课程名称：密码学导论
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）︰2014/02/25
考试时限（分钟）：90分(不是很确定)
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
Introduction to Cryptography
Quiz (2014/02/25)
1. What is the order of the following group?
(a) |(Z_132*, x)| = _________, (b) |(Z_75*, x)| = _________.
2. In the multiiplicative group (Z_12*, x), compute
(a) 7^(-1) = _________, (b) o(5) = _________.
3. In the symmetric group S_5, compute
(a) (14325)^(-1) = __________, (b) (123)(14)(245) = _________.
4. What is the order of the following group?
(a) |GL_3(Z_5)| = __________, (b) |SL_3(Z_5)| = _________.
5. Let (G, x) be a group. Prove that (a x b)^(-1) = b^(-1) x a^(-1) for all
a, b \in G.
\in代表∈符号，怕有人显示不出来