Breaking Enigma with Index of Coincidence on a Commodore 64

Everything we’ve done so far requires a crib. The brute-force cracker tested candidate settings against known plaintext. Turing’s Bombe used contradictions between known plaintext and ciphertext to eliminate wrong settings. No crib, no attack.

But what if you intercepted a message and had no idea what it said? No weather report header, no formulaic greeting, no re-sent traffic. Just ciphertext.

William Friedman developed a tool for exactly this problem in 1922. It doesn’t need known plaintext. It doesn’t even need to know the language. It measures whether a piece of text looks like language at all or whether it looks like random noise. He called it the index of coincidence.

What the Index of Coincidence Measures

Pick two random letters from a piece of English text. What’s the probability they’re the same letter? Not very high, but higher than you’d think, because letter frequencies aren’t uniform. E appears about 13% of the time. Z appears less than 0.1%. Two randomly chosen letters are more likely to both be E than to both be Z.

For English text, the probability of a match is about 0.0667. For German it’s about the same (0.0762 by some measurements, but the exact number depends on the text). For truly random text where all 26 letters are equally likely, it’s 1/26 = 0.0385.

That difference is the entire attack. Decrypt a ciphertext with the wrong Enigma settings and the output looks random: IC near 0.038. Decrypt with the right settings and the output is German: IC near 0.067. No crib needed. The statistical properties of the language itself are the signal.

The Formula

The IC of a text with N letters is:

$$IC = \frac{\sum_{i=0}^{25} n_i \cdot (n_i - 1)}{N \cdot (N - 1)}$$

where $n_i$ is how many times letter $i$ appears. The numerator counts how many ways you could pick two copies of the same letter. The denominator counts how many ways you could pick any two letters. The ratio is the probability that two randomly chosen letters match.

For a C64 implementation, we don’t need the division. We just compute the numerator (call it the IC sum) and compare it to a threshold. If IC should be above 0.050, that means the sum should be above $0.050 \times N \times (N-1)$. For a 60-character message, that’s $0.050 \times 60 \times 59 = 177$. A 16-bit integer comparison. No floating point needed. The C64’s BASIC ROM has a full floating-point engine, but we don’t have to touch it.

Why the Plugboard Doesn’t Matter

This is the best part. The plugboard is a monoalphabetic substitution: it swaps pairs of letters before and after the rotors. If R and M are swapped, every R in the output becomes M and every M becomes R. But the total count of each pair stays the same. The letter that appeared 8 times still appears 8 times, it just has a different name.

The IC doesn’t care about which letters are frequent. It only cares about how frequent the most frequent letters are. A text where E appears 13% of the time has the same IC as a text where Q appears 13% of the time. The plugboard rearranges the labels on the frequency bins without changing the bin sizes.

This means IC attacks only the rotor settings (5.9 million candidates, or 103.9 billion with ring settings). Once you’ve found the right rotors and positions, you can solve the plugboard separately using frequency analysis. A Bombe solves both at once. IC splits them into two smaller problems.

The Scenario

In the brute-force cracker, we intercepted a U-boat weather report from the Bay of Biscay and used “WETTER” as a crib to find the settings. This time, we have a longer intercept from the same transmission, but we don’t know it’s a weather report. We don’t know anything about the plaintext. All we have is 60 characters of ciphertext:

YDMAOIGMPQZPFVRCIGIIKJVECBDNPDITBYRYNKOCNJHIIVWXYUJBCDYGKVHW

The correct settings are still rotors III-I-V at positions M-C-Q. We need to find them using nothing but the statistical fingerprint of the German language.

How Well Does It Work?

Before writing code, let’s check the numbers. Decrypt the ciphertext with all 17,576 positions for the correct rotor ordering (III-I-V) and compute the IC of each result.

The correct decryption (M-C-Q) has an IC of 0.0729 and an IC sum of 258. The text reads WETTERVORHERSAGEBISKAYAHEUTEREGENMITWINDSTAERKEFUENFAUSOSTEN. “Weather forecast Biscay, today rain with wind strength five from east.” A routine U-boat weather report.

