An elliptic curve random number generator (ECRNG) has been proposed in ANSI and NIST draft standards. This paper proves that, if three conjectures are true, then the ECRNG is secure. The three conjectures are hardness of the elliptic curve decisional Diffie-Hellman problem and the hardness of two newer problems, the x-logarithm problem and the truncated point problem.

We discuss a procedure, which should be called Lenstra's fix, for producing secure RSA moduli even when the random number generation is very poor. RSA is uniquely vulnerable to low entropy random number generation. If n = pq and n' = pq' are two (public) moduli, then the computation gcd(n,n') = p factors both moduli and totally compromises the security of both systems. Following a suggestion of...

Random and pseudorandom number generators (RNG and PRNG) are used for many purposes including cryptographic, modeling and simulation applications. For such applications a generated bit sequence should mimic true random, i.e., by definition, such a sequence could be interpreted as the result of the flips of a fair coin with sides that are labeled 0 and 1. It is known that the Shannon entropy of ...

This paper introduces fast LU and QR implementations on GPU which are extended from LAPACK routines. Using fast matrix-matrix multiplication algorithm on GPU, right-looking technique to parallelize the computation, look-ahead technique to override the CPU and GPU computation together with optimal block size on GPU make this implementation outperform its counterparts. It gains around 2~8x speedu...

Introduction Have you played a video game lately? Purchased something on the web? Trained a Neural Network? Used a Genetic Algorithm for optimization? Run software from Microsoft? Applied textures to a photograph? Played the stock market? If the answer is “yes” to any of these questions, Random Number Generator (RNG) have affected your life. Can you trust your Random Number Generator? Can you t...

On-chip communications peripherals include: Bluetooth Lower Link Controller, Universal Serial Bus (USB) 1.1 node, CAN, Microwire/Plus, SPI, ACCESS.bus, quad UART, 12-bit A/D converter, and Advanced Audio Interface (AAI). Additional on-chip peripherals include Random Number Generator (RNG), DMA controller, CVSD/PCM conversion module, Timing and Watchdog Unit, Versatile Timer Unit, Multi-Function...

A class of xorshift random number generators (RNGs) are introduced by Marsaglia. We have proposed an algorithm which constructs a full period xorshift RNG from a given primitive polynomial. It is shown there is a weakness present in those RNGs and is suggested its improvement. A separate algorithm is also proposed which returns a full period xorshift generator with desired number of xorshift op...

Introduction Have you played a video game lately? Purchased something on the web? Trained a Neural Network? Used a Genetic Algorithm for optimization? Run software from Microsoft? Applied textures to a photograph? Played the stock market? If the answer is “yes” to any of these questions, Random Number Generator (RNG) have affected your life. Can you trust your Random Number Generator? Can you t...