MaD Family Pseudorandom Number Generators

MaD is a family of ultrafast pseudorandom number generators (PRNGs). Currently it is composed of four nonlinear generators: MaD0, MaD1, and MaD2. MaD family generators have a novel two-layer structure: a byte-oriented layer for key scheduling and state initialization and an integer-oriented layer for state update and pseudorandom number generation. The state transition of the byte-oriented layer follows a pseudorandom permutation and the state transition of the integer-oriented layer follows a pseudorandom mapping.

MaD generators cover noncryptographic, cryptographic, deterministic, and nondeterministic categories, and can be used in a wide variety of applications such as computer simulation, data analysis, key generation, data encryption, lottery, etc.

MaD0

-- a general-purpose pseudorandom number generator (PRNG)

• Features:
• Noncryptographic
• Speed: 0.46 cycle/byte on an Intel Core i3 processor
• Randomness: passed NIST, Diehard, and TestU01batteries of statistical tests
• Period: 2^1120 expected
• Internal state: 2304 bits
• Built-in initialization function that meets the strict avalanche criterion
• Quick recovery from biased states
• Ease of use for parallel and distributed applications
• Source code
• Paper: Jie Li, Jianliang Zheng, and Paula Whitlock, MaD0: An Ultrafast Nonlinear Pseudorandom Number Generator, ACM Transactions on Modeling and Computer Simulation (TOMACS), Volume 26 Issue 2, Article 13, January 2016.
  
  

MaD1

-- a pseudorandom number generator that can run in deterministic mode or nondeterministic mode

• Features:
• Cryptographically secure
• Deterministic or nondeterministic mode
• Key length: up to 64 bytes
• Speed: 0.61 cycle/byte on an Intel Core i3 processor
• Randomness: passed NIST, Diehard, and TestU01 batteries of statistical tests
• Period: 2^4224 expected
• Internal state: 8448 bits
• Strong resistance against various attacks
• A talk entitled "Efficient Deterministic and Nondeterministic Pseudorandom Number Generation" was given in the 10th IMACS Seminar on Monte Carlo Methods (MCM2015), Linz, Austria, July 2015.
  
• Paper: Jie Li, Jianliang Zheng, and Paula Whitlock, Efficient Deterministic and Nondeterministic Pseudorandom Number Generation, Mathematics and Computers in Simulation, Volume 143, pp 114-124, January 2018.
  
  

MaD2

-- a stream cipher

• Features:
• stream cipher
• Key length: up to 64 bytes
• Speed: 0.68 cycle/byte on an Intel Core i3 processor in the 2015 revised version
• Randomness: passed NIST, Diehard, and TestU01 batteries of statistical tests
• Internal state: 8448 bits
• Strong resistance against various attacks
• Paper: Jie Li and Jianliang Zheng, MaD2: An Ultra-Performance Stream Cipher for Pervasive Data Encryption, Foundations and Practice of Security, Lecture Notes in Computer Science, Volume 7743, pp 1-17, Springer 2013.
  
  

Contact: jie dot li at farmingdale dot edu