At different thresholds, here’s how many of the 17,576 positions survive for a single rotor ordering (III-I-V):

The BASIC version searches one ordering at a time, so a threshold of 177 (IC >= 0.050) is reasonable at 286 candidates per ordering. The assembly version searches all 336 orderings, so it uses a tighter threshold of 194 (IC >= 0.055) to keep the output manageable. At 194, roughly 49 candidates survive per ordering, about 18,165 total across all 336.

Even with that filtering, you can’t just sort by IC and pick the winner. The correct answer ranks #42 out of those 18,165 candidates. The top 10 are all gibberish with repeated letters that inflate the score.

With only 60 characters, random letter distributions can outscore real language. The correct answer stands out because it’s the only one that reads like German, not because it has the highest score. You find it by reading the printer output, not by sorting a spreadsheet.

Longer messages stabilize the IC. With 200+ characters, the correct decryption reliably scores highest. With 60, you need a threshold that keeps a manageable number of candidates for human review.

Pseudocode

for each rotor ordering (336 permutations):
  for each starting position (17,576 per ordering):
    decrypt the entire ciphertext with this setting
    count letter frequencies (26 bins)
    compute IC sum = sum of n_i * (n_i - 1)
    if IC sum >= threshold:
      CANDIDATE FOUND, print settings and decryption

The per-candidate cost is higher than the brute-force cracker. That approach tested the first character of the crib and bailed immediately on mismatch, averaging about one encryption per candidate. IC requires encrypting the entire message: 60 encryptions for our 60-character ciphertext, plus the frequency counting and sum computation.

But there’s no crib to find. No interrogating captured submariners, no stealing codebooks. Just raw ciphertext and math.

Across all 5.9 million candidates (336 orderings), a threshold of 0.050 produces about 94,887 hits (1.6%). The correct answer is among them, but so are thousands of gibberish decryptions that happen to have uneven letter distributions. A human scanning the output would spot the readable German, but an automated system would need additional filtering (bigram frequencies, dictionary checks, or a higher threshold that risks missing the answer).

BASIC Version

The BASIC version searches all 17,576 positions for a single rotor ordering. The rotor wiring, stepping, and encryption subroutines are identical to the cracker. The new code is the IC computation.

