Abstract: Received is a main program representing one Engineering Design Optimization Problem (EDOP), the EDOP including polynomial terms with product values. A number (N) of available parallel processors for parallel processing are identified. The main program is partitioned into N subprograms, N being a positive integer greater than one. The N subprograms have fewer overlapping product values between them compared to existing solutions, and the partitioning is prime-number based. Each of the available parallel processors then independently solve a unique subprogram of the N subprograms, resulting in N unique solutions. A best solution is automatically chosen from among the N unique solutions and the best solution is automatically applied to the EDOP.

Abstract: A system for performing operations using linear integer programming for RSA factorization is provided, including an n/e extractor, a prime factorization calculator, a private key determiner, and a decryptor. The n/e extractor is configured to extract a modulus and a public key exponent from a public key. The prime factorization calculator is configured to: determine a semi-prime number of the modulus according to the modulus; use a tail digit and a head digit set of the semi-prime number of the modulus to perform decomposition and factorization with respect to the semi-prime number into two prime factors. The private key determiner is configured to determine a private key using the public key exponent and the two prime numbers. The decryptor is configured to decrypt an encrypted message using the private key so as to generate a decrypted message.

Abstract: A system for performing operations using linear integer programming for RSA factorization is provided, including an n/e extractor, a prime factorization calculator, a private key determiner, and a decryptor. The n/e extractor is configured to extract a modulus and a public key exponent from a public key. The prime factorization calculator is configured to: determine a semi-prime number of the modulus according to the modulus; use a tail digit and a head digit set of the semi-prime number of the modulus to perform decomposition and factorization with respect to the semi-prime number into two prime factors. The private key determiner is configured to determine a private key using the public key exponent and the two prime numbers. The decryptor is configured to decrypt an encrypted message using the private key so as to generate a decrypted message.

Abstract: Received is a main program representing one Engineering Design Optimization Problem (EDOP), the EDOP including polynomial terms with product values. A number (N) of available parallel processors for parallel processing are identified. The main program is partitioned into N subprograms, N being a positive integer greater than one. The N subprograms have fewer overlapping product values between them compared to existing solutions, and the partitioning is prime-number based. Each of the available parallel processors then independently solve a unique subprogram of the N subprograms, resulting in N unique solutions. A best solution is automatically chosen from among the N unique solutions and the best solution is automatically applied to the EDOP.

Abstract: A universal color coding system, and method of analyzing objects with multiple attributes using the color coding system. The color coding system includes a color mapper arranged to map a plurality of colors with a plurality of numerical codes, wherein the each of the plurality of numerical codes is a unique integer determined based on a combination of prime numbers; wherein each of the plurality of numerical codes is arranged to represent a unique color in color space wherein each of the prime numbers represents a respective basic color of the color space; and wherein the plurality of numerical codes are integers calculated based on addition and multiplication of a plurality of prime numbers.

Abstract: A universal color coding system, and a system and a method of manipulating colors using such color coding system. The color coding system includes a color mapper arranged to map a plurality of colors with a plurality of numerical codes, wherein the each of the plurality of numerical codes is a unique integer determined based on a combination of prime numbers.

Abstract: A universal color coding system, and a system and a method of manipulating colors using such color coding system. The color coding system includes a color mapper arranged to map a plurality of colors with a plurality of numerical codes, wherein the each of the plurality of numerical codes is a unique integer determined based on a combination of prime numbers.

Abstract: A universal color coding system, and method of analyzing objects with multiple attributes using the color coding system. The color coding system includes a color mapper arranged to map a plurality of colors with a plurality of numerical codes, wherein the each of the plurality of numerical codes is a unique integer determined based on a combination of prime numbers; wherein each of the plurality of numerical codes is arranged to represent a unique color in color space wherein each of the prime numbers represents a respective basic color of the color space; and wherein the plurality of numerical codes are integers calculated based on addition and multiplication of a plurality of prime numbers.