# Lahouari Ghouti, Dhahran SA

## Lahouari Ghouti, Dhahran SA

Patent application number | Description | Published |
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20100166174 | Hash functions using elliptic curve cryptography - The hash functions using elliptic curve cryptography are hash functions that are produced using both an elliptic curve and a twist of the elliptic curve. Hash points are assigned values that either correspond to points on the elliptic curve or to points on the twist, depending upon whether the scalar value of the corresponding message block produces a quadratic residue or a quadratic non-residue when substituted as the x-value into the elliptic curve equation. The corresponding hash point x-coordinates are concatenated to form the hash bit string. The hash points may be doubled, and the hash functions may be applied to multimedia data by applying a media compression method to the message data before computing the hash points. | 07-01-2010 |

20100166175 | Cryptographic hash functions using elliptic polynomial cryptography - The cryptographic hash functions using of elliptic polynomial polynomials are based on the elliptic polynomial discrete logarithm problem, which is well known as a computationally hard problem. The hash functions are based on the elliptic polynomial equation in their generation, where different elliptic polynomials are used for different blocks of the same plain text. Particularly, the hash functions use an elliptic polynomial with more than one independent x-coordinate. More specifically, a set of elliptic polynomial points are used that satisfy an elliptic polynomial equation with more than one independent x-coordinate which is defined over a finite field F. | 07-01-2010 |

20100166176 | Elliptical polynomial-based message authentication code - The elliptic-polynomial based Message Authentication Code (MAC) provides MAC generation methods based on the elliptic polynomial discrete logarithm problem. It is well known that an elliptic polynomial discrete logarithm problem is a computationally “difficult” or “hard” problem. The methods use both an elliptic polynomial polynomial and its twist, even if the polynomial and its twist are not isomorphic. Since both the polynomial and its twist are used, multiple x- and y-coordinates can be used to embed bit strings into a point that satisfies the elliptic polynomial, and the embedding process is non-iterative, so that the time required to embed the bit string is independent of the bit string content. | 07-01-2010 |

20100169644 | Message authentication code with elliptic polynomial hopping - The message authentication code with elliptic polynomial hopping provides methods for the generation of message authentication codes (MACs) utilizing elliptic curves, which are based on the elliptic curve discrete logarithm problem. The elliptic curve discrete logarithm problem is well known to be a computationally “difficult” or “hard” problem, thus providing enhanced security for the MACs. Different elliptic polynomials are used for different blocks of the same plaintext, each elliptic polynomial for each message block being selected at random using an initial secret key and a random number generator. | 07-01-2010 |

20100169657 | Message authentication code with blind factorization and randomization - The message authentication code with blind factorization and randomization is a computational method for improving the security of existing Message Authentication Code (MAC) methods through the use of blind integer factorization. Further, blind randomization is used as a countermeasure to minimize collision attacks where different plaintexts produce the same MAC. | 07-01-2010 |

20100169658 | Elliptic curve-based message authentication code - The elliptic curve-based message authentication code is a computational method for improving the security of existing message authentication code (MAC) generating methods through the use of elliptic curve cryptography. Particularly, the message authentication codes and elliptic curve cryptography are based on an elliptic curve discrete logarithm problem, which is well known in mathematics to be a computationally hard problem. | 07-01-2010 |

20100177890 | Hash functions with elliptic polynomial hopping - The hash functions with elliptic polynomial hopping are based upon an elliptic polynomial discrete logarithm problem. Security using hash functions is dependent upon the implementation of a computationally hard problem, and the elliptic polynomial discrete logarithm problem provides enough relative difficulty in computation to ensure that the produced hash functions, as applied to message bit strings, are optimally secure. The hash functions are produced as functions of both the elliptic polynomial as well as the twist of the elliptic polynomial, particularly using a method of polynomial hopping. | 07-15-2010 |

20110200185 | Method of performing elliptic polynomial cryptography with elliptic polynomial hopping - The method of performing elliptic polynomial cryptography with elliptic polynomial hopping allows for the encryption of messages through elliptic polynomial cryptography, i.e., using elliptic polynomials with multi x-coordinates, and particularly with the utilization of elliptic polynomial hopping based upon both the elliptic polynomial and its twist, regardless of whether the elliptic polynomial and its twist are isomorphic with respect to one another. Each plaintext block is encrypted by a different elliptic polynomial, and the elliptic polynomials used are selected by an initial secret key and a random number generator. The method is particularly useful for symmetric encryption systems, and provides a block cipher fundamentally based upon a computationally hard problem. | 08-18-2011 |

20110200186 | Method of cipher block chaining using elliptic curve cryptography - The method of cipher block chaining using elliptic curve cryptography allows for the encryption of messages through elliptic curve cryptography and, particularly, with the performance of cipher block chaining utilizing both the elliptic curve and its twist, regardless of whether the elliptic curve and its twist are isomorphic with respect to one another. The method of performing elliptic curve cryptography is based on the elliptic curve discrete logarithm problem. It is well known that an elliptic curve discrete logarithm problem is a computationally “difficult” or “hard” problem. | 08-18-2011 |

