Abstract: A device may store raw random data in a raw random data store. The raw random data may include a first plurality of data strings. The device may generate, using a quotient ring transform (QRT), cryptographic random data based on the raw random data. The cryptographic random data includes a second plurality of data strings that is transformed from the first plurality of data strings based on an extraction state stored in an extraction state store. The device may store the cryptographic random data in a cryptographic random data store and may use the cryptographic random data for various purposes.

Abstract: A first device may determine a prime integer for generating public keys, wherein the prime integer is based on a set of distinct prime integers. The first device may generate a set of multiple public keys based on a set of secret keys. The first device may combine the set of multiple public keys into a single value based on the prime integer and the set of distinct prime integers. The first device may transmit the single value to a second device.

Abstract: A device may select a first pseudorandom integer within a range of integers. The device may generate a first candidate prime, based on the first pseudorandom integer, for primality testing. Based on determining that the first candidate prime fails a primality test, the device may select a second pseudorandom integer within the range of integers. The device may generate a second candidate prime, based on the second pseudorandom integer, for primality testing. The device may determine whether the second candidate prime satisfies the primality test. The device may selectively: re-perform, based on the second candidate prime failing the primality test, the selecting the second pseudorandom integer, the generating the second candidate prime, and the determining whether the second candidate prime satisfies the primality test, or using, based on the second candidate prime satisfying the primality test, the second candidate prime as a prime integer in a cryptographic protocol.

Abstract: A device may select a first pseudorandom integer within a range of integers. The device may generate a first candidate prime, based on the first pseudorandom integer, for primality testing. Based on determining that the first candidate prime fails a primality test, the device may select a second pseudorandom integer within the range of integers. The device may generate a second candidate prime, based on the second pseudorandom integer, for primality testing. The device may determine whether the second candidate prime satisfies the primality test. The device may selectively: re-perform, based on the second candidate prime failing the primality test, the selecting the second pseudorandom integer, the generating the second candidate prime, and the determining whether the second candidate prime satisfies the primality test, or using, based on the second candidate prime satisfying the primality test, the second candidate prime as a prime integer in a cryptographic protocol.

Abstract: A device may receive a set of cryptographic parameters associated with an integer, wherein the set of cryptographic parameters includes a linked list of potential prime integers, in an order, used to generate the integer. The device may determine, iteratively and in the order, whether each potential prime integer included in the linked list of potential prime integers is a prime integer using a primality test or a lookup operation based on a set of proven prime integers. The device may determine whether the integer is a proven prime integer based on determining whether each potential prime integer included in the linked list of potential prime integers is a prime integer. The device may authorize, when the integer is a proven prime integer, the integer for use in a cryptographic protocol.

Abstract: A device may receive a set of cryptographic parameters associated with an integer, wherein the set of cryptographic parameters includes a linked list of potential prime integers, in an order, used to generate the integer. The device may determine, iteratively and in the order, whether each potential prime integer included in the linked list of potential prime integers is a prime integer using a primality test or a lookup operation based on a set of proven prime integers. The device may determine whether the integer is a proven prime integer based on determining whether each potential prime integer included in the linked list of potential prime integers is a prime integer. The device may authorize, when the integer is a proven prime integer, the integer for use in a cryptographic protocol.

Abstract: A device may select a first pseudorandom integer within a range of integers. The device may generate a first candidate prime, based on the first pseudorandom integer, for primality testing. Based on determining that the first candidate prime fails a primality test, the device may select a second pseudorandom integer within the range of integers. The device may generate a second candidate prime, based on the second pseudorandom integer, for primality testing. The device may determine whether the second candidate prime satisfies the primality test. The device may selectively: re-perform, based on the second candidate prime failing the primality test, the selecting the second pseudorandom integer, the generating the second candidate prime, and the determining whether the second candidate prime satisfies the primality test, or using, based on the second candidate prime satisfying the primality test, the second candidate prime as a prime integer in a cryptographic protocol.

Abstract: A device may store raw random data in a raw random data store. The raw random data may include a first plurality of data strings. The device may generate, using a quotient ring transform (QRT), cryptographic random data based on the raw random data. The cryptographic random data includes a second plurality of data strings that is transformed from the first plurality of data strings based on an extraction state stored in an extraction state store. The device may store the cryptographic random data in a cryptographic random data store and may use the cryptographic random data for various purposes.

Abstract: A device may store raw random data in a raw random data store. The raw random data may include a first plurality of data strings. The device may generate, using a quotient ring transform (QRT), cryptographic random data based on the raw random data. The cryptographic random data includes a second plurality of data strings that is transformed from the first plurality of data strings based on an extraction state stored in an extraction state store. The device may store the cryptographic random data in a cryptographic random data store and may use the cryptographic random data for various purposes.

