Breaking Caesar

All 26 shifts scored against English letter frequency, so a loop picks the winner instead of a person.

CryptanalysisChi-squaredemo

Objectives

Compute a chi-square distance from English and say what it measures.
Rank every candidate decryption and identify the key without reading them.
Explain why brute force needs a scoring function before it needs a bigger machine.

33%

χ² = Σ (observed − expected)² / expected, over the 26 letters. Lower is more English.

Plaintext

Shift k the sender used

ciphertext, which is all the attacker gets

ZHKDY HDPRO HDERU WWKHG HDO

Brute force needs a second thing nobody writes down: a way to recognize the right answer. Chi-square is that recognizer. It compares the letter counts of a candidate against English and returns one number, so a loop can pick the winner instead of a person.

Every shift, scored against English

k	χ²	candidate decryption
3	18.2	WEHAV EAMOL EABOR TTHED EAL
22	51.9	DLOHC LHTVS LHIVY AAOLK LHS
14	97.1	LTWPK TPBDA TPQDG IIWTS TPA
0	117.0	ZHKDY HDPRO HDERU WWKHG HDO
19	126.0	GORKF OKWYV OKLYB DDRON OKV
2	131.5	XFIBW FBNPM FBCPS UUIFE FBM
12	151.4	NVYRM VRDFC VRSFI KKYVU VRC
7	152.1	SADWR AWIKH AWXKN PPDAZ AWH
21	157.2	EMPID MIUWT MIJWZ BBPML MIT
9	164.3	QYBUP YUGIF YUVIL NNBYX YUF
16	177.0	JRUNI RNZBY RNOBE GGURQ RNY
25	243.3	AILEZ IEQSP IEFSV XXLIH IEP
5	260.3	UCFYT CYKMJ CYZMP RRFCB CYJ
15	318.8	KSVOJ SOACZ SOPCF HHVSR SOZ
11	335.0	OWZSN WSEGD WSTGJ LLZWV WSD
18	346.3	HPSLG PLXZW PLMZC EESPO PLW
1	401.2	YGJCX GCOQN GCDQT VVJGF GCN
23	476.7	CKNGB KGSUR KGHUX ZZNKJ KGR
6	729.3	TBEXS BXJLI BXYLO QQEBA BXI
10	736.7	PXATO XTFHE XTUHK MMAXW XTE
20	774.0	FNQJE NJVXU NJKXA CCQNM NJU
24	933.5	BJMFA JFRTQ JFGTW YYMJI JFQ
13	963.3	MUXQL UQCEB UQREH JJXUT UQB
4	1085.6	VDGZU DZLNK DZANQ SSGDC DZK
17	1228.1	IQTMH QMYAX QMNAD FFTQP QMX
8	1784.7	RZCVQ ZVHJG ZVWJM OOCZY ZVG

Sorted best first, so the answer is the top row. Shift 0 is in the list on purpose: a message nobody encrypted has to be able to win, or the attack cannot report “this was not a Caesar cipher”.

k = 3 beats the runner-up by 2.8×. On 23 letters that margin is thin. On a paragraph it is hundreds to one, and that is the whole reason the method scales past a keyspace you could read by eye.

step 1/3

CPE 645 / CS 685

Breaking Caesar

Letter Frequency Analysis

Breaking Monoalphabetic Substitution