20110200187 | Elliptic polynomial cryptography with secret key embedding - Elliptic polynomial cryptography with secret key embedding is a method that allows for the encryption of messages through elliptic polynomial cryptography and, particularly, with the embedding of secret keys in the message bit string. The method of performing elliptic polynomial cryptography is based on the elliptic polynomial discrete logarithm problem. It is well known that an elliptic polynomial discrete logarithm problem is a computationally “difficult” or “hard” problem. | 08-18-2011 |

20110200188 | Method of performing cipher block chaining using elliptic polynomial cryptography - The method of performing cipher block chaining using elliptic polynomial cryptography allows for the encryption of messages through elliptic polynomial cryptography and, particularly, with the utilization of cipher block chaining based upon both the elliptic polynomial and its twist, regardless of whether the elliptic polynomial and its twist are isomorphic with respect to one another. The method of performing cipher block chaining is based on the elliptic polynomial discrete logarithm problem. It is well known that an elliptic polynomial discrete logarithm problem is a computationally “difficult” or “hard” problem. | 08-18-2011 |

20110202773 | Method of generating a password protocol using elliptic polynomial cryptography - The method of generating password protocols based upon elliptic polynomial cryptography provides for the generation of password protocols based on the elliptic polynomial discrete logarithm problem. It is well known that an elliptic polynomial discrete logarithm problem is a computationally “difficult” or “hard” problem. | 08-18-2011 |

20120140920 | RNA-BASED CRYPTOGRAPHIC SYSTEM AND METHOD - The RNS-based cryptographic system and method uses a symmetric residue number system (RNS) for encryption and decryption of messages, i.e., the sender and receiver agree upon a set of relatively prime numbers, referred to as the basis, whose product is an integer, and both the RNS and the integer are kept secret. To break the cipher, an attacker must factor the secret integer, which is unknown to the attacker, given only the upper bound of the unknown integer, a problem referred to as blind factorization of the unknown integer, which is a computationally hard problem. The method may be combined with a discrete logarithm problem, and the ciphertext may be padded with random values to hide the upper bound of the unknown integer. When the ciphertext requires multiple blocks, subsets of the basis and/or the random number padding may be used to prevent collision attacks. | 06-07-2012 |

20120140921 | RSA-ANALOGOUS XZ-ELLIPTIC CURVE CRYPTOGRAPHY SYSTEM AND METHOD - The RSA-analogous XZ-elliptic curve cryptography system and method provides a computerized system and method that allows for the encryption of messages through elliptic polynomial cryptography and, particularly, in a manner which is analogous to RSA cryptography but which does not require multiple private keys, as in the RSA scheme. The RSA-analogous XZ-elliptic curve cryptography method is based on the integer factorization problem. It is well known that the integer factorization problem is a computationally “difficult” or “hard” problem. | 06-07-2012 |

20120237030 | ELLIPTIC CURVE-BASED MESSAGE AUTHENTICATION CODE SYSTEM AND METHOD - The elliptic curve-based message authentication code is a computational method for improving the security of existing message authentication code (MAC) generating methods through the use of elliptic curve cryptography. Particularly, the message authentication codes and elliptic curve cryptography are based on an elliptic curve discrete logarithm problem, which is well known in mathematics to be a computationally hard problem. | 09-20-2012 |

20130094724 | METHOD OF PERFORMING FINGERPRINT MATCHING - The method of performing fingerprint matching includes a matching algorithm that combines affine moment invariants (AMIs) and translation, rotation and scaling invariants (TRS) based on moments analysis without requiring minutiae detection. Preprocessing normalizes the fingerprint image using the Federal Bureau of Investigation's wavelet scalar quantification (WSQ) compression standard definition. Analysis of the orientation field reliably and accurately determines the reference point. The area within a predetermined range around the detected reference point is used as a region of interest (ROI) for feature extraction. A directional filter bank transform (DFB) obtains directional components of the image. An invariant moment analysis on sub-bands of the filtered images extracts features while limiting the effects of noise and non-linear distortions. Absolute distance is used to match the fingerprints. | 04-18-2013 |

20130202104 | XZ-ELLIPTIC CURVE CRYPTOGRAPHY SYSTEM AND METHOD - The XZ-elliptic curve cryptography system and method provides a computerized method that allows for the encryption of messages through elliptic polynomial cryptography and, particularly, with the embedding of either a symmetric secret key or a public key in the message bit string. The method of performing XZ-elliptic polynomial cryptography is based on the elliptic polynomial discrete logarithm problem. It is well known that an elliptic polynomial discrete logarithm problem is a computationally “difficult” or “hard” problem. | 08-08-2013 |

20130318016 | METHOD OF PREDICTING GAS COMPOSITION - The method of predicting gas composition in a multistage separator includes solutions to the regression problem of gas composition prediction that are developed using an ensemble of hybrid computational intelligence (CI) models. Three separate homogeneous and one heterogeneous ensemble of hybrid computational intelligence (EHCI) models are developed using a parallel scheme. The homogeneous models have the same types of CI models used as base learners, and the heterogeneous model has of different types of CI models used as base learners. Various popular CI models, including multi-layer perceptron (MLP), support vector regression (SVR) and adaptive neuro-fuzzy inference system (ANFIS), are used as base learners of ensemble models. | 11-28-2013 |