CS361: Introduction to Computer Security
Cryptography I
Dr. Bill Young
Department of Computer Sciences
University of Texas at Austin
Last updated: February 25, 2020 at 12:03
CS361 Slideset 5: 1 Cryptography I
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Introduction to Cryptography and Cryptanalysis, Lecture notes of Cryptography and System Security
An introduction to the key concepts of cryptography and how it is used as a tool for security. It also covers cryptanalysis and the attempt to extract the meaning of encrypted messages. terminology related to encryption and decryption, as well as examples of encryption and decryption processes. a set of lecture notes for CS361: Introduction to Computer Security at the University of Texas at Austin.
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CS361: Introduction to Computer Security
Cryptography I
Dr. Bill Young Department of Computer Sciences University of Texas at Austin
Last updated: February 25, 2020 at 12:
Elementary Cryptography
This is not a course in cryptography. The department offers one and you are advised to take it, if you plan to work in the security field.
Our point here will be to give some intuitions about: what are the key concepts of cryptography; how is it used as a tool for security; how effective is it in that regard.
A Thought Experiment
Suppose youāre confronted with a text that you believe to be the encryption of some message. Youād like to apply your cryptanalytic skills. How do you get started? What questions should you ask? What is the likely underlying language of the plaintext? What characteristics of the probable source text are relevant? What characteristics of the source language are relevant? Have any transformations/compressions been applied prior to encryption? What is the likely nature/complexity of the encryption algorithm? Anything else?
Thought Experiment: The Gold Bug
The setting: In the early 1800ās, a man named William Legrand finds a scrap of parchment on a South Carolina beach. The parchment appears blank, but when he holds it close to a candle flame to examine it, a strange encoded message appears. In one corner is a drawing of a goat. Legrand wonders if the message could be directions to the location of a treasure buried by the infamous pirate Captain Kidd.
An Aside: Talk Like a Pirate
A useful Pirate to English translator can be found at: http://www.talklikeapirate.com/translator.html
Information Theory and Cryptography
Information theory vitally informs cryptography in a number of ways: What effect does encoding a message have on the information content of the file? An attempt to decrypt a message is really an attempt to recover a message from a (systematically) noisy channel. How can redundancy in the source give clues to the decoding process? Is a perfect encryption possible (i.e., one that is theoretically unbreakable)?
Encryption / Decryption
The purpose of encryption is to render the message less useful / meaningful to the intruder. Conceptually, the process of encryption is quite simple:
Encrypt (^6) key e (optional)
plaintext (^) - ciphertext-
as is the process of decryption:
Decrypt (^6) key d (optional)
ciphertext (^) - plaintext-
Some Terminology
Encryption is the process of encoding a message so that its meaning is not obvious.
Decryption is the reverse process, transforming an encrypted message back to its original form.
The terms encrypt, encode, and encipher are used interchangeably, as are decrypt, decode, and decipher.
A system for encryption and decryption is called a cryptosystem.
The original form of a message is called plaintext and the encrypted form called ciphertext.
Keyed Algorithms
Often the encryption and decryption algorithms use a key K. The key selects a specific algorithm from the family of algorithms defined by E.
We write this dependence as:
C = E (P, KE ) and P = D(C , KD )
If KE = KD , then the algorithm is called symmetric. If not, then it is called asymmetric. In general,
P = D(E (P, KE ), KD )
An algorithm that does not use a key is called a keyless cipher.
Some Notation
Often the notation E (P, K ) and D(C , K ) becomes cumbersome. An alternative notation is often used, particularly in cryptographic protocols.
Weāll often use {M}K to denote E (M, K ), and sometimes to denote D(M, K ). For example,
P = D(E (P, KE ), KD ) = {{P}KE }KD.
This is usually appropriate since, in many of the most important commercial crypto systems, the same algorithm is used for both encryption and decryption (i.e., the algorithm is its own inverse).
Cryptanalysis
A cryptanalyst can attempt to do any or all of the following: to break a single message; to recognize patterns in encrypted messages; to infer some meaning without breaking the algorithm; to deduce the key; to find weaknesses in the implementation or environment or the use of encryption; to find weaknesses in the algorithm, without necessarily having intercepted any messages.
Cryptanalysis (Cont.)
The analyst works with: encrypted messages, known encryption algorithms, intercepted plaintext, data items known or suspected to be in a ciphertext message, mathematical and statistical tools and techniques, properties of languages, computers, ingenuity and luck.
Breakability Evolves
Suppose we use a more ingenious approach that reduces this to 1015 operations. An exhaustive approach would require only about one day. (But still not be needed, probably!)
Because of advances in computer technology, algorithms that were considered strong enough 20 years ago, can be effectively broken today.
You see the result in current discussion of increasing the key length for standard algorithms such as DES and RSA. Weāll consider this issue later.
Strong Encryption
A cryptosystem is strong if there are no āshort cutsā to breaking it. That is, there is no cryptoanalytic approach that is substantially faster than brute forceāi.e., trying all of the keys one by one. Most strong algorithms are still breakable.
For an n-bit block cipher with k-bit key, given a small number of plaintext/ciphertext pairs encrypted under key K , K can be recovered by exhaustive search in an expected time on the order of 2 kā^1 operations.
The larger the keyspace, the longer to find the key by search. Thus, an important question for any cryptosystem: What is the size of the keyspace? How does this relate to the size of the key?