QL YB, LO KLQ QL YB: QEXQ FP QEB NRBPQFLK.

2. What does this code say? QL YB, LO KLQ QL YB: QEXQ FP QEB NRBPQFLK. TEBQEBO 'QFP KLYIBO FK QEB JFKA QL PRCCBO. QEB PIFKDP XKA XOOLTP LC LRQOXDBLRP CLOQRKB. LO QL QXHB XOJP XDXFKPQ X PBX LC QOLRYIBP. XKA YV LMMLPFKD BKA QEBJ? QL AFB: QL PIBBM.

3. What does this code say? QL YB, LO KLQ QL YB: QEXQ FP QEB NRBPQFLK. TEBQEBO 'QFP KLYIBO FK QEB JFKA QL PRCCBO. QEB PIFKDP XKA XOOLTP LC LRQOXDBLRP CLOQRKB. LO QL QXHB XOJP XDXFKPQ X PBX LC QOLRYIBP. XKA YV LMMLPFKD BKA QEBJ? QL AFB: QL PIBBM. Substitution Cipher Original a b c d e f g h i j…Code Letter D F I Q K X M Z R P… There are over 400,000,000,000,000,000,000,000,000 different Substitution Ciphers

4. What is the initial state? The cipher text QL YB, LO KLQ QL YB: QEXQ FP QEB NRBPQFLK. TEBQEBO 'QFP KLYIBO FK QEB JFKA QL PRCCBO. QEB PIFKDP XKA XOOLTP LC LRQOXDBLRP CLOQRKB. LO QL QXHB XOJP XDXFKPQ X PBX LC QOLRYIBP. XKA YV LMMLPFKD BKA QEBJ? QL AFB: QL PIBBM. What is the goal state? The plain text Note that this is an implicit goal state {Some English text}

5. What are the operators? QL YB, LO KLQ QL YB: QEXQ FP QEB NRBPQFLK. TEBQEBO 'QFP KLYIBO FK QEB JFKA QL PRCCBO. QEB PIFKDP XKA XOOLTP LC LRQOXDBLRP CLOQRKB. LO QL QXHB XOJP XDXFKPQ X PBX LC QOLRYIBP. XKA YV LMMLPFKD BKA QEBJ? QL AFB: QL PIBBM. Swap(Q,A) Swap(Q,B) Swap(Q,C) AL YB, LO KLAAL YB: AEXA FP AEB NRBPAFLK. TEBAEBO 'AFP KLYIBO FK AEB JFKA AL PRCCBO. AEB PIFKDP XKA XOOLTP LC LRAOXDBLRP CLOARKB. LO AL AXHB XOJP XDXFKPA X PBX LC AOLRYIBP. XKA YV LMMLPFKD BKA AEBJ? AL AFB: AL PIBBM. BL YB, LO KLBBL YB: BEXA FP BEB NRBPBFLK. TEBBEBO ‘BFP KLYIBO FK BEB JFKA BL PRCCBO. BEB PIFKDP XKA XOOLTP LC LRBOXDBLRP CLOBRKB. LO BL BXHB XOJP XDXFKPB X PBX LC BOLRYIBP. XKA YV LMMLPFKD BKA BEBJ? BL AFB: BL PIBBM. Swap(L,B) Swap(L,C) Swap(L,D) AC YB, CO KCAAL YB: AEXA FP AEB NRBPAFCK. TEBAEBO 'AFP KCYIBO FK AEB JFKA AL PRCCBO. AEB PIFKDP XKA XOOCTP CC CRAOXDBCRP CLOARKB. CO ACAXHB XOJP XDXFKPA X PBX CC AOCRYIBP. XKA YV CMMCPFKD BKA AEBJ? AL AFB: AC PIBBM. AB YB, BO KBAAL YB: AEXA FP AEB NRBPAFBK. TEBAEBO 'AFP KBYIBO FK AEB JFKA AL PRCCBO. AEB PIFKDP XKA XOOBTP BC BRAOXDBBRP CLOARKB. BO ABAXHB XOJP XDXFKPA X PBX BC AOBRYIBP. XKA YV BMMBPFKD BKA AEBJ? AL AFB: AB PIBBM.

