Cryptography Reference
In-Depth Information
App.49. 01010010, 10000011, 10101011.
App.50. 10101101, 11111100, 11010100.
App.51. 11110000, 00001111, 01010111.
App.52. 11111111, 10000000, 01111110.
Using the probability theory basics that we learned in Appendix E
(
pages
543-549
)
to solve Exercises App.53-App.56.
App.53. If you have two fair dice, thrown one at a time, find the probability
that the sum is 8. What is the probability that the first die is less than
the second die? What is the probability that the second die is a 4, given
that the first is a 3?
App.54. Given two cards dealt, one after the other, from a fair 52-card deck,
what is the probability that they are the same suit? What is the proba-
bility they are the same value?
App.55. Suppose that the probability that an event occurs is
p
=0
.
1%. Find
the probability that this event occurs no more than twice in a series of
1000 independent trials.
App.56. Assume that Alice buys a lottery ticket for $2, and her possible
winnings are $1
,
000, $10
,
000, and $100
,
000 with respective probabilities
of 0
.
3%, 0
.
005%, and 0
.
001%. Determine Alice's possible winnings.
Use Fermat's compositeness test on page 551 to determine show that the
values in Exercises App.57-App.60 are composite
App.57.
n
= 296977.
App.58.
n
= 36977.
App.59.
n
= 45671.
App.60.
n
= 77571.
App.61.
Use
the
Miller-Selfridge-Rabin
test
in
Section
F.2
on
page
552,
to
determine
the
(probable)
status
of
the
values:
n
∈
{
561
,
1729
,
14081
,
296987
}
.
App.62. Employ the algorithms for probable prime generation in Section F.4
on pages 558 and 559, to produce a list of a half dozen probable primes.
Search WWH ::
Custom Search