1
Encode IXLOVEXMATH
using the cryptosystem in Example 1.
LAORYHAPDWK
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Encode IXLOVEXMATH
using the cryptosystem in Example 1.
LAORYHAPDWK
Decode ZLOOA WKLVA EHARQ WKHA ILQDO
, which was encoded using the cryptosystem in Example 1.
Assuming that monoalphabetic code was used to encode the following secret message, what was the original message?
APHUO EGEHP PEXOV FKEUH CKVUE CHKVE APHUO EGEHU EXOVL EXDKT VGEFT EHFKE UHCKF TZEXO VEZDT TVKUE XOVKV ENOHK ZFTEH TEHKQ LEROF PVEHP PEXOV ERYKP GERYT GVKEG XDRTE RGAGA
What is the significance of this message in the history of cryptography?
Hint: V = E
, E = X
(also used for spaces and punctuation), K = R
.
What is the total number of possible monoalphabetic cryptosystems? How secure are such cryptosystems?
Prove that a matrix with entries in is invertible if and only if
Given the matrix
use the encryption function to encode the message CRYPTOLOGY
, where What is the decoding function?
Encrypt each of the following RSA messages so that is divided into blocks of integers of length 2; that is, if encode 14, 25, and 28 separately.
(a) 2791; (c) 112135 25032 442.
Compute the decoding key for each of the encoding keys in Exercise 7.
Decrypt each of the following RSA messages
(a) 31; (c) 14.
For each of the following encryption keys in the RSA cryptosystem, compute
(a) (c)
Encrypted messages are often divided into blocks of letters. A message such as THE WORLD WONDERS WHY
might be encrypted as JIW OCFRJ LPOEVYQ IOC
but sent as JIW OCF RJL POE VYQ IOC
. What are the advantages of using blocks of letters?
Find integers and such that
Is this a potential problem in the RSA cryptosystem?
Every person in the class should construct an RSA cryptosystem using primes that are 10 to 15 digits long. Hand in and an encoded message. Keep secret. See if you can break one another's codes.