5 PRINT CHR$(5)
10 PRINT CHR$(147);"  ENIGMA IC ATTACK"
20 PRINT "  INDEX OF COINCIDENCE":PRINT
100 DIM RF(7,25),RI(7,25),RE(25)
110 FOR R=0 TO 7:FOR I=0 TO 25
120 READ RF(R,I):NEXT I,R
200 DATA 4,10,12,5,11,6,3,16,21,25
210 DATA 13,19,14,22,24,7,23,20,18,15
220 DATA 0,8,1,17,2,9
230 DATA 0,9,3,10,18,8,17,20,23,1
240 DATA 11,7,22,19,12,2,16,6,25,13
250 DATA 15,24,5,21,14,4
260 DATA 1,3,5,7,9,11,2,15,17,19
270 DATA 23,21,25,13,24,4,8,22,6,0
280 DATA 10,12,20,18,16,14
290 DATA 4,18,14,21,15,25,9,0,24,16
300 DATA 20,8,17,7,23,11,13,5,19,6
310 DATA 10,3,2,12,22,1
320 DATA 21,25,1,17,6,8,19,24,20,15
330 DATA 18,3,13,7,11,23,0,22,12,9
340 DATA 16,14,5,4,2,10
350 DATA 9,15,6,21,14,20,12,5,24,16
360 DATA 1,4,13,7,25,17,3,10,0,18
370 DATA 23,11,8,2,19,22
380 DATA 13,25,9,7,6,17,2,23,12,24
390 DATA 18,22,1,14,20,5,0,8,21,11
395 DATA 15,4,10,16,3,19
400 DATA 5,10,16,7,19,11,23,14,2,1
410 DATA 9,18,15,3,25,17,0,12,4,22
420 DATA 13,8,20,24,6,21
450 REM COMPUTE INVERSE TABLES
460 FOR R=0 TO 7:FOR I=0 TO 25
470 RI(R,RF(R,I))=I
480 NEXT I,R
500 REM REFLECTOR UKW-B
510 FOR I=0 TO 25:READ RE(I):NEXT
520 DATA 24,17,20,7,16,18,11,3,15,23
530 DATA 13,6,14,10,12,8,4,1,5,25
540 DATA 2,22,21,9,0,19
600 REM NOTCH POSITIONS (TWO PER ROTOR)
610 DIM NO(7,1)
620 NO(0,0)=16:NO(0,1)=-1
630 NO(1,0)=4:NO(1,1)=-1
640 NO(2,0)=21:NO(2,1)=-1
650 NO(3,0)=9:NO(3,1)=-1
660 NO(4,0)=25:NO(4,1)=-1
670 NO(5,0)=25:NO(5,1)=12
680 NO(6,0)=25:NO(6,1)=12
690 NO(7,0)=25:NO(7,1)=12
700 REM CIPHERTEXT (60 CHARS, 0-25)
710 DIM CT(59)
720 CT$="YDMAOIGMPQZPFVRCIGIIKJV"
725 CT$=CT$+"ECBDNPDITBYRYNKOCNJHII"
727 CT$=CT$+"VWXYUJBCDYGKVHW"
730 FOR I=0 TO 59
740 CT(I)=ASC(MID$(CT$,I+1,1))-65
750 NEXT
760 NL=60:TH=177
770 DIM FR(25)
800 PRINT "SELECT 3 ROTORS (1-8)"
810 INPUT "LEFT ROTOR";RL
820 INPUT "MIDDLE ROTOR";RM
830 INPUT "RIGHT ROTOR";RR
840 RL=RL-1:RM=RM-1:RR=RR-1
850 PRINT:PRINT "SEARCHING 17,576 POSITIONS"
860 PRINT "FOR ROTORS";RL+1;"-";RM+1;"-";RR+1
865 PRINT "THRESHOLD:";TH
870 PRINT:TI$="000000":SC=0
900 FOR L0=0 TO 25
910 PRINT CHR$(L0+65);" ";
920 FOR M0=0 TO 25:FOR R0=0 TO 25
930 GOSUB 5000
940 IF F=1 THEN GOSUB 7000
950 NEXT R0,M0,L0
960 PRINT:PRINT
970 PRINT SC;"CANDIDATES FOUND"
975 PRINT "TIME:";INT(TI/60);"SECONDS"
980 END
2000 REM STEP ROTORS
2010 IF MP<>NO(RM,0)ANDMP<>NO(RM,1) THEN 2040
2020 LP=LP+1:LP=LP-INT(LP/26)*26
2030 MP=MP+1:MP=MP-INT(MP/26)*26
2040 IF RP<>NO(RR,0)ANDRP<>NO(RR,1) THEN 2060
2050 MP=MP+1:MP=MP-INT(MP/26)*26
2060 RP=RP+1:RP=RP-INT(RP/26)*26
2070 RETURN
3000 REM ENCRYPT (FORWARD)
3010 E=(C+RP):E=E-INT(E/26)*26
3020 C=RF(RR,E)
3030 C=(C-RP+26):C=C-INT(C/26)*26
3040 E=(C+MP):E=E-INT(E/26)*26
3050 C=RF(RM,E)
3060 C=(C-MP+26):C=C-INT(C/26)*26
3070 E=(C+LP):E=E-INT(E/26)*26
3080 C=RF(RL,E)
3090 C=(C-LP+26):C=C-INT(C/26)*26
3100 REM REFLECTOR
3110 C=RE(C)
3120 REM ENCRYPT (INVERSE)
3130 E=(C+LP):E=E-INT(E/26)*26
3140 C=RI(RL,E)
3150 C=(C-LP+26):C=C-INT(C/26)*26
3160 E=(C+MP):E=E-INT(E/26)*26
3170 C=RI(RM,E)
3180 C=(C-MP+26):C=C-INT(C/26)*26
3190 E=(C+RP):E=E-INT(E/26)*26
3200 C=RI(RR,E)
3210 C=(C-RP+26):C=C-INT(C/26)*26
3220 RETURN
5000 REM IC TEST
5010 LP=L0:MP=M0:RP=R0
5020 REM CLEAR FREQUENCY TABLE
5030 FOR I=0 TO 25:FR(I)=0:NEXT
5040 REM DECRYPT AND COUNT
5050 FOR I=0 TO NL-1
5060 C=CT(I):GOSUB 2000:GOSUB 3000
5070 FR(C)=FR(C)+1
5080 NEXT
5090 REM COMPUTE IC SUM
5100 S=0
5110 FOR I=0 TO 25
5120 S=S+FR(I)*(FR(I)-1)
5130 NEXT
5140 IF S>=TH THEN F=1:RETURN
5150 F=0:RETURN
7000 REM SHOW CANDIDATE
7010 SC=SC+1
7020 PRINT:PRINT "CANDIDATE";SC
7030 PRINT "POSITION: ";CHR$(L0+65);"-";
7035 PRINT CHR$(M0+65);"-";CHR$(R0+65)
7040 PRINT "IC SUM:";S
7050 LP=L0:MP=M0:RP=R0
7060 FOR I=0 TO NL-1
7070 C=CT(I):GOSUB 2000:GOSUB 3000
7080 PRINT CHR$(C+65);
7090 NEXT
7100 PRINT:RETURN

