[試題] 103-2 陳君明 密碼學導論 第一次小考
課程名稱︰密碼學導論
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)︰2015/3/3
考試時限(分鐘):30分鐘左右(最後一節課)
試題 :
Student ID: ______ Name: ______
s = ___ = 12 -“the last digit of your ID”, 3 ≦ s ≦ 12
*
1) Consider the group G = (Z , ×mod 17)
17
-1
a) s (the multiplicative inverse of s) is ___
b) o(s) (the order of s) = ___
c) The index [G : < s >] = ___
d) Explain why G is a cyclic group
*
2) Consider the homomorphism f:(Z , + mod 16) → (Z , ×mod 17) defined by
16 17
f(1) = s
a) f(0) = ___ b) f(2) = ___ c) Is f an isomorphism? Explain
3) |GL (Z )| = ____, |SL (Z )| = ____
2 17 2 17
4) Consider the symmetric group S :
4
-1
(1 2 3 4) (1 2 3 4) (1 2 3 4)
a) |S | = ___ b) ( ) = _____ c) ( )。( )= ___
4 (3 1 4 2) (3 1 4 2) (2 1 4 3)
5) Suppose H is a subgroup of G, prove that two left cosets g H = g H if and
1 2
-1
only if g g ∈ H
1 2
註:雖然小考題目會放在ceiba上,但小考前應該不會放,所以我還是PO了,給以後修課學
生參考
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04/07 00:47, , 1F
04/07 00:47, 1F