Question

1. Explain why the DES keys consisting of all 0-bits or 1-bits will provide poor security (Note: Don’t consider parity bits.)
   
2. How many multiplications are needed to compute x¹⁰²⁴? (Do not tell me 1024 multiplication because it is much, much less!) Show your algorithm.
   
3. Bob downloaded a 50Gb tar.gz file from Alice’s server today. Bob needs to know if he downloaded the correct file and that there were no errors in the transmission, before attempting to unzip/untar it (since uncompressing such a big file might take a long time and computational resources). Unfortunately, Alice and Bob do not share any keys nor do they have a common CA. How can Bob ensure the correctness of the file? Alice and Bob know each other personally, and they are scheduled to meet in a couple of days.

Answer 1

solution:

The block cipher DES has a few specific keys termed "weak keys"semi-weak keys". These are keys that cause the encryption mode of DES to act identically to the decryption mode of DES (albeit potentially that of a different key).

In operation, the secret 56-bit key is broken up into 16 subkeys according to the DES key schedule; one subkey is used in each of the sixteen DES weak keys produce sixteen identical subkeys. This occurs when the key (expressed in hexadecimal) is:^[1]

• Alternating ones + zeros (0x0101010101010101)
• Alternating 'F' + 'E' (0xFEFEFEFEFEFEFEFE)
• '0xE0E0E0E0F1F1F1F1'
• '0x1F1F1F1F0E0E0E0E'

If an implementation does not consider the parity bits, the corresponding keys with the inverted parity bits may also work as weak keys:

• all zeros (0x0000000000000000)
• all ones (0xFFFFFFFFFFFFFFFF)
• '0xE1E1E1E1F0F0F0F0'
• '0x1E1E1E1E0F0F0F0F'

Using weak keys, the outcome of the Permuted Choice 1 (PC-1) in the DES key schedule leads to round keys being either all zeros, all ones or alternating zero-one patterns.

Since all the subkeys are identical, and DES is a Feistel network, the encryption function is self-inverting; that is, despite encrypting once giving a secure-looking cipher text, encrypting twice produces the original plaintext.

Ans2.

x

x² one multlipication that is x multiplied x = x²

x⁴ one more multliplication that is x² multlipied by x² = x⁴

in this way proceed till x¹⁰²⁴ to get in total 10 multplipication operations

answer is total 10 multlipications needed

Ans 3

Since they are going to meet soon so they can use the timestamp.....means bob can ask alice to ckeck on what time i have downaloded the file from your server if alice answer correct time then there is no trasmission error else there might be a cyber attack

please give me thumb up