作者fei6409 (fei6409)
看板NTU-Exam
标题[试题] 100下 陈君明 密码学 第一次小考
时间Tue Apr 3 00:05:41 2012
课程名称︰密码学
课程性质︰选修
课程教师︰陈君明
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2012/3/21
考试时限（分钟）：40 min
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
s = ____ = 12 - "the last digit of your ID", 3 <= s <= 12
1) Consider the group G = (Z17*, ×mod 17)
a) s^-1(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:(Z16, + mod 16) →(Z17*, ×mod 17), defined by
f(1) = s.
a) f(0) = ____ b) f(2) = ____ c) Is f an isomorphism? Explain.
3) |GL2(Z17)| = ____, |SL2(Z17)| = ____
4) Consider the sumtric group S4
a) |S4| = ____
b) ╭1 2 3 4╮
│ │= ____
╰3 1 4 2╯
c) ╭1 2 3 4╮ ╭1 2 3 4╮
│ │．│ │= ____
╰3 1 4 2╯ ╰2 1 4 3╯
5) Which rins are integral domains? ____
a) Z b) Z6 c) Z7 d) Z[x]/<x^2+1> e)Z[x]/<x^2-1>
6) Suppose H is a subgroup of G, prove that two left cosets g1H = g2H if and
only if (g1^-1)g2 属於 H
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