Overview
AKS Primality Test is a primality testing method for deterministic primality testing. It works by checking polynomial congruences that characterize prime numbers.
SpecializedSource checked
AKS Primality Test
AKS Primality Test addresses deterministic primality testing by checking polynomial congruences that characterize prime numbers.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Cryptography
- Difficulty
- Advanced
- Family
- Primality Testing
- Tier
- Specialized
- Status
- Verified
- Review
- Source Checked
- Sources
- 3
- Formulas
- 0
- Relationships
- 2
- Code example
- Not ready
- Visualization
- Ready
Core Concepts
deterministic primality testingprimality testingmodular arithmeticcryptography
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(k)
Average
O(k^2)
Worst
O(k^3)
Space
O(k)
When to Use
- Use AKS Primality Test when solving deterministic primality testing and you want to benefit from checking polynomial congruences that characterize prime numbers.
- Choose it when O(k^2) average/worst-case time and O(k) memory match your workload profile.
- Prefer it over Extended Euclidean Algorithm or Binary GCD when the problem structure favors deterministic primality testing.
When Not to Use
- Avoid custom production implementations unless they are independently reviewed.
- Avoid when nonce, key, or randomness requirements cannot be satisfied.
What It Does
- Computes deterministic primality testing within Primality Testing workloads (O(k^2) time, O(k) space).
- Works by checking polynomial congruences that characterize prime numbers.
- Maintains key invariants across deterministic primality testing, primality testing, modular arithmetic.
Use Cases
- Production and research workloads requiring deterministic primality testing via checking polynomial congruences that characterize prime numbers.
- Primality Testing pipelines where O(k^2) time and O(k) space fit system constraints.
- Engineering comparisons against Extended Euclidean Algorithm and Binary GCD when tuning deterministic primality testing.
Inputs
- Message, key, modulus, seed, or public parameters
- Security parameter or nonce when required
Outputs
- Cryptographic value such as signature, random bits, proof, or modular result
Pseudocode
- 1.Initialize the input structures and parameters for AKS Primality Test (deterministic primality testing).
- 2.Set up the working state for deterministic primality testing (primality testing).
- 3.Execute the core step by checking polynomial congruences that characterize prime numbers.
- 4.Update invariants and check termination or convergence criteria.
- 5.Return the resulting deterministic primality testing output.
Canonical Example
- Input
- Message, key, modulus, seed, or public parameters configured for a representative deterministic primality testing test case
- Output
- Cryptographic value such as signature, random bits, proof, or modular result satisfying AKS Primality Test invariants
- Explanation
- AKS Primality Test processes the input by checking polynomial congruences that characterize prime numbers, tracking deterministic primality testing and primality testing to produce the verified deterministic primality testing result.
Implementation Notes
- Use vetted libraries for production implementations.
- Keep randomness, nonce, and key-lifetime requirements explicit.
- Validate modulus sizes, input ranges, and any randomness requirements before relying on production results.
Common Pitfalls
- Using the primitive directly without the required protocol context.
- Reusing nonces, seeds, or one-time values.
- Ignoring parameter bounds, arithmetic preconditions, or randomness assumptions can make results unreliable.
Interactive Mechanism Walkthrough
Graph Frontier & Edge RelaxationShow checking polynomial congruences that characterize prime numbers on a small deterministic primality testing example.
Step 1 of 5: Initialize the input structures and parameters for AKS Primality Test (deterministic primality testing).
cryptography-mechanismNotes
AKS Primality Test operates in O(k^2) time and O(k) space within the Primality Testing family. Often compared with Extended Euclidean Algorithm and Binary GCD.
Sources (3)
What each reference supports for this entry.
Handbook of Applied Cryptography
BookCryptographic reference for AKS Primality Test's number-theoretic primitive, modular arithmetic, primality, or factorization context.
Open sourceModern Computer Arithmetic
BookReference for AKS Primality Test's arithmetic operations, modular arithmetic, multiplication, division, or number-theoretic implementation details.
Open sourcePRIMES is in P
PaperOriginal AKS reference proving deterministic polynomial-time primality testing.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageConceptual neighborExtended Euclidean Algorithm
AKS Primality Test and Extended Euclidean Algorithm share a concrete primality testing mechanism for deterministic primality testing.
Conceptual neighborBinary GCD
AKS Primality Test and Binary GCD share a concrete primality testing mechanism for deterministic primality testing.
Related Algorithms
Tags
Cryptography