The History of Secrets Cryptography and Privacy

1. The History of SecretsCryptography and Privacy Patrick Juola Duquesne University Department of Mathematics and Computer Science

2. Secret Writings • Used to write to authorized people • Good guys : • Business partners, lovers, fellow soldiers • Bad guys : • Competitors, parents, enemies, foreign agents • Secrets can be military, diplomatic, commercial, personal, et cetera.

3. An Early Example • Write in foreign alphabet • Works surprisingly well in era of mostly illiterate people attack at dawn attack at dawn

4. Caesar cypher (40 BCE) YGYKNNCVVCEMQPVJGYGUVUKFGQHVJGECOR CVFCYPUVQRRNGCUGDGTGCFAVQUQTVKGVQQW TCUUKUVCPEGLECGUCT CVVC -- “bATTAlion”? “inDEED”? “ATTAck”? “cigarETTE”/ “bESSEmer converter”? CUUKU -- “pOSSESsion”? “ASSIStance”? C -> A U -> S K -> I

5. Caesar cypher (cont.) • Caesar and his reader know something the enemy doesn’t • Can be as simple as replacing letters • Termed the “key” to a cypher • Easier to solve with key than without • Ratio of without/with defines “work factor” WEWILLATTACKONTHEWESTSIDEOFTHECAMPAT DAWNSTOPPLEASEBEREADYTOSORTIETOOUR ASSISTANCEJCAESAR

6. Nomenclators (1500 ACE) • Systematic replacement of one letter by a single other symbol : monoalphabet cypher • Nomenclator : monoalphabetic cypher with codebook extension for specific words • Weakness : every appearance of a given letter is encyphered identically

7. Polyalphabetics (16th-20th c.) • Use multiple alphabets to disguise frequent letters • Playfair cypher -- encrypt letters in groups, so TA and TE may have nothing in common • Vigenere cypher -- vary Caesar “key” during encryption • Considered “le chiffre indechiffrable” until early 20th century

8. Vigenere example • AT becomes both NH and SX in cyphertext • O in cyphertext corresponds to both A, W • Simple frequency analysis no longer works ATTACKATDAWN NOSENOSENOSE NHLEPYSXQOOR

9. Vigenere decryption • Weakness : key letters repeat • If the key is 4 characters long • 1st, 5th, 9th, etc. characters use same key letter • 2nd, 6th, 10th, 14th, etc. likewise • Frequency characteristic of monoalphabetic (Caesar) cypher • Crack four different Caesar cyphers, and you’re in!

10. What if the key doesn’t repeat? • A re-used key can give the same effect • BUT • If the key is sufficiently random • Only used once • And never repeats • The resulting cypher is called the Vernam cypher (1917) and is provably unbreakable. • Sometimes called One-Time Pad

11. Who kept the secrets? • Development and use of cryptography to this point mostly military and diplomatic. • “Obviously” required substantial talent to do, beyond what most people had • Civilian cryptography -- secret notes to lovers, business codes -- still used monoalphabetic cyphers • Methods of analysis becoming available in literature (The Gold Bug, The Dancing Men)

12. What’s a good cypher? • Kirchoff’s criteria (1883) • Security should reside in the key • System doesn’t need to be kept secret • System should be easy to use in the field • Keys/apparatus should be easily changeable • Impossible to meet all in practice • Naval ships (submarines) can carry much more equipment than PFC Ryan

13. Enigma • Machine cryptography developed in early 20th century; requires bulky apparatus, but far too complex to crack by hand • ENIGMA -- Main code system of Nazi’s • Three (later four) rotating wheels like odometer of car. Each wheel position yields different key. • 159,000,000,000.000,000,000 keys

14. The Computer Revolution • Rejewski/Turing cracked Enigma, but had to invent the computer to do it. • And were also scarily, scarily good mathematicians… • Early computers (bombes) could search entire keyspace in about five hours.

15. Viva la revolution! • Enigma breakthrough classified MOST SECRET until 1975(!); some of Turing’s papers are still classified. Computer encryption is just too dangerous. • BUT, it’s also too useful, especially for civilian/industrial uses like financial transfers • Enter Data Encryption System (DES)

16. DES • Approved in 1975 by US govt. (NSA) • Non-classified uses only • 32,000,000,000,000,000 possible keys • Created “civilian” cryptography • Most analyzed system ever

17. Questions about DES • Why so few keys (fewer than 30 year old Enigma, but better mathematical structure)? • NSA approved IBM’s initial design only after making a few changes. Why? • Is there a secret “back door”? Is the government holding a master key? • Is there a good replacement?

18. Replacing DES • DES held out much longer than originally planned, but (as expected) had too few keys. • Modern computers can crack DES very fast. • … but no one really had a good replacement • 3DES used (late 90s) to extend keyspace • Advanced Encryption System (Rijndahl) finally designed in 2001 as replacement. • No “secret” governmental involvement

19. Public key encryption • Problem with all cryptography, AES included -- a need for shared secret prior to communication • How do I establish a shared secret with Amazon.com if I don’t work there? Can we avoid this? • Surprising answer : Yes! • Decryption key can be different than encryption key, allowing “public” keys!

20. Merkle Puzzles (1975) • I publish a huge collection of “puzzles.” You pick one to solve, and send me the solution. • I look up the solution, and recognize which puzzle you solved. Everyone else has to solve all of the puzzles to recognize the solution. • Work factor is number of puzzles • Avoids having to communicate beforehand

21. RSA Encryption • Named for inventors : Rivest, Shamir, and Adelman (Turing award winners, 2003) • Uses a large product of two primes -- easy to multiply, but very hard to factor • Two keys, d and e : you encrypt with e, while only I know (and can decrypt with) d. • Reversible! I encrypt with d, you decrypt with e and you know I encrypted it!. In other words, it can be used as a signature! • Work factor can be arbitrarily large -- “It’s easier to break thumbs than it is to break RSA”

22. Power to the People : PGP • Pretty Good Privacy • Written c. 1990 by Phil Zimmermann. Military/diplomatic strength encryption, using private and public key cryptography. • Believed unbreakable by anyone short of major governments, but “freely” available for personal/corporate use • PGPfone -- similar technology for phones

23. Political issues • Should people be permitted this kind of security technology? • I can keep secrets from my competitors, but also from law enforcement/national security enforcers! • ITAR -- cryptographic equipment regulated as munitions (like machine guns) • Only govt-approved (breakable) encryption permitted.

24. More politics • Clipper/Capstone chip -- “secure” phone with Law Enforcement Access Field to ensure wiretap capacity • 40-bit (1,000,000,000,000 key) limit on commercially exported software • Criminalization of cryptography per se (France, some other countries) • USA/PATRIOT wiretap provisions • FBI operation CARNIVORE

25. Discussion points • The genie appears to be out of the bottle, in that the technology for secure encryption is widely available • The roadblocks to widespread implementation are primarily social and political. • Is civilian/personal cryptography a good thing or not?

26. Conclusions • Secret writing has a long (2000 yr) history • Military/diplomatic communications driving force for most of history; personal/industrial privacy is secondary • Modern cryptographic systems are both highly secure and widely available • Omnipresent computers and ‘Net forcing us to re-evaluate view on security and privacy