A Brief History of Cryptography

1. A Brief History of Cryptography Sandy Kutin CSPP 532 University of Chicago

2. What is cryptography? • “hidden writing” • Until recently: military tool • Like any military technology: methods change over time • Two sides: designing codes breaking codes (cryptanalysis) • Computers have changed both

3. How do we encrypt? Protocol, or scheme: method of encryption Cryptovariable, or key: secret information plaintext protocol ciphertext cryptovariable Symmetric encryption: decryption is the same

4. Example: Caesar Shift • Protocol: shift each letter by the same amount • Cryptovariable: amount to shift IBM HAL -1 Veni, vidi, vici Foxs, fsns, fsms 10 • Decryption: shift back the same amount

5. How could we break this? • Case I: we don’t know the protocol • Hard problem in cryptanalysis • “Clark Kent” effect • Case II: we know the protocol • Need to guess the cryptovariable • Only 26 possibilities

6. auffcuxcpcmuymnchnlymjulnym bvggdvydqdnvznodiomznkvmozn cwhhewzereowaopejpnaolwnpao dxiifxafsfpxbpqfkqobpmxoqbp eyjjgybgtgqycqrglrpcqnyprcq fzkkhzchuhrzdrshmsqdrozqsdr galliadivisaestintrespartes Decrypt key = 6 Encrypt key = 20

7. Substitution Cipher • Allow any permutation of the alphabet • Key = permutation; 26! possibilities • 26! = 403,291,461,126,605,635,584,000,000 • Roughly 288: checking 1 billion per second, would take 12 billion years • Is there a better way? • al-Kindi, ninth century: frequency analysis

8. H EKGGLHQNL KZEL AKGB PL ARHA ARL CKSGB CHV XNGG KX UHB VLENSTAF VFVALPV CSTAALZ UF OLKOGL CRK SLHB HOOGTLB ESFOAKQSHORF. - USNEL VERZLTLS, VLESLAV HZB GTLV L occurs 18 times, A occurs 10 times.

9. E E E T E T T H EKGGLHQNL KZEL AKGB PL ARHA T E ARL CKSGB CHV XNGG KX UHB E T TE TTE VLENSTAF VFVALPV CSTAALZ UF E E E E OLKOGL CRK SLHB HOOGTLB T ESFOAKQSHORF. E E E E ET E - USNEL VERZLTLS, VLESLAV HZB GTLV

10. E E E T E TH T H EKGGLHQNL KZEL AKGB PL ARHA THE ARL CKSGB CHV XNGG KX UHB E T TE TTE VLENSTAF VFVALPV CSTAALZ UF E E H E E OLKOGL CRK SLHB HOOGTLB T H ESFOAKQSHORF. E H E E E ET E - USNEL VERZLTLS, VLESLAV HZB GTLV

11. A EA E E T E THAT H EKGGLHQNL KZEL AKGB PL ARHA THE A A ARL CKSGB CHV XNGG KX UHB E T TE TTE VLENSTAF VFVALPV CSTAALZ UF E E H EA A E OLKOGL CRK SLHB HOOGTLB T A H ESFOAKQSHORF. E H E E E ET A E - USNEL VERZLTLS, VLESLAV HZB GTLV

12. A OLLEA E O E TOL E THAT H EKGGLHQNL KZEL AKGB PL ARHA THE O L A LL O A ARL CKSGB CHV XNGG KX UHB SE T S STE S TTE VLENSTAF VFVALPV CSTAALZ UF PEOPLE HO EA APPL E OLKOGL CRK SLHB HOOGTLB PTO APH ESFOAKQSHORF. E S H E E SE ETS A L ES - USNEL VERZLTLS, VLESLAV HZB GTLV

13. A COLLEAGUE ONCE TOLD ME THAT H EKGGLHQNL KZEL AKGB PL ARHA THE WORLD WAS FULL OF BAD ARL CKSGB CHV XNGG KX UHB SECURITY SYSTEMS WRITTEN BY VLENSTAF VFVALPV CSTAALZ UF PEOPLE WHO READ APPLIED OLKOGL CRK SLHB HOOGTLB CRYPTOGRAPHY. ESFOAKQSHORF. BRUCE SCHNEIER, SECRETS AND LIES - USNEL VERZLTLS, VLESLAV HZB GTLV

