Encryption and Security

1. Encryption and Security

2. Outline • Overview of encryption • Terminology • History • Common issues • Secret-key encryption • Block and stream ciphers • DES • RC5

3. Overview • Intro, history and terminology • Symmetric-key encryption • Techniques • DES, RC5 • Public-key encryption • RSA, hash functions, digital signatures • Key exchange, certificates, PKI

4. Overview • Types of attacks and countermeasures • Application layers • S-HTTP, SSL • Steganography and digital watermarking • Security and trust

5. Terminology • Code • Replacement based on words or semantic structures • Cipher • Replacement based on symbols

6. Terminology • Cryptography • The science of encrypting or hiding secrets. • Cryptanalysis • The science of decrypting messages or breaking codes and ciphers. • Cryptology • The combination of the two.

7. Terminology • Plaintext – an unencrypted message • Cyphertext – an encrypted message • Security: a combination of • Authentication • Access control

8. Three eras of cryptology • Pre-WWII • Cryptography as a craft • Widely used, but few provable techniques • 1940s-1970 • Secret key encryption introduced • Information theory used to characterize security • 1970-present • Public key systems introduced

9. Early cryptography • Caesar cipher • Replace each letter l with l +3 mod 26 • “Attack at dawn” becomes • Dwwdfn dw gdzq • Two components: • Algorithm: Shift characters by a fixed amount • Key: the fixed amount. • Note: Knowing the algorithm (but not the key) makes this cipher much easier to crack • 26 possibilities vs 26!

10. Weaknesses of the Caesar Cipher • Word structure is preserved. • Break message into equal-length blocks. • dww dfn dwg dzq • Letter frequency is a big clue • e,t,a,o most common English letters. • Using a single key preserves frequency. • Solution: use multiple keys • E.g. shift by (3,5,7) • “Attack at dawn” becomes dya dhr dyk dbu • Better, but frequency information still present. • An attacker that knows the block size can separate out characters encoded with different keys.

11. Caesar Cipher • The Caesar cipher is still useful as a way to prevent people from unintentionally reading something. • ROT-13 • By decrypting, the user agrees that they want to view the content. • Fundamental problem: key length is shorter than the message.

12. Vernam Cipher • 1920’s: introduction of the one-time pad. • Randomly generated key • Same length as message • XORed with message • Theoretically unbreakable • Attacker can do no better than guessing • Ciphertext gives no information about plaintext.

13. Vernam Cipher • Example: winning lottery number is 117 • 1110101 (7 bits) • Randomly generated key: 0110101 • XOR: 1000000 • No two bits are encoded with the same mapping – an attacker has no frequency information to help guess the key. • Problem: keys are very large. • How to distribute this key? • Shared source of randomness?

14. Symmetric Key Encryption • The Caesar Cipher and the one-time pad are examples of symmetric-key (secret-key) encryption. • Single key shared by all users. • Fast • How to distribute keys?

15. Keyspace • The keyspace is the set of all possible keys. • Caesar cipher: keyspace = {0,1,2,…,25} • Vernam cipher: |keyspace| = 2n –1 • Size of the keyspace helps us estimate security. • Assumption: exhaustive search is the only way to find a key.

16. Substitution Ciphers • Symbols are replaced by other symbols according to a key. • Caesar cipher is a substitution cipher. • To escape frequency analysis, we can use a homophonic substitution cipher • Map symbols to multiple symbols. • e.g 0 -> {01, 10}, 1->{00,11} • 011010010 becomes: 011100101101011110 • Advantage: frequencies hidden • Disadvantage: message and key are longer • Substitution is said to add confusion • Measure of the relationship between plaintext and ciphertext

17. Transposition Ciphers • A transposition cipher is one that permutes the symbols of the message according to a preset pattern. • “Attack at dawn” becomes “cda tka wan tat” • Helps avoid detection of symbols based on correspondence. • ‘q’ followed by ‘u’. • Said to increase diffusion • Reduce redundancies in plaintext.

18. Product ciphers • By themselves, substitution and transposition ciphers are relatively insecure. • By combining these operations, we can produce a secure cipher. • This is how DES works. • M -> Sub(M) -> Trans(Sub(M)). • Might go through multiple rounds.

