the text data.

[0132] In some embodiments, data may be converted 415 to binary strings. In some embodiments, numeric values from the previous step are converted to binary strings. For example, the binary representation may facilitate hashing. For example, the binary conversion 415 may facilitate a consistent transformation and / or inhibit reversing the transformation.

[0133] In some embodiments, an irrational key is generated 420. For example, an irrational number may be created from the binary strings. This can be achieved by performing operations such as taking the square root of the binary number. Optionally, an irrational number is used to introduce mathematical complexity into the hash, potentially making it more secure. Optionally, multiple irrational keys may be generated 420.

[0134] In some embodiment, a hash key is extracted 425 from an irrational key. from the square root of an irrational number. The hash characters are extracted from the irrational number generated in the previous step. This extraction can be based on a predefined algorithm that selects specific digits from the decimal representation of the irrational number. In some embodiments, the extraction 425 of a key for one block may be dependent on the numerical values determined in a previous block (e.g., context dependent encryption). Optionally, a hash key may be generated 420 from multiple irrational keys.

[0135] In some embodiments, a hash output may be created 430. Optionally hash outputs are created 430 for each segment of the original input (e.g., each block). The length of the input blocks and / or hash output may vary and / or may be context dependent. Varying the block length may facilitate every part of the input contributing to the final hash value. The hash length can vary depending on the algorithm design and system requirements.

[0136] In some embodiments, the data and the hash output are merged 435 to result a unified Hash. For example, individual hash keys from each segment are combined with the data to create a single, unified hash output. For example, this may be done using various methods such as bitwise XOR operations or simple addition. The resulting hash optionally represents all the input data.

[0137] Fig. 7 is a schematic illustration of a Polarity-Gate System in accordance with some exemplary embodiments of the current invention.

[0138] In some embodiments, a polarity-gate system includes a Central Processing Unit 501 (CPU). In some embodiments, the Polarity-Gate algorithm is executed, by the CPU 501. For example, CPU 501 may receive of content, process data, compute irrational numbers, extract encoding parameters, decode binary strings and / or encode binary strings.

[0139] In some embodiments, a polarity-gate system includes an input port 503. Optionally, the input port 503 may include a data interface. Port 503 optionally accepts content input, binary encoded input, and / or encoding parameters.

[0140] In some embodiments, a polarity-gate system includes an output port 502. Optionally, the output port 502 may include a data interface. Output port 502 optionally transmits content input, binary encoded input, and / or encoding parameters.

[0141] In some embodiments, a polarity-gate system includes an encoding parameter input interface. For example, an Insertion Slot 504 may be supplied. For example, the slot 504 may allow inserting a medium (like a card or a chip) containing predefined encoding parameters which will be used by the CPU to encrypt data and / or decrypt data. Additionally or alternatively, some or all of the parameters may be dependent on the input data (e.g., content dependent encryption). For example, the parameters may include definitions of transformation key. Optionally, the transformation key may include an irrational number and / or the irrational number may be specified with a transcendental number and / or a rational number and a transformation that results in the irrational number.

[0142] In some embodiments, a polarity-gate system includes a power input 505. For example, the polarity gate system may receive electrical power through the power input 505. Operational Flow:

[0143] In some embodiments, the system receives input content via the input ports 502. Optionally, the input data is prepared for processing. For example, the CPU 501 carries out a byte sum and letter count operation and / or converts the data into another format (e.g., a binary format) and / or compresses the data (for example with conventional and / or known means). Optionally, the CPU 501 extracts seeds for generating irrational numbers. For example, the CPU may verify the seed will actually produce an irrational number (for example, if the transform of the seed is a square root operation, the seed will be checked whether it is a perfect square. In some embodiments, the performs an to convert a seed that would not give an irrational output to a seed that does produce an irrational output. For example, a seed with an integral square root may be converted into a seed with a non-integer square root. In some embodiments, the CPU 501 determines the length of the Polarity-Gate. For example, the determination may be based on the non-integer square root result.

[0144] In some embodiments, the CPU 501 identifies the starting point within an irrational key for data encoding purposes. Additionally or alternatively, the system may establish a frequency of 'jumps' or other transformations for encoding the data from the irrational key. All actions may be in accordance to the predefined rule and / or a content dependent rule. The output of the above steps may include a transform key.

