Cryptology - Unofficial St. Mary's College of California Web Site

11.8. EXERCISES 229
2. Given the weights 63, 39, 81, 57, 48 and 30, and being allowed to use them
possibly multiple times, can the weight 283 be achieved. If so, how
3. Given the weights 3, 7, 12, 23, 47, 95 and 190, and using each weight
at most once, which of the following amounts can be realized, and how
T = 323, T = 310, T = 117, T = 270.
4. Given the weights 3, 8, 13, 29 and 60, and P = 129, e = 10:
(a) Encipher gold.
(b) Decipher 32, 84, 62, 146.
5. Given the weights are 5, 8, 14, 29 and 58, and P = 127, e = 17. Decipher
111, 70, 97, 66, 75, 105.
6. Given the weights 6, 8, 17, 35, 81, 200, 403, 800, 1589, 3223 and e = 322,
P = 6551:
(a) Find the corresponding U’s.
(b) Encipher stalactite.
(c) Decipher 20632, 13837, 11968, 22524, 12265.
the next word in the dictionary.
Hint: it’s often
7. [Hellman] Hellman’s 1979 Scientific American article, The Mathematics of
Public-Key Cryptography, was one of the very first public announcement
of this new kind of cipher. Included in this article is an overview of public
vs. private key, and an introduction to the Knapsack Ciphers and RSA.
Here we look at his knapsack example.
(a) Show that 3, 5, 11, 20, 41, 83, 169, 340, 679, 1358 forms a superincreasing
sequence.
(b) Use P = 2731 and e = 764 to find the corresponding U ′ s.
(c) Hellman’s sample message was enciphered as pairs of letters (we
have 10 weights), with the binary starting at 00000, so a=00000
and z=11001. He also used the binary equivalent for 26 to represent
a space, and 29 to represent .
Encipher Hellman’s message: How are you.
(d) Find d.
(e) Decipher 2908, 7643, 9799.
8. The public key codes tend to be slower on a computer than the traditional
“private key” codes are. So they are most frequently used only to send
the key for a traditional method.
Decipher DNTFG EASCN HAFAO NNSBH SIOAI HEPTA CBROE EGFSR RBTGE
ISIOT LAIEM C. It was enciphered using the double transposition method
with keyword 94, 240, 155, 46, 197, 188, 151, 131.
Hint: the W’s are 2, 7, 13, 31, 55, with P = 157 and e = 23.