Cantor–Zassenhaus algorithm
E643836
The Cantor–Zassenhaus algorithm is a probabilistic method used to factor polynomials over finite fields efficiently, widely employed in computational algebra and cryptography.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Cantor–Zassenhaus algorithm canonical | 3 |
| Zassenhaus algorithm | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7115653 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Cantor–Zassenhaus algorithm Context triple: [Berlekamp’s algorithm for factoring polynomials over finite fields, influenced, Cantor–Zassenhaus algorithm]
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A.
Berlekamp’s algorithm for factoring polynomials over finite fields
Berlekamp’s algorithm for factoring polynomials over finite fields is a foundational deterministic method in computational algebra that efficiently decomposes polynomials into irreducible factors over finite fields and underpins many modern algorithms in coding theory and cryptography.
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B.
Adleman–Pomerance–Rumely primality test
The Adleman–Pomerance–Rumely primality test is an early deterministic algorithm in computational number theory used to determine whether a given number is prime, notable for its theoretical importance in the development of modern primality testing methods.
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C.
Berlekamp–Massey algorithm
The Berlekamp–Massey algorithm is a key algorithm in coding theory and cryptography used to efficiently determine the shortest linear feedback shift register that generates a given binary sequence.
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D.
Selfridge–Conway primality test
The Selfridge–Conway primality test is a probabilistic algorithm in number theory used to determine whether a given integer is prime.
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E.
Buchberger algorithm
The Buchberger algorithm is a fundamental procedure in computational algebra for computing Gröbner bases of polynomial ideals, enabling systematic solutions to systems of polynomial equations.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Cantor–Zassenhaus algorithm Target entity description: The Cantor–Zassenhaus algorithm is a probabilistic method used to factor polynomials over finite fields efficiently, widely employed in computational algebra and cryptography.
-
A.
Berlekamp’s algorithm for factoring polynomials over finite fields
Berlekamp’s algorithm for factoring polynomials over finite fields is a foundational deterministic method in computational algebra that efficiently decomposes polynomials into irreducible factors over finite fields and underpins many modern algorithms in coding theory and cryptography.
-
B.
Adleman–Pomerance–Rumely primality test
The Adleman–Pomerance–Rumely primality test is an early deterministic algorithm in computational number theory used to determine whether a given number is prime, notable for its theoretical importance in the development of modern primality testing methods.
-
C.
Berlekamp–Massey algorithm
The Berlekamp–Massey algorithm is a key algorithm in coding theory and cryptography used to efficiently determine the shortest linear feedback shift register that generates a given binary sequence.
-
D.
Selfridge–Conway primality test
The Selfridge–Conway primality test is a probabilistic algorithm in number theory used to determine whether a given integer is prime.
-
E.
Buchberger algorithm
The Buchberger algorithm is a fundamental procedure in computational algebra for computing Gröbner bases of polynomial ideals, enabling systematic solutions to systems of polynomial equations.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf | probabilistic algorithm ⓘ |
| appliesTo | squarefree polynomials of degree at least 2 ⓘ |
| basedOn |
Chinese remainder theorem for polynomials
ⓘ
Frobenius endomorphism ⓘ properties of finite fields ⓘ random splitting of factors ⓘ |
| complexityClass | expected polynomial time in degree and log(q) ⓘ |
| developedBy |
David G. Cantor
ⓘ
Hans Zassenhaus ⓘ |
| fieldOfUse |
computational algebra
ⓘ
computer algebra systems ⓘ cryptography ⓘ finite fields ⓘ |
| hasProperty |
Las Vegas type
ⓘ
efficient for large degree polynomials ⓘ expected polynomial-time complexity ⓘ randomized ⓘ splits squarefree polynomials ⓘ uses exponentiation modulo a polynomial ⓘ uses greatest common divisor computations ⓘ uses random polynomials ⓘ works on monic polynomials ⓘ works over finite fields of odd characteristic ⓘ |
| input |
finite field GF(q) with odd characteristic
ⓘ
squarefree polynomial over a finite field ⓘ |
| output |
complete factorization into irreducible factors
ⓘ
nontrivial factorization of the input polynomial ⓘ |
| relatedTo |
Berlekamp's algorithm
ⓘ
Kaltofen–Shoup algorithm ⓘ polynomial greatest common divisor algorithms ⓘ |
| step |
choose a random polynomial modulo the input polynomial
ⓘ
compute greatest common divisors with the input polynomial ⓘ raise the random polynomial to a power related to (q−1)/2 modulo the input polynomial ⓘ split the polynomial using nontrivial gcds ⓘ |
| successProbability | high for each random trial ⓘ |
| typicalImplementationLanguage |
C
ⓘ
C++ ⓘ Java ⓘ |
| usedFor |
cryptanalytic computations involving finite fields
ⓘ
factoring polynomials over GF(q) ⓘ factoring polynomials over finite fields ⓘ finding nontrivial factors of a squarefree polynomial ⓘ implementing polynomial factorization in computer algebra systems ⓘ splitting a polynomial into irreducible factors ⓘ |
| usedIn |
algebraic coding theory computations
ⓘ
implementations of finite field arithmetic ⓘ symbolic computation software ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Cantor–Zassenhaus algorithm Description of subject: The Cantor–Zassenhaus algorithm is a probabilistic method used to factor polynomials over finite fields efficiently, widely employed in computational algebra and cryptography.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
Berlekamp’s algorithm for factoring polynomials over finite fields
→
influenced
→
Cantor–Zassenhaus algorithm
ⓘ
Berlekamp’s algorithm for factoring polynomials over finite fields
→
relatedTo
→
Cantor–Zassenhaus algorithm
ⓘ
linked to: Cantor–Zassenhaus algorithm
Zassenhaus algorithm for factoring polynomials over the rationals
→
relatedTo
→
Cantor–Zassenhaus algorithm
ⓘ