Sometimes error propagation is an issue when choosing a mode of operation in pra
ID: 3588217 • Letter: S
Question
Sometimes error propagation is an issue when choosing a mode of operation in practice. In order to analyze the propagation of errors, let us assume a bit error (i.e., a substitution of a “0” by a “1” or vice versa) in a ciphertext block yi that corresponds to cleartext xi.
1. Assume an error occurs, during the transmission, in the ciphertext block yi. Which cleartext blocks are affected on Bob’s side when using the ECB mode? List such blocks with a comma to separate any two (e.g., xi,xi+1,xi+2)
2. Again, assume block yi contains an error introduced during transmission. Which cleartext blocks are affected on Bob’s side when using the CBC mode?
3. Suppose there is an error in the cleartext xi on Alice’s side. Which cleartext blocks are affected on Bob’s side when using the CBC mode?
4. Assume a single bit error occurs in the transmission of a ciphertext character in an 8-bit CFB mode. Which one of the following three statements is correct? (a) Only xi will be corrupted, (b) xi and a few additional blocks will be corrupted, (c) xi and all the consecutive blocks will be corrupted. Enter a or b or c.
Explanation / Answer
Solution :-
The solutions to the questions are given below.
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Answer - 1.
Given that, during the transmission an error occurs, in the ciphertext block yi. The ECB (Elecronic code book) mode is used for encryption and decryption. On the BOB's side only xi block of the plaintext will be affected. The cleartext block xi is decrypted from ciphertext block yi. The one bit error is in ciphertext block yi, so the corresponding decrypted block xi will be affected on the BOB's side.
Therfore the cleartext block affected on BOB's side is xi.
Explanation -
In ECB (Elecronic code book) mode the whole message is divided into blocks, and each block is encrypted and decrypted separately. No feedback or initiation vector used from previous blocks. Each block of message is encrypted and decrypted independently and parallely. Therfore if there is an error in some ciphertext blocks of the message then the corresponding decrypted blocks at the reciever side will be affected.
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Answer - 2.
Given that, during the transmission an error occurs, in the ciphertext block yi. The CBC (Cipher block chaining) mode is used for encryption and decryption. On the BOB's side xi block and xi+1 block of the plaintext will be affected.
The cleartext block xi is decrypted from ciphertext block yi. The one bit error is in ciphertext block yi, so the corresponding decrypted block xi will be affected on the BOB's side.
The ciphertext yi is used as the initiation vector in the decryption of ciphertext block yi+1, therefore the decrypted block xi+1 will also be affected.
Therfore the cleartext block affected on BOB's side is xi, xi+1.
Explanation -
In CBC (Cipher block chaining) mode the whole message is divided into blocks, and each block is encrypted decryped with the use of previous block. The initiation vector used in first ciphertext block for decryption and In consecutive blocks, previous ciphertext blocks are used as initiation vector for decryption.
Thus if yi ciphertext block is errornous then the coressponding decrypted block xi will be affected on the BOB's side. Now yi is used as initiation vector in the decryption of block yi+1, so decrypted block xi+1 also be affected. In decryption of ciphertext block yi+2, the ciphertext block yi+1 is used as initiation vector which is not errornous so the decrypted block xi+2 will not be affected on BOB's side.
Therfore the cleartext block affected on BOB's side is xi, xi+1.
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Answer - 3.
Given that, there is an error in the cleartext xi on Alice’s side. If CBC (Cipher block chaining) mode is used for encryption then during the encryption the error will occur in the ciphertext block yi and all the consecutive blocks will be corrupted.
In the decryption of all the ciphertext block which are errornous, all decrypted blocks will be affected on the BOB's side. Therefore, On the BOB's side block xi, xi+1, xi+2 and all the consecutive blocks will be affected.
Explanation -
In CBC (Cipher block chaining) mode the whole message is divided into blocks, and each block is encrypted decryped with the use of previous block.
In the encryption, if the plaintext block xi is errornous then the corresponding encrypted ciphertext block yi will be corrupted. Now the block yi will be used The initiation vector in the encryption of block xi+1. So the encrypted ciphertext block yi+1 will be corrupted. Now the block yi+1 will be used The initiation vector in the encryption of block xi+2. So the encrypted ciphertext block yi+2 will be corrupted. So if xi laintext block is errornous then all the consecutive encrypted ciphertext block will be affected.
In decryption, it is easily observed that all the ciphertext blocks are errornous then after decryption all the plaintext blocks will be affected on the BOB's side.Therefore, On the BOB's side block xi, xi+1, xi+2 and all the consecutive blocks will be affected.
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Answer - 4.
correct satatement is (b).
Given that, during the transmission an error occurs, in the ciphertext block yi. The CFB (Cipher feed back) mode is used for encryption and decryption. On the BOB's side xi block and xi+1 block of the plaintext will be affected. Therfore the correct satatement is -
(b) xi and a few additional blocks will be corrupted.
The cleartext block xi is decrypted from ciphertext block yi. The one bit error is in ciphertext block yi, so the corresponding decrypted block xi will be affected on the BOB's side.
The ciphertext yi is used as the initiation vector in the decryption of ciphertext block yi+1, therefore the decrypted block xi+1 will also be affected.
Therfore the cleartext block affected on BOB's side is xi, xi+1.
Explanation -
In CFB (Cipher feedback) mode the whole message is divided into blocks, and each block is encrypted decryped with the use of previous block. The initiation vector used in first ciphertext block for decryption and In consecutive blocks, previous ciphertext blocks are used as initiation vector for decryption.
Thus if yi ciphertext block is errornous then the coressponding decrypted block xi will be affected on the BOB's side. Now yi is used as initiation vector in the decryption of block yi+1, so decrypted block xi+1 also be affected. In decryption of ciphertext block yi+2, the ciphertext block yi+1 is used as initiation vector which is not errornous so the decrypted block xi+2 will not be affected on BOB's side.
Therfore the cleartext block affected on BOB's side is xi, xi+1.
Therfore the correct satatement is - (b) xi and a few additional blocks will be corrupted.
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