Period

As explained in Hacking Cryptography

The period is the number of generated steps in a repeating sequence before its values begin to recur.

A period is the number of generated steps a pseudorandom number generator (PRNG) takes before its output begins repeating. It reflects the cycle length of the generator’s mutating internal state. section 2.2.2

An LCG’s period

The implemented linear congruential generator uses a modulus of 2^31 − 1, multiplier 48271, and increment 0. Its period is 2^31 − 1: it starts repeating after 2,147,483,647 generated values. section 2.2.2

Figure 2.8 PRNGs have a state and are initialized with a seed. The PRNG algorithm keeps mutating the state.

Trace how a seed initializes PRNG state and how repeated algorithm steps mutate that state until the sequence cycles. section 2.2.2

How Hacking Cryptography covers it

How deep it goes

Defines repetition and quantifies an LCG’s cycle, but does not derive the period mathematically.

Examples

Uses an LCG with modulus 2^31 − 1 and observes repetition after 2,147,483,647 values.

What it assumes

Assumes familiarity with PRNG algorithms, seeds, and mutable state while defining period directly.

What you can do after

Evaluate a PRNG’s cycle length and recognize when its output sequence will recur.

How it connects

Connects period with PRNGs, seeds, internal state, and linear congruential generators.

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Also explained in

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  Acing the CCNA Exam: Volume 2 Advanced Networking and SecurityA period is the time required for one complete oscillation of a periodic wave.

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Related concepts

• Shor's algorithmaddressed by · Shor's algorithm is a quantum algorithm that efficiently factors integers and solves discrete logarithms using quantum period finding.
• seasonal naïve modelused by · A seasonal naïve model forecasts a value using the observed value from the corresponding position in a previous seasonal cycle.
• pseudo-random number generatormeasures · A pseudorandom number generator is a deterministic computational process that uses an initial seed or internal state to produce a sequence with random-like statistical properties.

This explainer was generated by Manning's knowledge graph from the text of Hacking Cryptography. The section links point to the parts of the book it draws on.