Understanding Symmetric Key Encryption: A Simple XOR Example

1. Cryptography

2. A simple example… • Text: U-M • ASCII Encoded: 01010101 00101101 01001101 • “Encoding” refers to convenient reformatting. • No secrecy here. Call it plaintext. • Let’s “Encrypt” it, i.e. hide its meaning from nosy 3rd parties.

3. A simple example… • Let’s generate 24 random bits, call it a key. • Say, by coin flips. • Tails  1. Heads  0 -------- -------- -------- 01010101 00101101 01001101 • For each bit, if the same, result is 0. If they’re different, result is 1. This is the XOR (exclusive OR) function.

4. A simple example… _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ • The result is an encrypted string. Call it ciphertext. • This simple XOR method is unbreakable. • Even by the CIA or NSA or Microsoft. • Even by the most hard working hacker. • IF…

5. Simple XOR • To decrypt, need to know: • That simple XOR is in use. • The key pattern. • Strength of the system depends on: • Secrecy of the key

6. Encryption • Generally, you need to understand the process and have the key. • In the Practical Cryptography’s notation: c := E(Ke, m)

7. Decrypting • Undoing the encryption is easy for this simple example. -------- -------- -------- -------- -------- -------- Once more: For each bit, if the same, result is 0. If they’re different, result is 1. This is the XOR (exclusive OR) function.

8. Decryption • Generally, you need to understand the encryption method and have the key. • In the Practical Cryptography’s notation: m := D(Ke, c) • We have assumed the same key is used for encryption and decryption.

9. Secrecy of XOR Example? • Unbreakable, if: • Key remains secret • Key never reused

10. SKE • Using the same key for both encryption and decryption is called SKE: • Symmetric Key Encryption • Secret Key Encryption

11. SKE – The Whole Thing

12. PCs Changed The World • Evolution of encryption methods: • Pencil & paper • Machines, e.g. German Enigma • Computers, e.g. PC • Computers allow much more sophisticated methods. • Internet allows rapid dissemination of information, including computer code, algorithms, commentary, and analysis.

13. Kerckhoffs’ Principle • Genuine security lies in keeping the key secret, not in keeping the process secret. • Why? • Public algorithms have public analysis. • Weaknesses are publicly exposed. • Analogous to open source software. • This is a machine era notion.

14. How can I attack SKE? • For any encryption scheme there are two strategies: Brute Force and Analytic Attacks. • Brute Force • I know the algorithm, so I just try different keys until I get lucky. • Highly dependent on machine power. • The bigger the “key space” the more tries it takes to get lucky.

15. Moore’s Law • Often quoted as “Computers double in speed every two years.” • Gordon Moore noted exponential growth in the # of transistors per integrated circuit. • 1965 • A brute force attack that takes 8 days with current technology will take 4 days in two years…?!? • Practical Cryptography suggests 50-year horizon…

16. “Computationally Impractical” • You know what to do and can write a program to do it, but the program takes so long to run that it’s effectively useless.

17. Analytic Attack • Instead of systematically trying all the keys, we attempt to determine the key based on: • The ciphertext • What we know about the plaintext • What we know about the algorithm

18. Symmetric Key Encryption

19. The Problem with SKE • The intended recipient must know the process and have the key. • A cracker seeks these, too. • The problem, then, is to get the key to the recipient. • Worse if you communicate with many people! • The Key Distribution Problem

20. Some Key Distribution Solutions • “One time pads.” • Run out eventually. • Keep using the same key. • Every transmission provides data for crackers. • Transmit new keys using old keys. • Or have a special key used only for transmission of new keys.

21. Some Key Distribution Solutions • Couriers • Can be intercepted/bribed. • Algorithmic key construction • Key based on day of month • Key based on readily available data • from newspapers? radio broadcast? • Special hardware for key construction

22. Gotcha • If the key is secret, SKE can be made very secure. • long keys • complex processes • Weakness is the necessity to distribute the key.

23. SKE & Big Five Attributes of Security • Availability – Need to make sure algorithm isn’t too computationally onerous. • Integrity – Will mostly handle separately. • If key uncompromised & algorithm chosen well: • Confidential – Sure. • Authenticated – Sure. • Non-repudiated – Sure.

24. PKE - Public Key Encryption • Suppose we could encrypt and decrypt with different, but uniquely corresponding keys. • The public key is public – • Hand it out freely • Post it on web • Email it to your friends • The private key is private – • Guard it closely. • aka Asymmetric Key Encryption

25. PKE, More Formally • The ciphertext is based on the recipient’s public key: • c := E(PBob, m) • The decryption process uses the recipient’s private key: • m := D(SBob, c) • This means: • m = D(SBob, E(PBob, m)) Always.

26. PKE, Graphically

27. The Secrecy Here . . . • . . . is in the keys. • Usually the processes themselves are publicly available. • Most commonly used: • RSA • Rivest, Shamir and Adleman

28. Message Authentication • You can encrypt using either key of the pair. You then decrypt with its partner. • If you can decrypt using my public key, the encryption must have been done with my private key. • If I can decrypt using my private key, the encryption must have been done with my public key.

29. Hash Functions • Consider this text: “John went to OSU.” • Count the occurrences of the letters. • a b c d e f g h i j k l m n

30. Another simple example… • Text: U-M • ASCII Encoded: 01010101 00101101 01001101

31. Another simple example… • Let’s XOR them sequentially: 01010101 00101101 01111000 01001101 00110101 • What’s the connection between “U-M” and 00110101? • Let’s call this function H for hash. • 00110101 = H(“U-M”)

32. Another simple example… • It’s not unique. • Other strings give 00110101 as their H value. • Easy to find others. • Note: • There are 28 (= 256) 8-bit strings. • There are an infinite number of possible text strings.

33. Another simple example… • It’s not reversible. • Given 00110101, it’s not possible to say “this came from ‘U-M’”. • Easy to find others.

34. Suppose • H(“U-M”) = MD5(“U-M”) = c57b94ee2455d6932eae85efa2bfc091 • This is the MD5 function. • All input strings produce 16-byte output, usually written as hex string. • MD5(451 syllabus) = 86721e0212256155e170a413a899a76a • Not unique, but ‘computationally impractical’ to find others. • Not reversible except by trial & error.

35. What Good Is It? • Error Detection • Transmit block of data, append MD5. • Recipient calculates MD5, compares.

36. Suppose • We have a document: important, but not necessarily confidential. • I do this: • Compute the MD5 digest. • Encrypt the digest with my private PKE key. • Call the result a signature.

37. Then you… • You get the document & signature. • You can… • Compute the MD5 digest of the file. • Decrypt the signature file using my public PKE key, yielding a message digest. • Compare the two. • This means… what?

38. ITS 453 – Encrypted Communication • How, when, where to use encryption methods. • What protocol layer? • What specific encryption techniques? • Solving key distribution problems.

39. ITS 453 – Encrypted Communication • Basics of encryption, hash functions. • NSA, RSA, etc. • PGP: encrypted files / digital signatures • Public Key Infrastructure • Trust arrangements • Digital certificates, etc. • Authentication • Kerberos • WEP / WPA wireless encryption