1. Ceasar Cipher is one of the earliest classical substitution ciphers. It invol
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Question
1. Ceasar Cipher is one of the earliest classical substitution ciphers. It involves replacing each letter in the plaintext by a shifted letter in the alphabet used.
Mathematically it can be expressed as follows:
c = E(p) = (p + k) mod (26)
p = D(c) = (c – k) mod (26)
where p and c refer to the plaintext and ciphertext, respectively; E(p) and D(C ) are the encryption and decryption functions, respectively; and k is the secret key.
a.) Show the encryption and decryption processes of the plaintext “Attack at dawn” using a key value of 4;
b.) Explain how a brute force attack can break this simple cryptosystem;
c.) Use a brute force attack to decrypt (decipher) the following message: “TEBKFKQEBZLROPBLCERJXKBSBKQP”. What is the original plaintext and the encryption key used?
2. We consider a Cipher-Block Chaining Mode (CBC mode) for a block cipher which implements the encryption as Ci = E(Mi Ci-1 ; K) for i > 0 where M1M2M3 … is the message and C0 is a randomly chosen initial vector.
a.) Explain how decryption is done, and write down the decryption equation.
b.) How does a bit error in the ciphertext influence decryption? (Assume that Ci is obtained corrupted because of a bit error. How does it affect the next decryption steps?)
3. Using the Vigenère cipher, encrypt the word “explanation” using the key leg
4. This problem explores the use of a one-time pad version of the Vigenère cipher. In this scheme, the key is a stream of random numbers between 0 and 26. For example, if the key is 3 19 5 . . . , then the first letter of plaintext is encrypted with a shift of 3 letters, the second with a shift of 19 letters, the third with a shift of 5 letters, and so on.
a.) Encrypt the plaintext sendmoremoney with the key stream 9 0 1 7 23 15 21 14 11 11 2 8 9
b.) Using the ciphertext produced in part (a), find a key so that the cipher text decrypts to the plaintext cashnotneeded
5. Consider a substitution cipher where 52 symbols were used instead of 26. In particular, each symbol in the cipher text is for either a lowercase English letter, or an uppercase English letter. (For example, let E be the encryption function then we could have E(S) = p and E(s) = m). Such a modification augments the key space to 52! Does this provide added security compared to a standard substitution cipher? Why or why not?
6. Argue for or against the following proposition. Ciphers that the government cannot cryptanalyze should be outlawed. How would your argument change if such ciphers could be used provided that the users registered the keys with the government?
Explanation / Answer
a) Text : "Attack at dawn" : E(p) : "Zsszbj zs czvm" -- shifting the alphabet
Key(25) has been used here.
Example : To encrypt A, one takes the alphabet and look 25 letters after : Z. So A is crypted with Z.
To decrypt : To decrypt Z, one takes the alphabet and look 25 letters before : A. So Z is decrypted with A.
b) Ceaser cipher can be decrypted very easily with brute force attack by trying every possible decryption key. In ceaser cipher technique only 25 keys are possible and by seeing the result you can easily guess the message.
c) D(C)= TEBKFKQEBZLROPBLCERJXKBSBKQP
E(p)= WHENINTHECOURSEOFHUMANEVENTS
Possible encryption are as following :
By seeing all the results you can easily guess that 23 is the key.
k=23
+23 WHENINTHECOURSEOFHUMANEVENTS
+24 VGDMHMSGDBNTQRDNEGTLZMDUDMSR
+10 JURAVAGURPBHEFRBSUHZNARIRAGF
+19 ALIRMRXLIGSYVWISJLYQERIZIRXW
+9 KVSBWBHVSQCIFGSCTVIAOBSJSBHG
+17 CNKTOTZNKIUAXYKULNASGTKBKTZY
+22 XIFOJOUIFDPVSTFPGIVNBOFWFOUT
+25 UFCLGLRFCAMSPQCMDFSKYLCTCLRQ
+18 BMJSNSYMJHTZWXJTKMZRFSJAJSYX
+16 DOLUPUAOLJVBYZLVMOBTHULCLUAZ
+20 ZKHQLQWKHFRXUVHRIKXPDQHYHQWV
+21 YJGPKPVJGEQWTUGQHJWOCPGXGPVU
+15 EPMVQVBPMKWCZAMWNPCUIVMDMVBA
+13 GROXSXDROMYEBCOYPREWKXOFOXDC
+11 ITQZUZFTQOAGDEQARTGYMZQHQZFE
+4 PAXGBGMAXVHNKLXHYANFTGXOXGML
+5 OZWFAFLZWUGMJKWGXZMESFWNWFLK
+3 QBYHCHNBYWIOLMYIZBOGUHYPYHNM
+2 RCZIDIOCZXJPMNZJACPHVIZQZION
+6 NYVEZEKYVTFLIJVFWYLDREVMVEKJ
+7 MXUDYDJXUSEKHIUEVXKCQDULUDJI
+1 SDAJEJPDAYKQNOAKBDQIWJARAJPO
+12 HSPYTYESPNZFCDPZQSFXLYPGPYED
+8 LWTCXCIWTRDJGHTDUWJBPCTKTCIH
+14 FQNWRWCQNLXDABNXOQDVJWNENWCB
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