Pseudo Random Number Generation: a Reinforcement Learning approach

Pasqualini, Luca; Parton, Maurizio

doi:10.1016/j.procs.2020.03.057

Cited by 24 publications

(19 citation statements)

References 7 publications

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“…Most digital logic and computing systems are base-2, but algorithms such as Cooley-Tukey [17] offer equivalent mixed-radix representations to achieve the same overall calculation, but as a parallel composition of many small RNS operations. In particular, most PRNG methods were designed to produce bistate binary values, and methods to quantify PRNG output randomness usually require their binary form [18]. Consequently, the most common output of a PRNG is a k-bit binary word that may be viewed as an element r ∈ Z 2 k .…”

Section: Introductionmentioning

confidence: 99%

Shannon Entropy Loss in Mixed-Radix Conversions

Vennos

Michaels

2021

Entropy

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This paper models a translation for base-2 pseudorandom number generators (PRNGs) to mixed-radix uses such as card shuffling. In particular, we explore a shuffler algorithm that relies on a sequence of uniformly distributed random inputs from a mixed-radix domain to implement a Fisher–Yates shuffle that calls for inputs from a base-2 PRNG. Entropy is lost through this mixed-radix conversion, which is assumed to be surjective mapping from a relatively large domain of size 2J to a set of arbitrary size n. Previous research evaluated the Shannon entropy loss of a similar mapping process, but this previous bound ignored the mixed-radix component of the original formulation, focusing only on a fixed n value. In this paper, we calculate a more precise formula that takes into account a variable target domain radix, n, and further derives a tighter bound on the Shannon entropy loss of the surjective map, while demonstrating monotonicity in a decrease in entropy loss based on increased size J of the source domain 2J. Lastly, this formulation is used to specify the optimal parameters to simulate a card-shuffling algorithm with different test PRNGs, validating a concrete use case with quantifiable deviations from maximal entropy, making it suitable to low-power implementation in a casino.

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Section: Introductionmentioning

confidence: 99%

Shannon Entropy Loss in Mixed-Radix Conversions

Vennos

Michaels

2021

Entropy

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“…A Deep Reinforcement Learning (DRL) pipeline can then be used on this MDP to train a PRNG agent. This DRL approach has been used for the first time in [6] with promising results, see modeling details in Section 2.2. This is a probabilistic approach that generates pseudo-random numbers with a "variable period", because the learned policy will generally be stochastic.…”

Section: Introductionmentioning

confidence: 99%

“…However, the MDP formulation in [6] has an action set where the size grows linearly with the length of the sequence. This is a severe limiting factor, because when the action set is above a certain size it becomes very difficult, if not impossible, for an agent to explore the action space within a reasonable time.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we overcome the above limitation with a different MDP formulation, using a partially observable state. By observing only the last part of the sequence, and using the hidden state of a Long-Short Term Memory (LSTM) neural network to extract important features of the full state, we significantly improve the results in [6], see Section 3. The code for this article can be found at GitHub repository [7].…”

Section: Introductionmentioning

confidence: 99%

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Pseudo Random Number Generation through Reinforcement Learning and Recurrent Neural Networks

Pasqualini

Parton

2020

Algorithms

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A Pseudo-Random Number Generator (PRNG) is any algorithm generating a sequence of numbers approximating properties of random numbers. These numbers are widely employed in mid-level cryptography and in software applications. Test suites are used to evaluate the quality of PRNGs by checking statistical properties of the generated sequences. These sequences are commonly represented bit by bit. This paper proposes a Reinforcement Learning (RL) approach to the task of generating PRNGs from scratch by learning a policy to solve a partially observable Markov Decision Process (MDP), where the full state is the period of the generated sequence, and the observation at each time-step is the last sequence of bits appended to such states. We use Long-Short Term Memory (LSTM) architecture to model the temporal relationship between observations at different time-steps by tasking the LSTM memory with the extraction of significant features of the hidden portion of the MDP’s states. We show that modeling a PRNG with a partially observable MDP and an LSTM architecture largely improves the results of the fully observable feedforward RL approach introduced in previous work.

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“…Such ideal random sequences can easily be produced from natural resources, for example, atmospheric noises, radioactive decay and other natural phenomena. However, reproducibility of such sequences is impossible mathematically because of variation in natural resources [4,5]. Due to this disadvantage, sources of such true random sequences are unreliable for practical computer applications.…”

Section: Introductionmentioning

confidence: 99%

Pseudo Random Binary Sequence Based on Cyclic Difference Set

Mamun

Akhter

2020

Symmetry

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With the increasing reliance on technology, it has become crucial to secure every aspect of online information where pseudo random binary sequences (PRBS) can play an important role in today’s world of Internet. PRBS work in the fundamental mathematics behind the security of different protocols and cryptographic applications. This paper proposes a new PRBS namely MK (Mamun, Kumu) sequence for security applications. Proposed sequence is generated by primitive polynomial, cyclic difference set in elements of the field and binarized by quadratic residue (QR) and quadratic nonresidue (QNR). Introduction of cyclic difference set makes a special contribution to randomness of proposed sequence while QR/QNR-based binarization ensures uniformity of zeros and ones in sequence. Besides, proposed sequence has maximum cycle length and high linear complexity which are required properties for sequences to be used in security applications. Several experiments are conducted to verify randomness and results are presented in support of robustness of the proposed MK sequence. The randomness of proposed sequence is evaluated by popular statistical test suite, i.e., NIST STS 800-22 package. The test results confirmed that the proposed sequence is not affected by approximations of any kind and successfully passed all statistical tests defined in NIST STS 800-22 suite. Finally, the efficiency of proposed MK sequence is verified by comparing with some popular sequences in terms of uniformity in bit pattern distribution and linear complexity for sequences of different length. The experimental results validate that the proposed sequence has superior cryptographic properties than existing ones.

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Pseudo Random Number Generation: a Reinforcement Learning approach

Cited by 24 publications

References 7 publications

Shannon Entropy Loss in Mixed-Radix Conversions

Shannon Entropy Loss in Mixed-Radix Conversions

Pseudo Random Number Generation through Reinforcement Learning and Recurrent Neural Networks

Pseudo Random Binary Sequence Based on Cyclic Difference Set

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