CS 70
Discrete Mathematics for CS
Spring 2005
Clancy/Wagner
HW 8
Due Thursday, March 31
Coverage:
This assignment involves topics from the lectures of March 1, 8, 10, 15, 17, and from Rosen
section 2.6 and chapter 4.
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Homework exercises:
1. (6 pts.)
Repeated squaring
The algorithm for computing
a
b
mod
c
by repeated squaring does not necessarily lead to the minimum
number of multiplications. Give an example of
b
(
b
>
10) where the exponentiation can be performed
using fewer multiplications, by some other method.
2. (10 pts.)
RSA
Let
p
and
q
be primes and let
N
=
pq
. Show how to determine
p
and
q
given
N
and
(
p

1
)(
q

1
)
. (In
other words, given the public key
(
e
,
N
)
,
e
the encryption exponent and
N
the RSA modulus, and the
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 Fall '08
 PAPADIMITROU
 Cryptography, Exponentiation, Prime number

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