The IC test at line 5000 is where the action is. It decrypts all 60 characters, counts the frequency of each letter in the FR array, then computes the IC sum: $\sum n_i \times (n_i - 1)$. If the sum meets the threshold (177, corresponding to IC >= 0.050), it’s a candidate.

Line 7000 prints each candidate with its position, IC sum, and decrypted text so you can scan for readable German.

The threshold of 177 comes from $0.050 \times 60 \times 59 = 177$. Lower it and you get more candidates (and more false positives). Raise it and you might miss the correct answer if the IC is noisy. For a 60-character message, 177 is a reasonable middle ground.

To check that it’s working, enter rotors 3, 1, 5 (the correct ordering from the previous articles). The program searches all 17,576 positions and prints each candidate that passes the threshold. Most of the output is gibberish with IC sums in the 180-200 range. But candidate 146 jumps out:

CANDIDATE 146
POSITION: M-C-Q
IC SUM: 258
WETTERVORHERSAGEBISKAYAHEUTEREGENMITWINDSTAERKEFUENFAUSOSTEN

That’s readable German. IC sum 258, well above the threshold of 177. Out of 286 total candidates for this rotor ordering, this is the only one that’s actual language. The rest are random letter salad that happened to have uneven frequency distributions.

Try entering a wrong ordering like 1, 2, 3. You’ll still get candidates (any ordering produces a few statistical flukes), but none of them will be readable. That’s the difference: wrong settings produce noise that occasionally looks uneven, while the right settings produce text that looks like German because it is German.

Assembly Version

The assembly version does the full search: all 336 rotor orderings, all 17,576 positions each. The structure is identical to the cracker, with the crib test replaced by the IC computation.

Here’s what the C64 has to chew through:

Over two billion rotor passes on a 1 MHz processor. The C64’s theoretical peak is about 0.5 MIPS (all 2-cycle instructions, which never happens in practice). Real-world throughput with mixed instructions is closer to 0.3 MIPS. Over 82 hours, the 6510 executes roughly 87 billion instructions and burns through 303 billion clock cycles. For more on what the 6510 can and can’t do at 1 MHz, see How Fast Can a 6502 Transfer Memory?.

The brute-force cracker averaged about one encryption per candidate thanks to early exit. The IC attack does 60 every time, no shortcuts.

The IC Test

The IC test decrypts the entire message, counts letter frequencies in a 26-byte table, and computes the IC sum as a 16-bit value:

; ic test
; decrypts ciphertext, computes ic sum
; returns z flag set if sum >= threshold
testic
          ; clear frequency table
          ldx #25
          lda #0
ticlr    sta freq,x
          dex
          bpl ticlr

          ; set starting positions
          lda trylp
          sta leftpos
          lda trymp
          sta midpos
          lda tryrp
          sta rightpos

          ; decrypt and count
          ldx #0
tidec    lda cipher,x
          stx savex
          jsr encrypt
          ; increment freq[a]
          tax
          inc freq,x
          ldx savex
          inx
          cpx #60
          bne tidec

