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Section 2: Basic Cryptography In this section we learn about cryptography. Reference: [Mark Stamp] Chapter 2 46 You can use a password to protect your computer; however, once the data leaves your computer and goes through a public data network (such as Internet), what can you do to protect it? Answer: data security by cryptography Data sent over public channels is subject to being intercepted and read by others. Encrypting data can keep data confidential even if read while on public channels. Data sent over public channels may also be modified during transit by an attacker or corrupted accidently. Encrypted data may also be modified or corrupted so encryption doesn’t necessarily solve that problem. 47 Objective of this section are: to learn the concept of data encryption, decryption, relationship between key size and data security. 48 49 Figure shows encryption. Encryption is the process of converting plaintext to the ciphertext. Decryption is the opposite: conversion of the ciphertext back to plaintext. A cryptographic system may use keys (string of bits) for encryption and decryption. In practice, the encryption method and decryption method should be public. The decryption key may be kept confidential for ensuring data security. 50 Cryptography may be used to setup a secure communication system. In symmetric key Cryptography, a single shared key may be used to encrypt and decrypt the message as shown in the above diagram. For security reasons, the key should be a secret known only by sender and receiver (i.e., the people who are authorized to read the message). Problem: how can sender and receiver agree on a key securely on the Internet? They need to share a key BEFORE they can encrypt messages to each other, but if one of them sends the key to the other over public channels, it‘s vulnerable to interception. Later, we will see some clever strategies that allow them to share a key securely. 51 That system is public key cryptography – i.e., use two keys: one for encryption and one for decryption. The encryption key can be made public. So long as decryption key is kept private, the information remains private. This is the basis of public key system. 52 In public key cryptography, every user has two keys. One key is public. The other key is kept private, only the owner can access the private key. Given the public key, it is not computationally feasible to compute the corresponding private key. For confidential communication, the receiver’s public key is used for encryption and receiver’s private key is used for decryption. Since no one else has the private key other than the owner of the private key, no one else can use the key to decrypt the message. 53 For integrity in communication, the sender’s private key is used for encryption and the sender’s public key is used for decryption. The encrypted message is NOT private since anyone can use the sender’s public key to decrypt it. However, only the sender could have encrypted that message, so the fact that the ciphertext decrypts with some particular user’s public key is proof that that message originally came from that user. A message encrypted with a private key is considered to be “digitally signed” by that private key’s owner. Digital signatures are important for many online business applications. Note that the public key cryptography does not completely eliminate the key distribution problem. The public key has to be distributed through a reliable channel or somehow make sure that we are using the right public key for encryption. Also, the private key has to be protected from disclosure or tampering. 54 55 First step is to decide on the encryption approach. Part of the system may be made public knowledge, especially if widespread adaptation of the system is desirable. 56 Why should anyone trust a cryptosystem that is proprietary/classified/non-public? Attempts to replace open systems with “black box” cryptosystems (e.g. Clipper Chip) failed for 2 reasons: 1) the system’s designers could not publish their security analysis (to convince others), and 2) security experts could not do their own security analysis. Some also worry that the designer of a black box cryptosystem might build a “backdoor” into the system for their own use. In short: those in charge of securing data assets could not trust black box systems. The system MUST be public for security experts to trust it to secure assets under their protection. In modern practice, design of the system is public. It is assumed that an enemy can and will uncover any encryption system. Security of the system depends only on the key. Keeping the key safe is an important requirement for data security. 57 The above six principles still continue to be relevant even today. 58 Users want privacy. However, they often find it hard to use cryptographic tools because they don’t understand how they work – they also don’t know what should and should not be done to ensure security. Administrators on the other hand are trying hard to make sure all sensitive data is encrypted. Trudy wants to find out the type of cipher used first, so that he can try to break it. Active Learning Task: With your partner analyze the use of cryptography for data security from three different perspectives. 59 Shift cipher is an encryption system where each character in the input text is shifted by a numerical key. Key in the above example is 2. There are other types of shift ciphers as well. You can vary the shifts for each character position: first character shifted by 2, second by -3, third by 5 and so on. 60 For a single shift cipher, there can be as many keys as there are characters – so, the key can be between 0 and 255, assuming an extended ASCII character set of 256 letters, symbols, and special characters. 61 Simple substitution cipher is similar to shift cipher. Each letter is substituted by a letter or symbol from the substitution table. Thus, the plain text “CAB” is encrypted to “(@!”. Try to decrypt the above with the help of the substitution table. 62 Brute-force method involves trying to break a cipher just by trying different keys to see if they work. For an attacker to guess the substitution table correctly, how many trials are needed. Assume that there are n possible characters. The first letter may be substituted with any of the n characters. The second letter may be substituted with one of the other n-1 character and so on. So total possibilities: = n * (n-1) * (n-2) * (n-3) ……….. 2 * 1 = n! If n is 256, find out the number of possibilities. Assume each combination would take one millisecond to try out and verify, how long will it take on an average to uncover the message? 63 All letters in English language text are not equally likely. i.e., some letters appear more often than others. For example, “e” is the most commonly found letter. Since the plaintext statistics are reflected in the simple substitution ciphertext as well, it is easy to find the one to one correspondence between plaintext and ciphertext characters. 64 The above text is probably not enough to perform cryptanalysis unless we get lucky. Given that it is a shift cipher, things may get a little easier. If no information is given, one can only try out different possibilities. You may use an online tool. (e.g., http://www.cs.uri.edu/cryptography/classicalshiftdemo.htm) 65 Each word in the input message is encrypted with the help of a codebook. In this example, “Nuke Device Ready” is converted to “Cat Food Empty”. From the table, it is clear that Nuke = Cat, Device = Food, and so on. 66 Transposition ciphers (or permutation ciphers) are like jumbles. There is no substitution here, but the letters are permuted as can be seen from the above example. Keys: 3, 1, 2, etc. will tell which position the letter will go to. C goes to third position, A goes to 1st position and so on. To decrypt a permutation cipher, you would need to try out different possibilities. One way would be to write a program which will re-arrange characters to see if you are getting something that makes sense. With short ciphertext, someone can intuitively try to rearrange the letters to uncover the message. 67 In double transposition ciphers, a message entered into a grid. Spaces are often removed or substituted with random characters. Both row transposition and column transposition are done. The first row becomes the second row, second row becomes the first, third row becomes fourth, and the fourth row becomes the third (key: 2, 1, 4, 3). For column transformation: first column becomes fifth, second becomes first, third remains the same, fourth becomes second and fifth goes to fourth. (key: 5, 1, 3, 2, 4). Some double transposition ciphers are quite difficult to break for a large body of text. 68 Even if the plaintext characters are not disguised, they are re-arranged thus diffusing the plaintext characteristics (e.g. breaking up common 2-letter digrams like th and er). Column and row transposition make it harder to identify the words. It is a non- trivial cipher, especially for a large body of text. What are the total number of possible combinations? For an (m x n) column of text, it is m! * n!. 69 Remember, all characters are stored in a computer system as 1s and 0s. So, the plaintext “Hello world” is encoded using the above table resulting in the binary string “01000 00101 01100 01100 01111”.
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