DES in cipher feedback mode CFB

user108810

4/12/24, 1:08 PM

We use DES in cipher feedback mode (CFB) to encrypt a plaintext $m = m_1\mathbin\|m_2\mathbin\|\ldots\mathbin\|m_{100}$ into a ciphertext $c_1\mathbin\|c_2\mathbin\|\ldots\mathbin\|c_{100}$, where each $m_i$ is 8-bit long. The ciphertext is sent to Bob. If $c_{15}$ and $c_{25}$ are missing and $c_8$ and $c_{88}$ are received as $c_8'$ and $c_{88}'$ wrongly, what $m_i$s can B compute correctly from the received ciphertext?

A transmission error in $c_i$ affects correctness of $m_i$ and the next $n/s$ plaintext blocks. n means the plaintext. ||=||=-bits

I am not sure $c_8'$ transmission error affects $8$ to $20$, $c_{88}'$ transmission error affects $88$ to $100$. $c_{15}$ and $c_{25}$ are missing. Therefore, $100 - 26 - 2 = 72$ can B compute correctly from the received ciphertext.

I was wonder if trasmission error caused error from the current ciphertext $_c8'$ to the next $[100/8]=13$ plaintext which is 20. $c_{88}'$ transmission error affects $88$ to $100$.

if $c_{15}$ and $c_{25}$ are missing, how to compute it? Are they regarded as 2 error and 100 - 13- 13 - 2= 72 or regarded 2 missing text as shifting the entire text after c16?

Thank you so much!

242

0 + 7

des

cfb

poncho

4/12/24, 1:19 PM

This is the same question as last time; however this time you did put in some small effort at solving it yourself (note: if you are a native English speaker, please try to be express what you mean more fully, it is hard to figure out what you're saying; if English is a second language, well, you're doing the best you can). However, as I commented on the previous question, any such answer would depend on the 'stride' used within CFB (that is, how many bits of DES output is xor'ed into the plaintext), is it CFB-1, CFB-8 or CFB-64?

fgrieu

4/12/24, 1:25 PM

You have not followed my earlier hint: "Write down the equation applied on encryption. Deduce the equation applied on decryption. Examine what influences the decryption of $m_i$. Conclude.". Additional hints: if no stride is specified or given in a reference material, the most natural is the width of a DES block. No value of stride can make your current answer correct, even if we assume that what bytes are missing is known by who deciphers. Further, "what"≠"how many".

user108810

4/12/24, 1:47 PM

A transmission error in $c_i$ affects correctness of $m_i$ and the next $n/s$ plaintext blocks.

fgrieu

4/12/24, 2:16 PM

Right, but only if "plaintext block" is understood to be of size $s$, and $n$ is the cipher's block size, and $s$ divides $n$ (otherwise things get more complex; $\lceil n/s\rceil$ won't quite fix it). I wish students would not be expected to _learn_ such things (rather, be able to derive them; I think that's more effective at solving actual problems, and I guess even this exercise). Notice that for some $s$ (e.g. $s=n$ or $s=n/2$), the next "plaintext block" may not immediately follow $m_i$.

user108810

4/12/24, 3:42 PM

Thank you for your reply. I was wonder if n means the plaintext and ||=||=-bits, which is 8 bits.

fgrieu

4/12/24, 3:51 PM

In the rule you stated, $n$ is not the message size. Again, $n$ is the width of a block in the block cipher, here DES, which gives $n$. You must ascertain what variant of CFB encryption is used. If there is no mention of $s$ in your course, my bet is on [full block CFB](https://en.wikipedia.org/wiki/Block_cipher_mode_of_operation#Full-block_CFB). On the other hand if your course mention $s$, and $s$ is not in the problem statement, then $s=|m_i|=8$ is logical (that would be CFB-8). Note: "missing" can be understood as "suppressed" or "of unknown value"; that does not change much.

user108810

4/13/24, 8:55 AM

Thank you so much!

Elon Musk

I sit in a Tesla and translated this thread with Ai:

EN: DES in cipher feedback mode CFB

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