          ; compute ic sum (16-bit)
          ; sum = sigma(freq[i]*(freq[i]-1))
          lda #0
          sta iclo
          sta ichi
          ldx #0
tisum    lda freq,x
          beq tiskip
          ; a = n = freq[i]
          ; compute n*(n-1)
          ; freq values max ~10 for 60 chars
          ; so product fits in one byte
          tay
          dey
          sty temp
          iny
          lda #0
          clc
timul    adc temp
          dey
          bne timul
          ; add to 16-bit sum
          clc
          adc iclo
          sta iclo
          bcc tiskip
          inc ichi
tiskip   inx
          cpx #26
          bne tisum

          ; compare sum to threshold (194)
          ; 16-bit compare: ichi:iclo >= 0:194
          lda ichi
          bne tipass
          lda iclo
          cmp #194
          bcs tipass
          lda #1
          rts
tipass   lda #0
          rts

The frequency counting is simple: decrypt each character with jsr encrypt, use the result as an index into freq, and increment. After all 60 characters, loop through the 26 frequency bins computing $n \times (n-1)$ for each. The maximum possible IC sum (if all 60 characters were the same letter) would be $60 \times 59 = 3540$, which fits in 16 bits. We accumulate the total in iclo/ichi.

The multiplication uses repeated addition. With frequency values rarely above 10 for a 60-character message, this loop runs at most 10 iterations per bin. For bins with count 0 or 1, the product is zero and we skip the multiply entirely.

The threshold compare is a 16-bit check. If the high byte is nonzero, the sum is at least 256, which is above 194, so it passes immediately. Otherwise compare the low byte to 194.

The assembly version uses a tighter threshold (194, IC >= 0.055) than the BASIC version (177, IC >= 0.050). The BASIC version searches one rotor ordering at a time, so 286 candidates is manageable. The assembly version searches all 336 orderings, and at 177 that would produce roughly 95,000 candidates. At 194, it drops to about 16,500. The correct answer scores 258, so it passes either threshold easily.

The Search Loop

The position loop calls testic instead of the loop test and crib verification. There’s no two-phase filtering here, just one test:

sprp
          ; test ic
          jsr testic
          beq tifound

          ; failed
          inc tryrp
          lda tryrp
          cmp #26
          bne sprp
          inc trymp
          lda trymp
          cmp #26
          bne spmp
          inc trylp
          lda trylp
          cmp #26
          bne splp
          rts

tifound
          ; print candidate
          jsr showcand
          ; keep searching (don't stop)
          jmp tinext

One difference from the cracker: we don’t stop at the first match. The IC test produces multiple candidates, so we print each one and keep searching. The operator reads the output and picks the one that looks like German.

In practice, you’d want a printer connected. The search runs for hours and produces thousands of candidates. They scroll off a 25-line screen long before the search finishes. With a printer, you get a paper log to read through when it’s done. open 4,4:cmd 4 before running redirects output to a Commodore printer. print#4:close 4 when finished.

Showing Candidates

When a candidate passes the IC test, we print the rotor ordering, position, IC sum, and the first 40 characters of the decrypted text. The operator scans for readable German among the gibberish:

showcand
          lda #13
          jsr chrout
          ; print position
          lda trylp
          clc
          adc #65
          jsr chrout
          lda #45
          jsr chrout
          lda trymp
          clc
          adc #65
          jsr chrout
          lda #45
          jsr chrout
          lda tryrp
          clc
          adc #65
          jsr chrout
          lda #32
          jsr chrout
          ; print ic sum
          lda ichi
          ldx iclo
          jsr $bdcd
          lda #32
          jsr chrout
          ; decrypt and print first 40 chars
          lda trylp
          sta leftpos
          lda trymp
          sta midpos
          lda tryrp
          sta rightpos
          ldx #0
scloop   lda cipher,x
          stx savex
          jsr encrypt
          clc
          adc #65
          jsr chrout
          ldx savex
          inx
          cpx #40
          bne scloop
          rts

The Full Listing

Here’s the complete IC attack. It assembles at $c000 and runs with sys 49152. The rotor wiring, stepping, encryption, and search structure are identical to the cracker. The only new code is testic and showcand. The border color changes with each new rotor ordering, so if it’s still cycling, it’s still searching.

