Miller algorithm
E860121
The Miller algorithm is an efficient computational method used in elliptic curve cryptography to evaluate pairings such as the Weil and Tate pairings.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Miller algorithm canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T10389271 — 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: Miller algorithm Context triple: [Weil pairing, relatedTo, Miller algorithm]
-
A.
Miller primality test
The Miller primality test is a randomized algorithm used to determine whether a number is prime with high confidence, forming the basis of the widely used Miller–Rabin primality test in computational number 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.
Cantor–Zassenhaus algorithm
The Cantor–Zassenhaus algorithm is a probabilistic method used to factor polynomials over finite fields efficiently, widely employed in computational algebra and cryptography.
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D.
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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E.
AKS primality test
The AKS primality test is a landmark deterministic polynomial-time algorithm that can conclusively determine whether a number is prime without relying on unproven assumptions.
- 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: Miller algorithm Target entity description: The Miller algorithm is an efficient computational method used in elliptic curve cryptography to evaluate pairings such as the Weil and Tate pairings.
-
A.
Miller primality test
The Miller primality test is a randomized algorithm used to determine whether a number is prime with high confidence, forming the basis of the widely used Miller–Rabin primality test in computational number 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.
Cantor–Zassenhaus algorithm
The Cantor–Zassenhaus algorithm is a probabilistic method used to factor polynomials over finite fields efficiently, widely employed in computational algebra and cryptography.
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D.
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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E.
AKS primality test
The AKS primality test is a landmark deterministic polynomial-time algorithm that can conclusively determine whether a number is prime without relying on unproven assumptions.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
cryptographic algorithm
ⓘ
pairing computation algorithm ⓘ |
| appliedIn |
Ate pairing variants
ⓘ
Tate pairing computation ⓘ Weil pairing computation ⓘ attribute-based encryption ⓘ identity-based encryption ⓘ key agreement protocols ⓘ pairing-based cryptographic protocols ⓘ reduced Tate pairing computation ⓘ short signature schemes ⓘ |
| assumption | elliptic curve group is cyclic of known order ⓘ |
| basedOn |
elliptic curve arithmetic
ⓘ
rational functions on elliptic curves ⓘ |
| complexity | O(log n) elliptic curve operations for scalar n ⓘ |
| computes | pairing value as a rational function evaluated at points ⓘ |
| domain |
finite fields of large characteristic
ⓘ
finite fields of small characteristic ⓘ |
| field | elliptic curve cryptography ⓘ |
| input |
an integer related to the group order
ⓘ
elliptic curve over a finite field ⓘ two points on an elliptic curve ⓘ |
| namedAfter | Victor S. Miller ⓘ |
| optimizedBy |
using denominator elimination techniques
ⓘ
using efficient line evaluation formulas ⓘ using projective coordinates ⓘ using special forms of elliptic curves ⓘ |
| output | element of a finite field extension ⓘ |
| property |
efficient
ⓘ
iterative ⓘ runs in time proportional to the bit length of the scalar ⓘ uses double-and-add style loop ⓘ |
| proposedBy | Victor S. Miller ⓘ |
| publicationContext | work on elliptic curve cryptography in the 1980s ⓘ |
| relatedTo |
bilinear map properties
ⓘ
double-and-add scalar multiplication ⓘ |
| requires |
finite field arithmetic
ⓘ
group law on elliptic curves ⓘ |
| step |
maintains a running value of a rational function
ⓘ
updates function value using line functions from point addition ⓘ updates function value using line functions from point doubling ⓘ |
| usedFor |
computing pairings on elliptic curves
ⓘ
efficient pairing computation ⓘ evaluating bilinear pairings ⓘ evaluating the Tate pairing ⓘ evaluating the Weil pairing ⓘ |
| usedIn | security proofs and constructions in pairing-based cryptography ⓘ |
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: Miller algorithm Description of subject: The Miller algorithm is an efficient computational method used in elliptic curve cryptography to evaluate pairings such as the Weil and Tate pairings.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.