Stream Ciphers - Understanding Cryptography - page 51

Problems
2.1. The stream cipher described in Definition 2.1.1 can easily be generalized to
work in alphabets other than the binary one. For manual encryption, an especially
useful one is a stream cipher that operates on letters.
1. Develop a scheme which operates with the letters A, B, ... , Z, represented by the
numbers 0,1, ... ,25. What does the key (stream) look like? What are the encryp-
tion and decryption functions?
2. Decrypt the following cipher text:
bsaspp kkuosp
which was encrypted using the key:
rsidpy dkawoa
3. How was the young man murdered?
2.2. Assume we store a one-time key on a CD-ROM with a capacity of 1 Gbyte.
Discuss the real-life implications of a One-Time-Pad (OTP) system. Address issues
such as life cycle of the key, storage of the key during the life cycle/after the life
cycle, key distribution, generation of the key, etc.
2.3. Assume an OTP-like encryption with a short key of 128 bit. This key is then
being used periodically to encrypt large volumes of data. Describe how an attack
works that breaks this scheme.
2.4. At first glance it seems as though an exhaustive key search is possible against
an OTP system. Given is a short message, let's say 5 ASCII characters represented
by 40 bit, which was encrypted using a 40-bit OTP. Explain exactly why an exhaus-
tive key search will not succeed even though sufficient computational resources are
available. This is a paradox since we know that the OTP is unconditionally secure.
That is, explain why a brute-force attack does not work.
Note: You have to resolve the paradox! That means answers such as “The OTP
is unconditionally secure and therefore a brute-force attack does not work” are not
valid.
2.5. We will now analyze a pseudorandom number sequence generated by a LFSR
characterized by ( c 2 = 1 , c 1 = 0 , c 0 = 1).
1. What is the sequence generated from the initialization vector ( s 2 = 1 , s 1 = 0 , s 0 =
0)?
2. What is the sequence generated from the initialization vector ( s 2 = 0 , s 1 = 1 , s 0 =
1)?
3. How are the two sequences related?
2.6. Assume we have a stream cipher whose period is quite short. We happen to
know that the period is 150-200 bit in length. We assume that we do not know
anything else about the internals of the stream cipher. In particular, we should not
assume that it is a simple LFSR. For simplicity, assume that English text in ASCII
format is being encrypted.