Cryptography

1. Cryptography Part 1

2. Terminology • Cryptography the art (and science) of making messages secret • plaintext the original intelligible message; i.e., <Send more troops> • ciphertext the transformed message; i.e., <XRYT SDUY WLPPVC> • We will look at many different ways to encrypt messages. • Why should we care?

3. A Simple but Important Example • Intercepted in Afghanistan around 2002 • Ciphertext: “Forty of the contractor’s friends here were taken by surprise by malaria a few days ago, following the telegram they sent, which was similar to Salah al-Din’s telegrams. The majority of them are from here, and two are from the contractor’s country.” • Plaintext:Forty of bin Laden’s friends here were arrested a few days ago, following the telegram they sent, which used the same code as Ayman al-Zawahiri’s telegrams. The majority of them are from Yemen, and two are from bin Laden’s country Saudi Arabia

4. Ciphertext: “We heard that al-Asmar had a sudden illness and went to the hospital. He will have a session with doctors early next month to see if he can be treated there, or if he should be sent for treatment in his country. “Osman called some days ago. He is fine but in intensive care. When his situation improves he will call. He is considering looking for work with Salah al-Din, as opportunities are scarce where he is, but his health condition is the obstacle.” • Plaintext: “We heard that al-Asmar was arrested and went to prison. He will have a session with lawyers early next month to see if he can be imprisoned there, or if he should be sent to Egypt, where jihadis are routinely tortured or hanged.“Osman called some days ago. He is fine but being monitored by the police. When his situation improves he will call. He is considering looking for work in Afghanistan, as opportunities are scarce where he is, but the fact that he is being monitored by the police is the obstacle.

5. How could you break such a code? • Battle of Midway, 1942. US had partially cracked the Japanese code. But some Japanese intercepts began to refer to a pending attack on an objective known as “AF”. • US Navy thought AF might refer to Midway Island. • So the commanding officer at Midway was instructed to send a radio message in plaintext that they were dangerously low on fresh water at Midway. (In reality, they weren’t.) • Soon after, the Japanese transmitted: “AF is short of water.” • US won the Battle of Midway, a turning point in the war. • General George Marshall: “As a result of Cryptoanalysis we were able to concentrate our limited forces to meet their naval advance on Midway when we otherwise would have been 3,000 miles out of place.”

6. Pigpen Cipher Used by Masons in 18th century From New York Times, 1957: “The solution was worked out with a tic-tac-toe chart. Working left to right, line after line, in the chart the cryptographer placed a single dot in each chart section. On a second round he put two dots in each section. On the third round, each section was separated, but left without marking, to complete the alphabet. On the first round of single dots the ninth, or last section, was used for two letters, “I” and “J”. That is the only double use of the single dot.”

7. Some Classical Ciphers

8. ATBASH Cipher • Appears in Book of Jeremiah. • In Hebrew: Aleph = Tav, Beth = Shin • In English, it would be “AZBY Cipher”. • It is a substitution code:Plain: ABCDEFGHIJKLMNOPQRSTUVWXYZCipher: ZYXWVUTSRQPONMLKJIHGFEDCBA • Exercise: Decrypt <Zhhbirzmh ziv mvzi>.

9. Spartan Scytales • From Plutarch’s Life of Lysander:“When the Ephors send an admiral or general on his way, they take two round pieces of wood, both exactly of a length and thickness, and cut even to one another; they keep one themselves, and the other they give to the person they send forth; and these pieces of wood they call Scytales. When, therefore, they have occasion to communicate any secret or important matter, making a scroll of parchment long and narrow like a leathern thong, they roll it about their own staff of wood, leaving no space void between, but covering the surface of the staff with the scroll all over. When they have done this, they write what they please on the scroll, as it is wrapped about the staff; and when they have written, they take off the scroll, and send it to the general without the wood. He, when he has received it, can read nothing of the writing, because the words and letters are not connected, but all broken up; but taking his own staff, he winds the slip of the scroll about it, so that this folding, restoring all the parts into the same order that they were in before, and putting what comes first into connection with what follows, brings the whole consecutive contents to view round the outside.”

10. Scytales must be the same size to be able to decipher a message

11. Spartan Scytales • Demo can be found at: http://www.counton.org/explorer/codebreaking/transposition-ciphers.php • Example of a transposition cipher (the code consists of jumbling up the letters)

12. Caesar’s Cipher • Suetonius description of Julius Caesar's cipher:“There are also letters of his to Cicero, as well as to his intimates on private affairs, and in the latter, if he had anything confidential to say, he wrote it in cipher, that is, by so changing the order of the letters of the alphabet, that not a word could be made out. If anyone wishes to decipher these, and get at their meaning, he must substitute the fourth letter of the alphabet, namely D, for A, and so with the others.” • Thus: plain: ABCDEFGHIJKLMNOPQRSTUVWXYZ cipher: DEFGHIJKLMNOPQRSTUVWXYZABC • Exercise: Decrypt the following message: WKH TXLFN EURZQ IRA

13. Augustus’ Cipher • Suetonius description of Augustus’ cipher:“Whenever he wrote in cipher, he wrote B for A, C for B, and the rest of the letters on the same principle, using AA for Z.” • Thus: plain: ABCDEFGHIJKLMNOPQRSTUVWXY Z cipher: BCDEFGHIJKLMNOPQRSTUVWXYZ AA • Exercise: Encode zebra

14. Cracking Subsitution Ciphers • Frequency Analysis (9th century, Arabic)

15. The Letter E • Gadsby, by Ernest Wright, 1939 Preface: “THE ENTIRE MANUSCRIPT of this story was written with the E type-bar of the typewriter tied down; thus making it impossible for that letter to be printed. This was done so that none of that vowel might slip in.” • Chapter 1:“If youth, throughout all history, had had a champion to stand up for it; to show a doubting world that a child can think; and, possibly, do it practically; you wouldn’t constantly run across folks today who claim that “a child don’t know anything.” A child’s brain starts functioning at birth; and has, amongst its many infant convolutions, thousands of dormant atoms, into which God has put a mystic possibility for noticing an adult’s act, and figuring out its purport.”

16. Exercise • (Handout) Use the frequency table to break the message which has been encoded using a substitution cipher. • Important: We don’t know what substitution cipher was used! • There are 403291461126605635584000000 possible substitution ciphers. • Conclusion: Despite there being so many of them, substitution ciphers are fairly easy to break.