Abstract: Generally discussed herein are systems, devices, and methods for entwined encryption and error correction and/or error detection. An entwined cryptographic encode device can include a memory including data indicating a set of relatively prime, irreducible polynomials stored and indexed thereon, entwined encryption encoding circuitry to receive data, transform the data to a set of data integers modulo respective polynomial integers representative of respective polynomials of the polynomials stored on the memory, and perform a Da Yen weave on the transformed data based on received cipher data, and provide the weaved transformed data to a medium.

Abstract: Generally discussed herein are systems, devices, and methods for entwined encryption and error correction and/or error detection. An entwined cryptographic encode device can include a memory including data indicating a set of relatively prime, irreducible polynomials stored and indexed thereon, entwined encryption encoding circuitry to receive data, transform the data to a set of data integers modulo respective polynomial integers representative of respective polynomials of the polynomials stored on the memory, and perform a Da Yen weave on the transformed data based on received cipher data, and provide the weaved transformed data to a medium.

Abstract: A method for distributing data to a plurality of storage locations in a computing network is provided. The method includes receiving, at a processor in the computing network, input data and an input random cryptovariable, transforming, at the processor, the input data and the input random cryptovariable into encrypted output using Da Yen processing, and distributing the encrypted output to the plurality of storage locations. The present design further includes a method for decrypting encrypted blocks of data distributed over a plurality of storage locations in a computing network. The method includes receiving, at a processor in the computing network, a plurality of cipher/key word pairs, and transforming, at the processor, the plurality of cipher/key word pairs and a salt key word into plaintext using Da Yen processing.

Abstract: A method for distributing data to a plurality of storage locations in a computing network is provided. The method includes receiving, at a processor in the computing network, input data and an input random cryptovariable, transforming, at the processor, the input data and the input random cryptovariable into encrypted output using Da Yen processing, and distributing the encrypted output to the plurality of storage locations. The present design further includes a method for decrypting encrypted blocks of data distributed over a plurality of storage locations in a computing network. The method includes receiving, at a processor in the computing network, a plurality of cipher/key word pairs, and transforming, at the processor, the plurality of cipher/key word pairs and a salt key word into plaintext using Da Yen processing.

Abstract: A method of treating a fluid stream underwater comprising integrally attaching a skid to a fluid stream treating vessel so that the fluid stream treating vessel can be disposed on an underwater floor in a position such that an opening in said vessel is at a highest point on said vessel when disposed on the underwater floor; remotely directing a fluid stream treating vessel to an underwater floor location sufficiently close to said fluid stream so that the fluid stream can be remotely attached in fluid communication with said fluid stream treating vessel; remotely connecting said underwater fluid stream to said fluid stream treating vessel for treatment of said fluid stream; treating said fluid stream by contact with a treatment media disposed within said treatment vessel, maintained at equilibrium water pressure at the depth of treatment; and flowing the treated fluid stream out of said treating vessel.

Abstract: A filter and one-way valve for protecting a dental patient from contamination by bacteria that may be picked up by water flowing through a supply line and to prevent cross contamination of patients from the reflux of fluid from inside a patient's mouth. Several different embodiments of the invention are disclosed, including a filter/one-way valve (38) that combines a filter (42) with a one-way valve (46) in an integral assembly. This assembly is installed in a water line (34) supplying water to an air/water syringe (20), or other dental instrument, such as a dental hand piece (160), or an ultrasonic scalar. Alternatively, a separate filter is installed in the water (and/or air) line upstream of the dental instrument, and a one-way valve (140) is installed between the head of the dental instrument and a tip through which water is injected into the mouth of a patient.

Abstract: A filter and one-way valve for protecting a dental patient from contamination by bacteria that may be picked up by water flowing through a supply line and to prevent cross contamination of patients from the reflux of fluid from inside a patient's mouth. Several different embodiments of the invention are disclosed, including a filter/one-way valve (38) that combines a filter (42) with a one-way valve (46) in an integral assembly. This assembly is installed in a water line (34) supplying water to an air/water syringe (20), or other dental instrument, such as a dental hand piece (160), or an ultrasonic scalar. Alternatively, a separate filter is installed in the water (and/or air) line upstream of the dental instrument, and a one-way valve (140) is installed between the head of the dental instrument and a tip through which water is injected into the mouth of a patient.

Abstract: A method and apparatus are disclosed for preventing bacterial contamination from being introduced into a dental patient's mouth from water flowing through a dental tool water line. A flexible water line typically used for supplying water to a dental syringe, high-speed hand piece, or ultrasonic scaler has been found to support and encourage the growth of a significant biofilm that serves as a source of bacteria. To prevent the bacteria from being introduced into a patient's mouth by water flowing through the line, and thus into the patient's system, an in-line water filter is installed within the water line supplying water to the dental tool, at a point adjacent thereto. Conventional Luer fittings on the in-line water filter facilitate its quick installation and replacement. In addition, a cap protects the sterility of the outlet port of the in-line water filter during the installation process.