1. Elementary Cryptography Steven Bogaerts

2. Goal of Cryptography ● Ensure security of communication over insecure medium  Privacy (secrecy, confidentiality)  Integrity ● Communicate even with possibility of adversaries

3. Approaches to Secure Communication ● Steganography  Hide message existence ● Cryptography  Hide message meaning

4. Childhood "Secret Codes"

5. Cryptosystem ● How does this help us accomplish our goals?  Privacy  Integrity

6. Security Failures ● Privacy failure  Intercept ● Integrity failure  Modify  Fabricate ● Block

7. So cryptography is, like, awesome. But how is it done?

8. Encryption Algorithms ● Two categories:  Keyless  Keyed ● Symmetric ● Asymmetric ● Character representation  A=0, B=1,..., Z=25  So A + 3 = D, etc.

9. Substitution Ciphers ● Replace each letter with another ● Caesar cipher  c i = E(p i ) = p i + 3  Ex: THE EAGLE HAS LANDED wkh hdjoh kdv odqghg  Easy to memorize  In general: c i = E(p i ) = p i + n

10. Other Substitution Ciphers ● Key: "professional" ABCDEFGHIJKLMNOPQRSTUVWXYZ profesinalbcdghjkmqtuvwxyz ● Every third letter ABCDEFGHIJKLMNOPQRSTUVWXYZ adgjmpsvybehknqtwzcfilorux

11. Cryptanalysis ● Brute force: 26! possibilities ● Hints:  Frequencies: ● Letter (general) E, T, A, O, N, I, R,... ● First letter ● Last letter  Guesses at message content ● Double letter ● Digraphs, trigraphs ● Small words

12. Cryptanalysis ● Example: wklv phvvdjh lv qrw wrr kdug wr euhdn

13. Cryptanalysis ● Example: wklv phvvdjh lv qrw wrr kdug wr euhdn ● wrr --> see, too, add, odd, off... wr --> to, of Best guess: w = T, r = O

14. Cryptanalysis ● Example: wklv phvvdjh lv qrw wrr kdug wr euhdn ● wrr --> see, too, add, odd, off... wr --> to, of Best guess: w = T, r = O ● lv --> so, is, in,... T_SO very unlikely... T_IS likely Best guess: l = I, v = S

15. Cryptanalysis ● Example: wklv phvvdjh lv qrw wrr kdug wr euhdn ● wrr --> see, too, add, odd, off... wr --> to, of Best guess: w = T, r = O ● lv --> so, is, in,... T_SO very unlikely... T_IS likely Best guess: l = I, v = S ● wklv phvvdjh lv qrw wrr kdug wr euhdn T-IS --SS--- IS -OT TOO ---- -- -----

16. Cryptanalysis wklv phvvdjh lv qrw wrr kdug wr euhdn THIS MESSAGE IS NOT TOO HARD TO BREAK ● Regularity ● Outside information

17. Cryptanalysis wklv phvvdjh lv qrw wrr kdug wr euhdn THIS MESSAGE IS NOT TOO HARD TO BREAK ● Regularity ● Outside information ● WWII: af to be target of a major assault  "Damaged" water distillery

18. One-Time Pad ● Avoid regularity ● Vernam Cipher example Key: CIHJTFDJZMEPQLFHXYRLS... Plaintext: HELLO CIHJT 2 8 7 9 19 HELLO + 7 4 11 11 14 9 12 18 20 7 7 = 33 mod 26 Ciphertext: J M S U H Remaining key: FDJZMEPQLFHXYRLS...

19. One-Time Pad ● Hard to maintain keys ● Facilitate key distribution  Novel  Phone book

20. Transposition ● (Substitution - replace one letter with another) ● Transposition - mix up plaintext message  Columnar

21. Transposition ● (Substitution - replace one letter with another) ● Transposition - mix up plaintext message  Columnar: T A L L C O M P U T E R S C I E N T I S T S R O C K x k g j --> tmsicapcskluitxlteskcenrgortoj

22. Much More To Discuss... ● What makes a "good" encryption algorithm ● Data Encryption Standard (DES)  Double and Triple DES ● Advanced Encryption Standard (AES) ● Public Key Encryption  Rivest-Shamir-Adelman (RSA)

23. Summary So Far ● Maintain privacy, integrity despite adversaries ● Cryptosystems  Substitution  Transposition ● Cryptanalysis

24. Bible Codes? ● Equidistant Letter Sequences (ELS) ● Rips, Witztum in Statistical Science  Reviewers not convinced, but nothing formally wrong

25. Bible Codes? ● Refutations  McKay, Bar-Natan, Kalai, Bar-Hillel in Statistical Science  Moby Dick "predicts" assassinations

26. Scripture ● "... Ask and it will be given to you; seek and you will find; knock and the door will be opened to you." (Luke 11:9) ● "...the counselor, the Holy Spirit, whom the Father will send in my name, will teach you all things and will remind you of everything I have said to you." (John 14:26) ● "The secret things belong to the LORD our God, but the things revealed belong to us and to our children forever, that we may follow all the words of this law." (Deuteronomy 29:29)