Same advice about the printer applies here. The assembly version searches all 336 orderings and produces thousands of candidates over several hours. Hook up a printer before running, or you’ll only see whatever’s still on screen when it finishes:

OPEN 4,4:CMD 4:SYS 49152:PRINT#4:CLOSE 4

; ==============================
; enigma ic attack
; index of coincidence search
; commodore 64
; rotors i-viii (m3), no plugboard
; turbo macro pro / tmpx
; by michael doornbos 2026
; mike@imapenguin.com
;
; decrypts ciphertext with each
; candidate setting, computes ic
; of the result, flags candidates
; with ic above threshold
;
; no crib needed
;
; .null/.text = screen codes
; use .byte for petscii strings
; ==============================

* = $c000

; --- zero page ---
ptr       = $50
rightpos = $fb
midpos   = $fc
leftpos  = $fd
temp      = $fe

chrout    = $ffd2

; === entry point ===
          ; zero jiffy clock and accumulator
          lda #0
          sta $a2
          sta $a1
          sta $a0
          sta jtotal
          sta jtotal+1
          sta jtotal+2
          sta jtotal+3

          ; cls, white text
          lda #$93
          jsr chrout
          lda #5
          jsr chrout
          lda #13
          jsr chrout

          ; header
          ldx #<stitle
          ldy #>stitle
          jsr print
          lda #13
          jsr chrout
          ldx #<ssub
          ldy #>ssub
          jsr print
          lda #13
          jsr chrout
          lda #13
          jsr chrout

          ; searching message
          ldx #<ssearch
          ldy #>ssearch
          jsr print
          lda #13
          jsr chrout

          ; init candidate count
          lda #0
          sta candlo
          sta candhi

          ; run search
          jsr searchall

          ; restore border
          lda #14
          sta $d020

          ; show total
          lda #13
          jsr chrout
          lda #13
          jsr chrout
          ldx #<stotal
          ldy #>stotal
          jsr print
          lda candhi
          ldx candlo
          jsr $bdcd
          ldx #<scands
          ldy #>scands
          jsr print
          lda #13
          jsr chrout

          ; show elapsed time
          ldx #<stime
          ldy #>stime
          jsr print
          jsr jiffysec
          lda #13
          jsr chrout
          rts

; === search all orderings ===
; p(8,3) = 336 permutations
searchall
          lda #0
          sta tryl
saleft   lda #0
          sta trym
samid    lda trym
          cmp tryl
          beq sasm
          lda #0
          sta tryr
saright  lda tryr
          cmp tryl
          beq sasr
          cmp trym
          beq sasr
          ; valid permutation
          jsr searchpos
sasr     inc tryr
          lda tryr
          cmp #8
          bne saright
sasm     inc trym
          lda trym
          cmp #8
          bne samid
          inc tryl
          lda tryl
          cmp #8
          bne saleft
sadone   rts

; === search positions ===
; 26^3 = 17,576 per ordering
searchpos
          ; accumulate jiffy clock, then zero it
          ; prevents kernal midnight reset (24h)
          sei
          clc
          lda jtotal
          adc $a2
          sta jtotal
          lda jtotal+1
          adc $a1
          sta jtotal+1
          lda jtotal+2
          adc $a0
          sta jtotal+2
          bcc jnoc
          inc jtotal+3
jnoc      lda #0
          sta $a2
          sta $a1
          sta $a0
          cli
          ; configure rotors
          lda tryl
          sta leftsel
          lda trym
          sta midsel
          lda tryr
          sta rightsel
          ; border color = progress
          inc $d020
          ; sweep all positions
          lda #0
          sta trylp
splp     lda #0
          sta trymp
spmp     lda #0
          sta tryrp
sprp
          ; test ic
          jsr testic
          beq tifound
          ; failed
          jmp tinext
tifound
          ; show candidate
          jsr showcand
tinext   inc tryrp
          lda tryrp
          cmp #26
          bne sprp
          inc trymp
          lda trymp
          cmp #26
          bne spmp
          inc trylp
          lda trylp
          cmp #26
          bne splp
          rts

