Algebraic Aspects of Cryptography
E831066
Algebraic Aspects of Cryptography is a graduate-level textbook that develops modern public-key cryptography using tools from algebraic number theory, algebraic geometry, and finite fields.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Algebraic Aspects of Cryptography canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T9931758 — 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: Algebraic Aspects of Cryptography Context triple: [Neal Koblitz, authorOf, Algebraic Aspects of Cryptography]
-
A.
Koblitz curves
Koblitz curves are a special class of elliptic curves defined over binary fields that enable particularly efficient and fast implementations of elliptic curve cryptography.
-
B.
Algebraic Coding Theory
Algebraic Coding Theory is a foundational mathematical text that systematically develops the theory and applications of error-correcting codes using algebraic methods.
-
C.
Elliptic Curve Cryptography
Elliptic Curve Cryptography is a public-key cryptographic approach that uses the mathematics of elliptic curves over finite fields to provide strong security with relatively small key sizes.
-
D.
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.
-
E.
The Design of Rijndael
The Design of Rijndael is a technical book by Joan Daemen and Vincent Rijmen that explains the design principles, structure, and security rationale of the Rijndael cipher, which became the Advanced Encryption Standard (AES).
- 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: Algebraic Aspects of Cryptography Target entity description: Algebraic Aspects of Cryptography is a graduate-level textbook that develops modern public-key cryptography using tools from algebraic number theory, algebraic geometry, and finite fields.
-
A.
Koblitz curves
Koblitz curves are a special class of elliptic curves defined over binary fields that enable particularly efficient and fast implementations of elliptic curve cryptography.
-
B.
Algebraic Coding Theory
Algebraic Coding Theory is a foundational mathematical text that systematically develops the theory and applications of error-correcting codes using algebraic methods.
-
C.
Elliptic Curve Cryptography
Elliptic Curve Cryptography is a public-key cryptographic approach that uses the mathematics of elliptic curves over finite fields to provide strong security with relatively small key sizes.
-
D.
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.
-
E.
The Design of Rijndael
The Design of Rijndael is a technical book by Joan Daemen and Vincent Rijmen that explains the design principles, structure, and security rationale of the Rijndael cipher, which became the Advanced Encryption Standard (AES).
- F. None of above. chosen
Statements (39)
| Predicate | Object |
|---|---|
| instanceOf |
cryptography book
ⓘ
mathematics book ⓘ non-fiction book ⓘ textbook ⓘ |
| academicDiscipline |
algebraic geometry
ⓘ
algebraic number theory ⓘ cryptography ⓘ finite fields ⓘ |
| aimsTo | develop modern public-key cryptography from algebraic viewpoint ⓘ |
| covers |
cryptographic protocols
ⓘ
digital signatures ⓘ public-key encryption ⓘ |
| educationLevel | graduate-level ⓘ |
| emphasizes |
algebraic structures underlying cryptosystems
ⓘ
rigorous mathematical treatment ⓘ |
| field |
mathematics
ⓘ
theoretical computer science ⓘ |
| focusesOn |
algebraic methods in cryptography
ⓘ
mathematical foundations of cryptography ⓘ number-theoretic cryptography ⓘ public-key cryptosystems ⓘ |
| format |
hardcover
ⓘ
print ⓘ |
| genre | textbook ⓘ |
| hasPrerequisite |
abstract algebra
ⓘ
basic number theory ⓘ linear algebra ⓘ |
| intendedAudience |
advanced students in computer science
ⓘ
advanced students in mathematics ⓘ graduate students ⓘ researchers in cryptography ⓘ |
| isUsedFor |
graduate courses in cryptography
ⓘ
self-study in mathematical cryptography ⓘ |
| language | English ⓘ |
| title | Algebraic Aspects of Cryptography ⓘ |
| topic | public-key cryptography ⓘ |
| usesTool |
algebraic geometry
ⓘ
algebraic number theory ⓘ finite field theory ⓘ |
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: Algebraic Aspects of Cryptography Description of subject: Algebraic Aspects of Cryptography is a graduate-level textbook that develops modern public-key cryptography using tools from algebraic number theory, algebraic geometry, and finite fields.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.