14. A harder example YIRLAZ MRACIRB CR PKORI CRP: MRPPVAMQAY MRLACZRGA, VAYQAVW RA • Shorter = less information • R occurs 10 times, A occurs 9 times • (all others occur 4 or fewer times) • Telegraph style; fewer short words

15. A harder example E E E E E E YIRLAZ MRACIRB CR PKORI CRP: E E E E MRPPVAMQAY MRLACZRGA, VAYQAVW RA E doesn’t begin any common 2-letter words

16. A harder example O O O O O O YIRLAZ MRACIRB CR PKORI CRP: O O O O MRPPVAMQAY MRLACZRGA, VAYQAVW RA A occurs 9 times. What could it be?

17. A harder example O N ON O O O O YIRLAZ MRACIRB CR PKORI CRP: O N N O N O N N N ON MRPPVAMQAY MRLACZRGA, VAYQAVW RA

18. A harder example O N ONT O TO O TO YIRLAZ MRACIRB CR PKORI CRP: O N N O NT O N N N ON MRPPVAMQAY MRLACZRGA, VAYQAVW RA

19. A harder example G O N ONT O TO O TO YIRLAZ MRACIRB CR PKORI CRP: O N ING O NT O N NGIN ON MRPPVAMQAY MRLACZRGA, VAYQAVW RA

20. A harder example GROUND CONTROL TO MAJOR TOM: YIRLAZ MRACIRB CR PKORI CRP: COMMENCING COUNTDOWN, ENGINES ON MRPPVAMQAY MRLACZRGA, VAYQAVW RA

21. What have we learned? • A large space of keys is not enough • Some of the key never got used (Q, Z, X) • We were able to guess a little bit at a time • Features of the plaintext can show through • The more plaintext we have, the easier it is to decode • Don’t use the same key too often

22. The perfect cryptosystem • One-time pad: encrypt each letter with its own key • Example: Caesar shift each letter separately • Ci = Pi + Ki (mod 26) • To encrypt n bits, use n bits of key • This uses up lots of key bits; need to prearrange • How do you generate key bits?

23. Vigenère Cipher • Blaise de Vigenère (c. 1562) • Ci = Pi + Ki (mod 26) • Key repeats with a short cycle • Frequency analysis doesn’t work • Caught on with the telegraph, considered “unbreakable” • Broken by Babbage, Kasiski (c. 1860)

24. Enigma Machine • German cryptosystem in World War II • Same idea: modify letters • Scrambler disks implement permutation • Rotate after each letter, so many different permutations used • Additional permutation provided by plugboard

27. Enigma Key • Key changed daily • 3 scramblers in one of 6 orders • In 1938: 3 of 5, so 60 arrangements • 263 = 17,576 settings for scramblers • Billions of plugboard settings • Alan Turing: bypassed plugboard • Used known plaintext, exhausted over space • British were able to read traffic

28. Navajo Code Talkers • Americans in the Pacific during WWII • Each troop had one Navajo • Even after figuring out system, Japanese couldn’t break it • Like a one-time pad: prearranged secret is a whole language • May not be feasible today

29. Modern Symmetric Cryptography • Assume the protocol is known to the enemy • Only the key is secret • Encryption, cryptanalysis use computers • Operate on bits, rather than letters • DES, AES • Open standards; let everyone try to break it • Closed design often fails (cell phones) • Don’t try this in-house

30. Intermission

31. Key Distribution • Secure communication requires a key • How do you exchange keys securely? • Military: codebooks in field could fall into enemy hands • Commerce: might not meet face-to-face • Seems to be a Catch-22

32. Paradigm Shift • Alice wants to mail Bob a letter securely • If they share a “key”, Alice locks, Bob unlocks • If not: Alice puts on padlock, sends box to Bob • Bob adds his padlock, sends box back to Alice • Alice removes her padlock, sends box to Bob • Bob unlocks box, reads letter • Problem: how to translate this to mathematics

33. Alice, Bob agree on information Y Alice computes A(Y) Mails it to Bob Bob computes B(Y) Mails it to Alice Alice computes A(B(Y)) Bob computes B(A(Y)) A(B(Y)) = B(A(Y)) = secret key “Eve” knows Y, A(Y), B(Y), but can’t compute key Problem: how do you make A(B(Y)) = B(A(Y))?

