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Pseudo-Random Number Generators in VHDL ========================================= This library contains a number of pseudo-random number generators (PRNG) in synthesizable VHDL code. The PRNGs in this library are useful to generate noise in digital signal processing and to generate random numbers for monte-carlo simulations or for games. The VHDL code is portable and should run on any FPGA/synthesis platform, but the designs are somewhat optimized for Xilinx FPGAs. These PRNGs are a good alternative to linear feedback shift registers (LFSR). Although LFSRs are commonly used, their output exhibits strong correlations. Furthermore, correctly generating multi-bit random words with LFSRs is tricky. NOTE: This library is not designed for cryptographic applications (such as generating passwords, encryption keys). Most of the RNGs in this library are cryptographically weak. Xoroshiro128+ RNG ------------------ Xoroshiro128+ is an RNG algorithm developed in 2016 by David Blackman and Sebastiano Vigna. It is a further development of the Xorshift algorithm invented by George Marsaglia See also http://xoroshiro.di.unimi.it/ This RNG passes many statistical tests. Its period, 2**128 - 1, is long compared to a typical LFSR, but much shorter than the Mersenne Twister. The output is 1-dimensionally equidistributed. The VHDL implementation produces 64 new random bits on every (enabled) clock cycle. It is quite efficient in terms of FPGA resources, but it does require a 64-bit adder. Output word length: 64 bits Seed length: 128 bits Period: 2**128 - 1 FPGA resources: general logic and 64-bit adder Synthesis results: 194 LUTs, 192 registers on Spartan-6 Timing results: 333 MHz on Spartan-6 LX45-3 Mersenne Twister RNG -------------------- The Mersenne Twister is an RNG algorithm developed in 1997 by Makoto Matsumoto and Takuji Nishimura. This library implements the most common variant of the algorithm, MT19937. See also M. Matsumoto, T. Nishimura, "Mersenne Twister: a 623-dimensionally equidistributed uniform pseudorandom number generator", ACM TOMACS, vol. 8, no. 1, 1998. This RNG is very popular in software applications. It is relatively fast, passes many statistical tests and has an enormous period. The VHDL implementation produces 32 new random bits on every (enabled) clock cycle. It uses a RAM block, 32 bits wide, 1024 elements deep, to store the RNG state. The most demanding part of the implementation is the seeding procedure. Seeding involves repeated multiplication by a 32-bit constant. This multiplication is implemented as a hand-coded series of shifts and adds when force_const_mul = true; the multiplication is left to the synthesizer when force_const_mul = false. The hand-coded variant is much more efficient on Xilinx Spartan-6, so the recommended setting is force_const_mul = true. After reset and after each reseeding, the RNG needs 2496 clock cycles to initialize its state. The RNG can not provide random data during this time. Output word length: 32 bits Seed length: 32 bits Period: 2**19937 - 1 FPGA resources: RAM block, 32 bits x 1024 elements Synthesis results: 279 LUTs, 297 registers, 2x RAMB16 on Spartan-6 Timing results: 300 MHz on Spartan-6 LX45-3 Trivium RNG ----------- Trivium is a stream cipher published in 2005 by Christophe De Canniere and Bart Preneel as part of the eSTREAM project. See also C. De Canniere, B. Preneel, "Trivium Specifications", http://www.ecrypt.eu.org/stream/p3ciphers/trivium/trivium_p3.pdf See also the eSTREAM portfolio page for Trivium: http://www.ecrypt.eu.org/stream/e2-trivium.html This library uses the key stream of the Trivium cipher as a sequence of random bits. The VHDL implementation produces up to 64 new random bits on every (enabled) clock cycle. The number of bits per clock cycle is configurade as a synthesis parameter. This RNG passes all known statistical tests. However, little is known about its period. The period depends on the seed value, and is believed to be long (at least 2**80) for the vast majority of seed choices. After reset and after each reseeding, the RNG must process 1152 bits to initialize its state. This takes up to 1152 clock cycles, depending on the configured number of bits per cycle. The RNG can not provide random data during this time. Output word length: configurable from 1 to 64 bits (must be power-of-2) Seed length: 80 bits key + 80 bits IV Period: unknown, depends on seed FPGA resources: only general logic (AND, XOR ports, registers) Synthesis results: 202 LUTs, 332 registers on Spartan-6 (32 bits output) Timing results: 380 MHz on Spartan-6 LX45-3 (32 bits output) Code organization ----------------- rtl/ Synthesizable VHDL code rtl/rng_xoroshiro128plus.vhdl Implementation of Xoroshiro128+ RNG rtl/rng_mt19937.vhdl Implementation of Mersenne Twister RNG rtl/rng_trivium.vhdl Implementation of Trivium RNG sim/ Test benches sim/Makefile Makefile for building test benches with GHDL sim/tb_xoroshiro128plus.vhdl Test bench for Xoroshiro128+ RNG sim/tb_mt19937.vhdl Test bench for Mersenne Twister RNG sim/tb_trivium.vhdl Test bench for Trivium RNG refimpl/ Reference software implementations of RNGs synth/ Top-level wrappers for synthesis testruns License ------- Copyright (C) 2016 Joris van Rantwijk This VHDL library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License s published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, see <https://www.gnu.org/licenses/old-licenses/lgpl-2.1.html> This package contains a few support files which are distributed under Creative Commons CC0. This is explicitly and clearly marked in the files to which it applies. --