6. The branching factor for the first level is 26, then 25 for the second level, then 24 etc The goal state (in fact, all terminal nodes) are at level 26. There are about 4.032 * 1026 terminal nodes If we search this blindly, we are in for a long wait…

7. Letter Frequency E 12.51 T 9.25 A 8.04 O 7.60 I 7.26 N 7.09 S 6.54 R 6.12 H 5.49 L 4.14 D 3.99 C 3.06 U 2.71 M 2.53 F 2.30 P 2.00 G 1.96 W 1.92 Y 1.73 B 1.54 V 0.99 K 0.67 X 0.19 J 0.16 Q 0.11 Z 0.09 Probability of Occurrence of Letters in English

8. Letter Frequency in Code A -> 0.030 B -> 0.121 C -> 0.030 D -> 0.024 E -> 0.042 F -> 0.054 G -> 0 H -> 0.006 I -> 0.024 J -> 0.018 K -> 0.072 L -> 0.121 M -> 0.018 N -> 0.006 O -> 0.066 P -> 0.084 Q -> 0.127 R -> 0.036 S -> 0 T -> 0.012 U -> 0 V -> 0.006 W -> 0 X -> 0.066 Y -> 0.030 Z -> 0 Letter Frequency in English E 0.125 T 0.925 A 0.804 O 0.760 I 0.726 N 0.709 S 0.654 R 0.612 H 0.549 L 0.414 D 0.399 C 0.306 U 0.271 M 0.253 F 0.230 P 0.200 G 0.196 W 0.192 Y 0.173 B 0.154 V 0.099 K 0.067 X 0.019 J 0.016 Q 0.011 Z 0.009

9. Letter Frequency in Code A -> 0.030 B -> 0.121 C -> 0.030 D -> 0.024 E -> 0.042 F -> 0.054 G -> 0 H -> 0.006 I -> 0.024 J -> 0.018 K -> 0.072 L -> 0.121 M -> 0.018 N -> 0.006 O -> 0.066 P -> 0.084 Q -> 0.127 R -> 0.036 S -> 0 T -> 0.012 U -> 0 V -> 0.006 W -> 0 X -> 0.066 Y -> 0.030 Z -> 0 Letter Frequency in English E 0.125 T 0.0925 A 0.0804 O 0.0760 I 0.0726 N 0.0709 S 0.0654 R 0.0612 H 0.0549 L 0.0414 D 0.0399 C 0.0306 U 0.0271 M 0.0253 F 0.0230 P 0.0200 G 0.0196 W 0.0192 Y 0.0173 B 0.0154 V 0.0099 K 0.0067 X 0.0019 J 0.0016 Q 0.0011 Z 0.0009 “E” is probably “B”, “L” or “Q” • Simple “trick” • Favor operators that are likely • Swap(B,E) • Swap(L,E) • Swap(Q,E) etc • How to do that?

10. Letter Frequency in Code A -> 0.030 B -> 0.121 C -> 0.030 D -> 0.024 E -> 0.042 F -> 0.054 G -> 0 H -> 0.006 I -> 0.024 J -> 0.018 K -> 0.072 L -> 0.121 M -> 0.018 N -> 0.006 O -> 0.066 P -> 0.084 Q -> 0.127 R -> 0.036 S -> 0 T -> 0.012 U -> 0 V -> 0.006 W -> 0 X -> 0.066 Y -> 0.030 Z -> 0 Letter Frequency in English E 0.125 • Give operators costs • Swap(B,E) = |f(B) – f(E)| = 0.004 • Swap(Z,E) = |f(Z) – f(E)| = 0.125 • Now we can do uniform search cost

11. Another idea We can tell that some states look more promising that others. Encode this information into a heuristic (not admissible) of some kind For example Imagine we are halfway down the tree and we need to find a swap for “S”…

12. Swap(O,S) Gives us no more new words TO YE, OSNOQ TO YE: THATIP THE NREPTION. THETHES 'TIP NOYIESINTHE JFNDTO PRCCES. THE PIINDP ANDASSOTP OC ORTSADELRP CLSTRNE. OSTOTAHEASJP ADAINPTA PEAOC TSORYIEP. AND YV OMMOPIND ENDTHEJ? TODIE: TO PIEEM. Swap(P,S) Gives us two more words, “IS” and “SEA” TO YE, OO NOQ TO YE: THATISTHE NRESTION. THETHEO 'TISNOYIEO INTHE JFNDTOSRCCEO. THESIINDSANDAOOOTSOC ORTOADELRS CLOTRNE. OO TOTAHEAOJSADAINSTASEAOC TOORYIES. AND YV OMMOSIND ENDTHEJ? TODIE: TOSIEEM.

13. To be, or not to be: that is the question: Whether 'tis nobler in the mind to suffer The slings and arrows of outrageous fortune Or to take arms against a sea of troubles And by opposing end them? To die: to sleep

14. Most Common Digrams and Trigrams in English

15. Brief Historical Context The idea that breaking codes is a search through many possibilities dates back to at least Roman times. The idea of using knowledge about the relative frequency of letters to act as a heuristic dates back to al-Kindi, an 9th century Arab scientist. However the first person to realize that code breaking could be mechanized was…

16. Alan Turing 1912-54 The Bombe

17. Highly recommended book