34. Diffie-Hellman-Merkle (1976) • Modular Arithmetic • Choose Y, modulus p • Alice’s function is YA (mod p) • Bob’s function is YB (mod p) • Key is YAB YBA (mod p) • Eve can’t compute YAB from Y, YA, YB • We think (no one can prove it) • One problem: must communicate to get key

35. One-way Functions • Easy to compute, hard to reverse • Example: f (A) = YA (mod p) • f -1(YA) is called “discrete log” • Hard to compute (we think) • Could always do exhaustive search • Here, there are p-1 choices

36. Cryptographic Primitives • Building blocks for algorithms • Example: one-way functions • Protocols built out of primitives • Example: Diffie-Hellman-Merkle • Protocols built out of other protocols • Example: • 1. Use Diffie-Hellman to exchange key • 2. Use symmetric encryption, key to encode message • Good, “modular” design

37. Trapdoor one-way functions • Another useful primitive • f (X) is easy to compute • f -1(Y) is hard for most people to compute • But: easy to compute if you know a secret • There are trapdoor one-way functions • Found by Rivest-Shamir-Adleman, 1977 • Rely on difficulty of factoring large integers

38. Idea behind public key • Bob publishes design specs for a padlock • Alice wants to send Bob a box • Alice builds a Bob padlock, locks the box • Bob unlocks box using his key • Eve intercepts box, knows design specs • Goal: Eve still can’t build a key • Padlock = trapdoor one-way function

39. Public Key Cryptography • Alice wants to talk to Bob: computes key X • Alice sends Bob fB (X) (Bob’s function) • Bob computes fB-1 (fB (X)) = X • Both Alice and Bob know X, use as key for symmetric encryption • Eve knows fB (X); can’t compute X • Asymmetric encryption • Whitfield Diffie, 1975

40. Digital Signature Scheme • Alice wants to send Bob a message, sign it • Alice sends Bob X and S = fA-1 (X) • Bob checks that fA (S) = X • Therefore Bob knows that S = fA-1 (X) • Only Alice can compute fA-1 (X) easily, so Alice must have sent the message • Same primitive, new protocol

41. Revolution • New ideas made cryptography an option for commerce • PCs gave everyone computing power • Zimmerman’s PGP: gave everyone access • SSL in web browsers • I use ssh every day

42. A COLLEAGUE ONCE TOLD ME THAT H EKGGLHQNL KZEL AKGB PL ARHA THE WORLD WAS FULL OF BAD ARL CKSGB CHV XNGG KX UHB SECURITY SYSTEMS WRITTEN BY VLENSTAF VFVALPV CSTAALZ UF PEOPLE WHO READ APPLIED OLKOGL CRK SLHB HOOGTLB CRYPTOGRAPHY. ESFOAKQSHORF. BRUCE SCHNEIER, SECRETS AND LIES - USNEL VERZLTLS, VLESLAV HZB GTLV

43. You are the weakest link • Cryptographic system only as strong as the weakest link • Example • 1. Use RSA to exchange a key • 2. Use key to generate permutation of 26 letters • 3. Encrypt message with substitution cipher • Schneier: defend castle with 100-foot pole • Often, users are the weakest link

44. Quantum Computation • Computers revolutionized cryptographic design and cryptanalysis • Quantum computers may one day do the same • Quantum key exchange: guaranteed secure • A quantum computer could factor large integers in polynomial time • We may never live to see one

45. Where do we go from here? • Math necessary to understand RSA, DES • Protocols using mathematics • Implementation issues: • Software (bugs, patches) • Hardware (tamper-resistant mechanisms) • Wetware (social engineering) • Politics (who makes cryptographic decisions) • Religion (Microsoft)

46. Recommended Reading Stallings, Chapter 2