1. Answer the questions

1. What is substitution cipher? 2. What examples of the simplest substitution ciphers can you give? 3. What is fractionation system? 4. What is block cipher? 5. Characterize stream cipher. 6. What are the ways to generate the keystream? 7. Define the types of cryptoanalysis.

2. Are the following statements true or false?

1. When a substitution cipher is used the actual order of units of the plaintext is not changed. 2. Caesar cipher is one of the most well-known block ciphers. 3. Double transposition ciphers are widely used till nowadays. 4. In manual systems pieces of the plaintext were usually single letters or characters. 5. Encryption and decryption differ a lot when a block cipher is used, 6. A block cypher is a type of symmetric-key encryption algorithm that changes a fixed-length block of the plaintext into the same length block of the ciphertext. 7. Block size is the relation between the number of blocks of the plaintext and the number of blocks of the ciphertext. 8. In a chosen ciphertext attack the cryptanalyst has the capability to find the ciphertext corresponding to an arbitrary plaintext message. 9. Modern block ciphers use 128 bits blocks. 10. A keastream is a sequence of bits which is used as a key.

4. Summarize the text using the following expressions:

merely; so forth; it is easy to guess; in fact; it is likely; whatsoever

5. Supplementary reading.

Text C

Public Key Criptography.

Since the invention of public key cryptography in 1976 by Whitfield Diffie and Martin Hellman, numerous public-key cryptographic system have been proposed. All of these systems rely on the difficulty of a mathematical problem for the security.

Before cryptographic systems and the corresponding math­ematical problems can be discussed, the difficulty of a problem must be defined. What does it mean for a mathematical problem to be difficult? To explain this concept, the notion of an algo­rithm is required. An algorithm is a process which describes the steps to take to solve a problem. For example, in high school everyone is taught an algorithm for adding two numbers — sim­ply a sequence of steps which takes as input two numbers a and b, to be added, and outputs their sum a+b. Now mathematical problem is difficult if the fastest algorithm to solve the problem takes a long time relative to the input size.

To analyze how long an algorithm takes, computer sci­entists introduced the idea of polynomial time algorithms and exponential time algorithms. Roughly speaking, an algorithm runs quickly relative ti the size of its input if it is a polynomial time algorithm, and slowly if it is an exponential time algo­rithm. Therefore, easy problems equate with polynomial time algorithms, and difficult problems equate with exponential time algorithms.

It is important to notice the words "relative to the input size" in the definition of polynomial time and exponential time algorithms. All problems are straightforward to solve if the input size is very small, but we are interested in how much harder a problem gets as the size of the input grows. For exam­ple, adding 2 and 12 to get 14 is straightforward, as is factor­ing 15 as 3x5.

However, addition is an example of an easy problem, because there is an algorithm to add numbers which runs in polynomial time, meaning that it would not take very long to add two enor­mous numbers. On the other hand, factoring is a hard problem be­cause, in general, factoring i\ large number takes a very long lime. Thus, when looking for a mathematical problem on which to base a public-key cryptographic system, cryptographers are searching for a problem for which the fastest algorithm takes exponential time. In broad terms, the longer it takes to compute the best algorithm for a problem, the more secure a public-key cryptosystem based on that problem will be.

The use of public-key cryptography is quite simple. Sup­pose Alice wants to communicate with Bob. Rather than Bob and Alice sharing a single secret key (as the case of symmetric key systems), Bob (the recipient of Alice's messages) instead has two keys —- a public key that is available to everyone in the world (including Trudy the intruder!) and a private key that is known only to Bob. In order to communicate with Bob, Alice first fetches Bob's public key. Alice then encrypts her message to Bob using Bob's public key and a known (e.g., standardized) encryption algorithm. Bob receives Alice's encrypted message and uses his private key and a known (e.g., standardized) de­cryption algorithm to decrypt Alice's message. In this manner, Alice can send a secret message to Bob without either of them having to have to distribute any secret keys!