; === test ic ===
; decrypts ciphertext
; computes ic sum
; returns z flag set if >= threshold
testic
          ; clear frequency table
          ldx #25
          lda #0
ticlr    sta freq,x
          dex
          bpl ticlr

          ; set starting positions
          lda trylp
          sta leftpos
          lda trymp
          sta midpos
          lda tryrp
          sta rightpos

          ; decrypt all 60 chars
          ldx #0
tidec    lda cipher,x
          stx savex
          jsr encrypt
          ; count frequency
          tax
          inc freq,x
          ldx savex
          inx
          cpx #60
          bne tidec

          ; compute ic sum (16-bit)
          lda #0
          sta iclo
          sta ichi
          ldx #0
tisum    lda freq,x
          beq tiskp
          cmp #1
          beq tiskp
          ; a = n, compute n*(n-1)
          tay
          dey
          sty temp
          iny
          lda #0
          clc
timul    adc temp
          dey
          bne timul
          ; add to 16-bit sum
          clc
          adc iclo
          sta iclo
          bcc tiskp
          inc ichi
tiskp    inx
          cpx #26
          bne tisum

          ; compare to threshold 194
          lda ichi
          bne tiyes
          lda iclo
          cmp #194
          bcs tiyes
          ; below threshold
          lda #1
          rts
tiyes    lda #0
          rts

; === show candidate ===
showcand
          ; increment count
          inc candlo
          bne scnoc
          inc candhi
scnoc
          lda #13
          jsr chrout
          ; print ordering
          ldx leftsel
          jsr printrn
          lda #45
          jsr chrout
          ldx midsel
          jsr printrn
          lda #45
          jsr chrout
          ldx rightsel
          jsr printrn
          lda #32
          jsr chrout
          ; print position
          lda trylp
          clc
          adc #65
          jsr chrout
          lda #45
          jsr chrout
          lda trymp
          clc
          adc #65
          jsr chrout
          lda #45
          jsr chrout
          lda tryrp
          clc
          adc #65
          jsr chrout
          lda #32
          jsr chrout
          ; print ic sum
          lda ichi
          ldx iclo
          jsr $bdcd
          lda #32
          jsr chrout
          ; decrypt first 40 chars
          lda trylp
          sta leftpos
          lda trymp
          sta midpos
          lda tryrp
          sta rightpos
          ldx #0
scloop   lda cipher,x
          stx savex
          jsr encrypt
          clc
          adc #65
          jsr chrout
          ldx savex
          inx
          cpx #40
          bne scloop
          rts

; === encrypt ===
; a = letter (0-25) in/out
; no plugboard (identity)
encrypt   pha
          jsr step
          pla
          ; right fwd
          ldx rightsel
          jsr setfwd
          ldx rightpos
          jsr rotorpass
          ; middle fwd
          ldx midsel
          jsr setfwd
          ldx midpos
          jsr rotorpass
          ; left fwd
          ldx leftsel
          jsr setfwd
          ldx leftpos
          jsr rotorpass
          ; reflector
          tax
          lda reflector,x
          ; left inv
          ldx leftsel
          jsr setinv
          ldx leftpos
          jsr rotorpass
          ; middle inv
          ldx midsel
          jsr setinv
          ldx midpos
          jsr rotorpass
          ; right inv
          ldx rightsel
          jsr setinv
          ldx rightpos
          jsr rotorpass
          rts

; === step rotors ===
; dual notch for vi-viii
step
          ldx midsel
          lda midpos
          cmp notch1,x
          beq dodouble
          cmp notch2,x
          bne nodouble
dodouble
          ; double step
          lda leftpos
          clc
          adc #1
          jsr mod26
          sta leftpos
          lda midpos
          clc
          adc #1
          jsr mod26
          sta midpos
          jmp stepright
nodouble
          ldx rightsel
          lda rightpos
          cmp notch1,x
          beq domid
          cmp notch2,x
          bne stepright
domid    lda midpos
          clc
          adc #1
          jsr mod26
          sta midpos
stepright
          lda rightpos
          clc
          adc #1
          jsr mod26
          sta rightpos
          rts

