Methods For Generating Secure Pseudorandom Floating Point Numbers

With the rapid development of computer network and increasing demand for information security, cryptographic technology has been widely utilized to ensure security of information systems. Pseudorandom number generator (PRNG) is crucial for information security since they are often used to generate various secret keys in cryptographic systems. This thesis aims to propose cryptographic secure generators for pseudorandom floating point numbers. To solve problems, e.g., some mathematic iterative algorithms cannot resist the next bit attack; key spaces must be expanded in order to resist exhaustive search when computing capacity of computer increases, this thesis mainly contributes to PRNG in the following three aspects.Two improved chaotic map algorithms are proposed for generating floating point pseudorandom number. First, an improved PRNG is proposed by incorporating the logistic chaotic map to eliminate the error seeds. As a result, the improved algorithm is insensitive to the initial values, has enlarged key space and much better statistical performance. Second, for the problems of chaotic map with infinite collapses and period windows, such as period window, limited parameters choices, and inconvenience for users, an improved algorithm is proposed by modifying the iterative equation. Consequently, the period window is removed, the key space and the Lyapunov are enlarged, and the statistical performance is much improved. In addition, the two improved algorithms utilize "numerical fingerprint" characteristic of the Hash function to shift the output sequences with confidential information from Hash, the next number attack is thus extremely difficult.A secure pseudorandom bit sequence generator is designed and the bit sequences are then transformed into floating point numbers. First of all, random sources such as keyboard inputs and system clock of a computer are used as keys. Then, the Hash function and a feed back shift register are combined to construct a new PRNG based on the inner product theorem and the expansion theorem. Since the keys are random and the Hash function has one way character, the proposed generator can resist the birthday attack and the force attack, and the generated floating point numbers are unpredictable.The software package for pseudorandom number generating and statistical testing is designed using VC. This package is convenient for future research, applications and tests of pseudorandom numbers.