HW #3: Public Key Cryptography
CS 392/6813: Computer Security
Fall 2009
[100pts] DUE 10/12/2009 at Midnight
Problem 1 [10*3=30pts]
1)
We discussed how to use the Euclidian algorithm to compute the GCD of two
numbers. Use this algorithm to compute the following values. Show all of the
steps involved.
a.
The GCD of 56 and 225.
b.
The GCD of 52 and 876.
2)
We also discussed the use of the Extended Euclidian algorithm to calculate
modular inverses. Use this algorithm to compute the following values. Show all of
the steps involved.
a.
957895
1
(mod 122939945)
b.
13
1
(mod 31)
3)
Let n be a product of two large primes p and q (i.e., n = pq). Assume that x, y, and
g are relatively prime to n.
a.
If x
≡
y (mod n), is g
x
≡
g
y
(mod n)? Show why or why not.
b.
If x
≡
y
(mod
Φ
(n)) instead, is g
x
≡
g
y
(mod n)? Show why or why not.
Problem 3 [30pts]
Download the RSA code found at
http://www.funet.fi/pub/crypt/cryptography/asymmetric/rsa/rsaref2.tar.gz
Review the RSA key generation, encryption, and decryption functions and the sample
code, then perform the following:
1)
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 Fall '09
 Saxena
 Cryptography, Computer Security, execution time, key generation, Signature Computation

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