[試題] 104-1 陳君明 橢圓曲線密碼學 小考
課程名稱︰橢圓曲線密碼學
課程性質︰數學系選修
課程教師︰陳君明
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2015/10/06
考試時限（分鐘）：5:30~6:30
試題 :
1. A group is a set G and an operation * for which the following axioms hold:
‧For any a,b∈G, the element a*b∈G.
‧......(please complete the definition) (6%)
2. (a) Show that (Z*,× mod 7) is a cyclic group. (6%)
7
(b) Show that (Z*,× mod 9) is a cyclic group. (6%)
9
(c) Show that (Z*,× mod 8) is not a cyclic group. (6%)
8
3. Suppose m is the multiplicative inverse of 52 in the Galois field F (GF )
313 313
(a) Use the Extended Euclidean Algorithm to find m. (6%)
(b) Describe how to use the Fermat Little Thorem to find m. (6%)
3
4. (a) How many elements are there in the quotient ring F [x]/<x + x + 1>?(6%)
2
2 3
(b) Find the multiplicative inverse of x + x in F [x]/<x + x + 1>. (6%)
2
2015
5. (a) Evaluate 3 mod 109. (6%)
2015
(b) Evaluate 3 mod 108. (6%)
3
6. (a) Factor x + 1 over R,C,F ,F ,F respectively. (10%)
2 3 7
16
(b) Factor x + x over F . (6%)
2
(c) How many irreducible polynomials of degree 5 over F ? (6%)
2
(d) How many irreducible polynomials of degree 6 over F ? (6%)
2
7. (a) Find an irreducible polynomial of degree 3 over F . (6%)
5
(b) Construct the Galois field F and explain its operations. (6%)
125
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 58.115.123.62
※ 文章網址: https://www.ptt.cc/bbs/NTU-Exam/M.1445157091.A.587.html
※ 編輯: SamBetty (58.115.123.62), 11/03/2015 20:39:41