| １． |
Outline |
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This course provides an introduction to the algebraic system, finite field and number theory. The items are as follows: Operation and algebraic system, semi group and group, ring and field, transmission of information, error of codes, detection and correction of errors, finite field, Hamming code, cyclic code, BCH code, cryptosystem, integer, prime number and factorization into prime factors, Euclidean algorithm, diophantine linear equation, congruent expression, Fermat’s little theorem, and the RSA cryptosystem.
The classes consist of lectures and exercises. Students will give presentations on homework assignments in the classes.
This subject is related to the clause 3 and 4 of the diploma policy of the Department of Information and Electronic Engineering.
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| ２． |
Objectives |
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The objectives of this course for students are to understand the basic concept of error correcting codes on the basis of finite field and the basic concept of the RSA cryptosystem which is one of the public key cryptosystems based on number theory.
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| ３． |
Grading Policy |
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The term-end examination (80%) and presentations on homework assignments in the classes (20%) will be evaluated. The acceptance line is accuracy rate of 60% in the above term-end examination and presentations on homework assignments.
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| ４． |
Textbook and Reference |
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Textbook:
“Basics of Information Mathematics”, F.Terada, N.Nakamura, T.Syakushi and T.Matsui, Saiensu-Sha (1999) in Japanese. （ISBN 4-7819-0914-0）
Reference:
“New Information Mathematics”, T.Ueda, Makinoshoten (2004) in Japanese. （ISBN 4-434-04087-1）
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| ５． |
Requirements (Assignments) |
|
Students are required to review the lectures and to do the homework assignments.
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| ６． |
Note |
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It is recommended for students to access the homework assignments on the LMS.
It is prohibited for students to refer the textbook and notebook in term-end examination and makeup examination.
|
| ７． |
Schedule |
|
| １. Algebraic system : Operation and algebraic system, Semi group and group |
| ２. Algebraic system : Ring and field |
| ３. Finite field and code : Transmission of information, Error of codes |
| ４. Finite field and code : Detection and correction of errors |
| ５. Finite field and code : Finite field |
| ６. Finite field and code : Hamming code |
| ７. Finite field and code : Cyclic code |
| ８. Finite field and code : BCH code |
| ９. Number theory and cryptosystem : Cryptosystem, Integer, Prime number and factorization into prime factors |
| 10. Number theory and cryptosystem : Euclidean algorithm |
| 11. Number theory and cryptosystem : Diophantine linear equation |
| 12. Number theory and cryptosystem : Congruent expression |
| 13. Number theory and cryptosystem : Fermat’s little theorem |
| 14. Number theory and cryptosystem : The RSA cryptosystem |
| 15. Review, Term-end examination |
|
| １． |
Outline |
|
This course provides an introduction to the algebraic system, finite field and number theory. The items are as follows: Operation and algebraic system, semi group and group, ring and field, transmission of information, error of codes, detection and correction of errors, finite field, Hamming code, cyclic code, BCH code, cryptosystem, integer, prime number and factorization into prime factors, Euclidean algorithm, diophantine linear equation, congruent expression, Fermat’s little theorem, and the RSA cryptosystem.
The classes consist of lectures and exercises. Students will give presentations on homework assignments in the classes.
This subject is related to the clause 3 and 4 of the diploma policy of the Department of Information and Electronic Engineering.
|
| ２． |
Objectives |
|
The objectives of this course for students are to understand the basic concept of error correcting codes on the basis of finite field and the basic concept of the RSA cryptosystem which is one of the public key cryptosystems based on number theory.
|
| ３． |
Grading Policy |
|
The term-end examination (80%) and presentations on homework assignments in the classes (20%) will be evaluated. The acceptance line is accuracy rate of 60% in the above term-end examination and presentations on homework assignments.
|
| ４． |
Textbook and Reference |
|
Textbook:
“Basics of Information Mathematics”, F.Terada, N.Nakamura, T.Syakushi and T.Matsui, Saiensu-Sha (1999) in Japanese. （ISBN 4-7819-0914-0）
Reference:
“New Information Mathematics”, T.Ueda, Makinoshoten (2004) in Japanese. （ISBN 4-434-04087-1）
|
| ５． |
Requirements (Assignments) |
|
Students are required to review the lectures and to do the homework assignments.
|
| ６． |
Note |
|
It is recommended for students to access the homework assignments on the LMS.
It is prohibited for students to refer the textbook and notebook in term-end examination and makeup examination.
|
| ７． |
Schedule |
|
| １. Algebraic system : Operation and algebraic system, Semi group and group |
| ２. Algebraic system : Ring and field |
| ３. Finite field and code : Transmission of information, Error of codes |
| ４. Finite field and code : Detection and correction of errors |
| ５. Finite field and code : Finite field |
| ６. Finite field and code : Hamming code |
| ７. Finite field and code : Cyclic code |
| ８. Finite field and code : BCH code |
| ９. Number theory and cryptosystem : Cryptosystem, Integer, Prime number and factorization into prime factors |
| 10. Number theory and cryptosystem : Euclidean algorithm |
| 11. Number theory and cryptosystem : Diophantine linear equation |
| 12. Number theory and cryptosystem : Congruent expression |
| 13. Number theory and cryptosystem : Fermat’s little theorem |
| 14. Number theory and cryptosystem : The RSA cryptosystem |
| 15. Review, Term-end examination |
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