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MATH/CSCI 4116
Cryptography
Assignment 5
- We know that ϕ(ab) = ϕ(a)ϕ(b) whenever gcd(a, b) = 1. Give
an example that shows that this identity is, in general, not true when
gcd(a, b) 6= 1. - Use the stream cipher discused in class (Section 2.6), with n = 7
and c0 = c1 = 1, c2 = c3 = 0, c4 = c5 = c6 = 1. Encrypt w = - 1110001 1010001 using the key k = 1010011.
- Find the sample space and probability distribution that model flipping
two coins. Describe the event“at least one coin comes up heads”
formally and compute its probability. - We throw two dice. Determine the probability that they both show
different numbers under the condition that the sum of both numbers is
even. - (a) Determine the integer n such that the probability for two of n
people having the same birthday is at least 9/10.
(b) Suppose the 4-digit PINs are randomly distributed. How many people
must be in a room such that the probability that two of them have
the same PIN is at least 1/2? (Here“4 digits”means that the PIN
cannot start with a 0.)
Note: Pay special attention to the direction of the inequality in the
formula(s) used for this question.
Due: Thursday, February 25, 2021, 11:30 pm
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