19. Block Ciphers • The ciphers we have seen so far are known as block ciphers. • Plaintext is broken into blocks of size k. • Each block is encrypted separately. • Advantages: random access, potentially high security • Disadvantages: larger block size needed, patterns retained throughout messages.

20. Stream Ciphers • A stream cipher encodes a symbol based on both the key and the encoding of previous symbols. • Ci = Mi XOR Ki XOR Mi-1 • Advantages: • can work on smaller block sizes – little memory/processing/buffering needed. • Disadvantages: • Random access difficult, hard to use large keys. • Sender and receiver must be synchronized • Inserted bits can lead to errors.

21. Combinations • Many ciphers combine stream and block properties. • Work on multiple symbols, but contain a feedback loop. • Electronic Code Book (ECB) • Pure block cipher, no feedback E-1 plaintext E ciphertext plaintext key key

22. Cipher-block Chaining • XOR previous block • Chaining dependency – order matters. • Some error propagation XOR plaintext plaintext key key E E-1 XOR ciphertext

23. Cipher-Block Chaining • Also incorporated into block ciphers. • Makes tampering easier to detect. • Helps prevent substitution and impersonation attacks. • Secret key can also be used to construct a running-key generator. • Longer sequence of pseudo-random numbers. • Can be used to build a one-time pad.

24. Modifications to CBC • Cipher feedback • Shift register is used to store data. • r-bit are shifted into mask of size m. • Allows a small number of bits to be immediately sent. • Output feedback • Like cipher feedback, but uses output of encryption function. • Eliminates error propagation.

25. DES • Data Encryption Standard • DEA is actually the algorithm. • First commercial-grade algorithm with open implementation details. • Uses a 64-bit key with 8 parity bits, for an effective key of 56 bits. • Keyspace = 256 = 1017

26. DES • Is a combination of a product cipher and a Feistel cipher. • Product cipher: transposition and substitution. • Feistel cipher: Iterates through a number of rounds of a product cipher mapping (L,R) to (R’, L’) • 16 rounds • Block size=48 • In each round, a different 48-bit subkey is selected from the 56-bit key.

27. Security of DES • Keyspace is approximately 1017 • Thought to be secure in 70’s. • Recently, 56-bit DES broken in under 1 day. • Combination of distributed.net & EFF’s DeepCrack. • Able to search several billion keys per second.

28. Extensions to DES • 3DES • Message is run through DES 3 times • C = k3 (k2 (k1(M))) • Backwards-compatible with DES if all three keys are the same. • Keyspace is 1042 • Drawback: bit-oriented operations are slow to implement in software

29. RC5 • Symmetric encryption algorithm • Word-oriented block cipher. • Can vary word length, number of rounds, and key length. • Goals: fast, easy to understand and implement, flexible, low memory requirements, secure. • Uses stream techniques to modify data

30. RC5 • Uses three mathematical operations: • Two’s complement addition • XOR • Left cyclic rotation by variable amounts. • These are all fast operations that are directly supported by most modern processors.

31. RC5 Algorithm • Parameters: K (key), w (word length), r (number of rounds) • Input: a 2w length plaintext in registers A and B. • Output: a 2w length ciphertext. • 1. Expand K into a table S[2(r+1)] keys. • To encrypt: • A =A + S[0]; B = B + S[1] • For i = 1 to r do • A = ((A xor B) << B) + S[2 * i] • B = ((B xor A) << A) + S[2*i + 1] • Decryption is the same thing in reverse.

32. RC5 • Simple algorithm – key is the data-dependent rotations. • Keys are accessed sequentially, allowing for small caches. • Security still unclear, but looks good. • 56-bit key: 250 days by distributed.net • 64-bit key: 1747 days by distributed.net • 1.02x10^11 keys/sec, 1.5 x10^19 keyspace • 72-bit key in progress. • 4.8x10^10 keys/sec, 4x10^21 keyspace • 100% in 788,747 days = 2160 years

33. Summary • Secret-key algorithms (DES, RC5) have been widely studied. • Fast • Potentially highly secure • Well-understood. • Excellent for repeated communication. • Hard to use in open environments, one-shot communications • Works for hiding secrets; what about signing things? • Public-key encryption evolved as an answer to this problem.