CS346 Cryptography, Fall 2009
Homework 3, SOLUTIONS
1. (8 points) Suppose that for using RSA, Bob has chosen a large public modulus
n
for
which the factorization cannot be found in a reasonable amount of time. Suppose Alice
sends a message to Bob representing each alphabetic character as an integer between
0 and 25, and encrypting each as a separate plaintext character. Describe how Oscar
can easily decrypt a message which is encrypted this way.
Solution:
Oscar can generate a table of the encrypted values corresponding to the 26 alphabetic
characters, since he knows the encryption key. Then Oscar can decrypt the ciphertext
character by character comparing the ciphertext with the entries of the table.
2. (8 points)
If an RSA user’s public key is
n
= 17
·
43 and
b
= 29, what is the private exponent
a
?
Explain what you do and include the partial results of your calculations.
HINT: Use the extended Euclidean algorithm. It will only take a few steps, you can
do it by hand.
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 Fall '10
 GAL
 Cryptography, Multiplicative inverse, Oscar, Extended Euclidean algorithm, public modulus

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