[0145] In some embodiments, the CPU 501 encodes and / or decodes data. Decoding may follow the transform key.

[0146] In some embodiments, the CPU 501 utilizes the encryption parameters from the content and / or insertion slot 504 and / or another input to convert the extracted data into a binary presentation.

[0147] The final binary string is optionally sent out through the output ports 503.

[0148] Fig. 8 is a block diagram illustration of a Polarity-Gate System in accordance with some exemplary embodiments of the current invention.

[0149] In some embodiments, the Polarity-Gate system includes components in the form of algorithms (e.g., executed by the CPU) and / or hardware and / or firmware. For example, an irrational key generator 610 may receive seed and / or transforms to calculate irrational numbers to a large number of significant digits e.g., between 10 to 103digits and / or between 103to 106digits and / or between 106to 109digits and / or 109 to 1012digits or more. Optionally, the irrational key generator 610 is configured to perform calculations efficiently (e.g., with efficient hardware and / or software, for example, for computing a transcendental number and or a mathematical transform on a seed number to result in an irrational number).

[0150] In some embodiments, the system includes a transform generator 620. For example, transform generator 620 uses rules and / or irrational keys to build transforms. In some embodiments, the system includes a data manipulator 625, for example, to search data and / or form indexes and / or recognize patterns. In some embodiments, the system includes an encoder / decoder 630, for example, to switch data between an encoded (encrypted and / or compressed) state and / or a standard state. Optionally, transform generator 620 and / or data manipulator 625 and / or encoder / decoder 630 include efficient data manipulating modules (e.g., hardware, software and / or firmware) as there may be very large quantities of data to transform and / or map and / or read and / or write.

[0151] In some embodiments, a polarity-gate system includes an Input module 603. Optionally, the input module 603 may include a data port and / or interface. Input module 603 optionally accepts content input, binary encoded input, and / or encoding parameters.

[0152] In some embodiments, a polarity-gate system includes an output module 602. Optionally, the output module 602 may include a data port and / or interface. Input module 602 optionally transmits content input, binary encoded input, and / or encoding parameters.

[0153] In some embodiments, a polarity-gate system includes an encoding parameter user interface 604. For example, the interface 604 may allow a user to control and / or supply manual input and / or inserting a memory device (like a card or a chip) containing predefined encoding parameters which will be used by the CPU to encrypt data and / or decrypt data. Additionally or alternatively, some or all of the parameters may be dependent on the input data (e.g., content dependent encryption). For example, the parameters may include definitions of transformation key. Optionally, the transformation key may include an irrational number and / or the irrational number may be specified with a transcendental number and / or a rational number and a transformation that results in the irrational number. In some embodiments, the system may include artificial intelligence 640. For example, the artificial intelligence 640 may be embodied as hardware, software and / or firmware. For example, the artificial intelligence 640 may be used to recognize patterns and / or generate a smart index and / or retrieve patterns and / or use the smart index.

[0154] It is expected that during the life of a patent maturing from this application many relevant technologies will be developed and the scope of the terms is intended to include all such new technologies a priori.

[0155] As used herein the terms “about” and “approximately” refer to ± 5 % unless stated explicitly.

[0156] The terms "comprises", "comprising", "includes", "including", “having” and their conjugates mean "including but not limited to".

[0157] The term “consisting of’ means “including and limited to”.

[0158] The term "consisting essentially of means that the composition, method or structure may include additional ingredients, steps and / or parts, but only if the additional ingredients, steps and / or parts do not materially alter the basic and novel characteristics of the claimed composition, method or structure.

[0159] As used herein, the singular form "a", "an" and "the" include plural references unless the context clearly dictates otherwise. For example, the term "a compound" or "at least one compound" may include a plurality of compounds, including mixtures thereof.

[0160] Throughout this application, various embodiments of this invention may be presented in a range format. It should be understood that the description in range format is merely for convenience and brevity and should not be construed as an inflexible limitation on the scope of the invention. Accordingly, the description of a range should be considered to have specifically disclosed all the possible subranges as well as individual numerical values within that range. For example, description of a range such as from 1 to 6 should be considered to have specifically disclosed subranges such as from 1 to 3, from 1 to 4, from 1 to 5, from 2 to 4, from 2 to 6, from 3 to 6 etc., as well as individual numbers within that range, for example, 1, 2, 3, 4, 5, and 6. This applies regardless of the breadth of the range. Whenever a numerical range is indicated herein, it is meant to include any cited numeral (fractional or integral) within the indicated range. The phrases “ranging / ranges between” a first indicate number and a second indicate number and “ranging / ranges from” a first indicate number “to” a second indicate number are used herein interchangeably and are meant to include the first and second indicated numbers and all the fractional and integral numerals therebetween. When multiple ranges are listed for a single variable, a combination of the ranges is also included (for example the ranges from 1 to 2 and / or from 2 to 4 also includes the combined range from 1 to 4).

[0161] It is appreciated that certain features of the invention, which are, for clarity, described in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features of the invention, which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable subcombination or as suitable in any other described embodiment of the invention. Certain features described in the context of various embodiments are not to be considered essential features of those embodiments, unless the embodiment is inoperative without those elements.

[0162] Although the invention has been described in conjunction with specific embodiments thereof, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. Accordingly, it is intended to embrace all such alternatives, modifications and variations that fall within the spirit and broad scope of the appended claims.

[0163] All publications, patents and patent applications mentioned in this specification are herein incorporated in their entirety by reference into the specification, to the same extent as if each individual publication, patent or patent application was specifically and individually indicated to be incorporated herein by reference. In addition, citation or identification of any reference in this application shall not be construed as an admission that such reference is available as prior art to the present invention. To the extent that section headings are used, they should not be construed as necessarily limiting.

Claims

WHAT IS CLAIMED IS:

1. A method of encoding electronic data comprising: receiving an input of data; supplying an irrational number; choosing selected digits from a rational approximation of the irrational number; and transforming the data using the input data using the selected digits to produce transformed data.

2. The method of claim 1, where the transformed data is encrypted data and further comprising: transmitting the encrypted data from a first party to a second party; and providing the second party with information on how to decrypt the data.

3. The method of claim 2, wherein the providing includes an exact expression of the irrational number.

4. The method of claim 2, wherein the providing includes a definition of the selected digits of the irrational number.

5. The method of claim 2, wherein the providing includes a content dependent parameter.

6. The method of claim 2, wherein said providing is via a channel different from said transmitting.

7. The method of claim 1, where the transformed data is encrypted data and further comprising: storing the encrypted data from a first party to a second party; and providing encryption parameters with information on how to decrypt the data.

8. The method of claim 7, wherein the providing includes an exact expression of the irrational number.

9. The method of claim 7, wherein the providing includes a definition of the selected digits of the irrational number.

10. The method of claim 7, wherein the providing includes a content dependent parameter.

11. The method of claim 2, wherein said providing includes storing said information on different media from said encrypted data.

12. The method of claim 1, wherein said irrational number has an exact expression that is a combination of a rational number and a function.

13. The method of claim 12, wherein the irrational number is a square root of a rational number which is not a perfect square.

14. The method of claim 1, wherein the data is text.

15. The method of claim 1, wherein said rational approximation is accurate to at least 10A6 significant figures in a decimal representation.

16. The method of claim 1, where the transformed data is compressed data and further comprising: storing the compressed data; and storing an encryption parameter with information on how to decrypt the data.

17. The method of claim 1, where the transformed data is compressed data and further comprising: finding patterns in the selected digits; and representing the patterns in the transformed data with a pointer.

18. The method of claim 17, further comprising using an artificial intelligence routine to perform said finding.

19. The method of claim 18, further comprising generating an index of said patters.

20. The method of claim 17, wherein said finding includes searching for nonconsecutive patterns.

21. A system for encrypting data comprising: an irrational key; andan encoder for encrypting the data to encrypted data based on the irrational key.

22. The system of claim 21, further comprising: a first communication channel for transmitting said encrypted data; and a second communication channel for transmitting said irrational key.

23. A system for compressing data comprising: an irrational key; and an encoder for compressing the data to compressed data based on the irrational key.

24. The system of claim 23, further comprising: an index of patterns in at least one of said irrational key and a rational approximation of said irrational key.

25. The system of claim 23, further comprising: a computer readable memory storing at least one of said irrational can and a rational approximation of said irrational key.

26. The system of claim 24, further comprising: an artificial intelligence routine configured for generating said index.

27. The system of claim 23, wherein said encoder includes a processor.

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