; === mod26 ===
mod26     cmp #26
          bcc m26done
          sbc #26
m26done   rts

; === rotor pass ===
rotorpass
          stx temp
          clc
          adc temp
          jsr mod26
          tay
          lda (ptr),y
          sec
          sbc temp
          clc
          adc #26
          jsr mod26
          rts

; === set table pointer ===
setfwd   ldy fwdlo,x
          sty ptr
          ldy fwdhi,x
          sty ptr+1
          rts

setinv   ldy invlo,x
          sty ptr
          ldy invhi,x
          sty ptr+1
          rts

; === print string ===
; x=lo, y=hi, null-terminated
print     stx ptr
          sty ptr+1
          ldy #0
ploop     lda (ptr),y
          beq pdone
          jsr chrout
          iny
          bne ploop
pdone     rts

; === print rotor name ===
; x = rotor index (0-7)
printrn
          lda rnlo,x
          sta ptr
          lda rnhi,x
          sta ptr+1
          ldy #0
rnloop    lda (ptr),y
          beq rndone
          jsr chrout
          iny
          bne rnloop
rndone    rts

; === jiffy clock to hours/minutes ===
; adds remaining jiffies to 32-bit total
; divides by 60 three times: jiffies->sec->min->hr
jiffysec
          ; add remaining jiffies to accumulator
          sei
          clc
          lda jtotal
          adc $a2
          sta dividend+3
          lda jtotal+1
          adc $a1
          sta dividend+2
          lda jtotal+2
          adc $a0
          sta dividend+1
          lda jtotal+3
          adc #0
          sta dividend
          cli
          ; 32-bit divide by 60
          lda #0
          sta remainder
          ldx #32
jsloop    asl dividend+3
          rol dividend+2
          rol dividend+1
          rol dividend
          rol remainder
          lda remainder
          cmp #60
          bcc jsskip
          sbc #60
          sta remainder
          inc dividend+3
jsskip    dex
          bne jsloop
          ; dividend = total seconds
          ; divide by 60 to get minutes
          lda dividend
          sta jsecs
          lda dividend+1
          sta jsecs+1
          lda dividend+2
          sta jsecs+2
          lda dividend+3
          sta jsecs+3
          lda #0
          sta remainder
          ldx #32
jsloop2   asl jsecs+3
          rol jsecs+2
          rol jsecs+1
          rol jsecs
          rol remainder
          lda remainder
          cmp #60
          bcc jsskp2
          sbc #60
          sta remainder
          inc jsecs+3
jsskp2    dex
          bne jsloop2
          ; divide minutes by 60 to get hours
          lda #0
          sta remainder
          ldx #32
jsloop3   asl jsecs+3
          rol jsecs+2
          rol jsecs+1
          rol jsecs
          rol remainder
          lda remainder
          cmp #60
          bcc jsskp3
          sbc #60
          sta remainder
          inc jsecs+3
jsskp3    dex
          bne jsloop3
          ; print hours
          lda jsecs+2
          ldx jsecs+3
          jsr $bdcd
          lda #72  ; 'h'
          jsr chrout
          lda #32
          jsr chrout
          ; print remaining minutes
          lda #0
          ldx remainder
          jsr $bdcd
          lda #77  ; 'm'
          jsr chrout
          rts

dividend  .byte 0,0,0,0
jsecs     .byte 0,0,0,0
remainder .byte 0

; === data ===

; search state
savex     .byte 0
jtotal    .byte 0,0,0,0
tryl     .byte 0
trym     .byte 0
tryr     .byte 0
trylp    .byte 0
trymp    .byte 0
tryrp    .byte 0

; rotor config
rightsel .byte 0
midsel   .byte 0
leftsel  .byte 0

; ic state
iclo     .byte 0
ichi     .byte 0
candlo   .byte 0
candhi   .byte 0

; frequency table (26 bytes)
freq      .repeat 26,0

; ciphertext (60 chars, 0-25)
cipher    .byte 24,3,12,0,14,8
          .byte 6,12,15,16,25,15
          .byte 5,21,17,2,8,6
          .byte 8,8,10,9,21,4
          .byte 2,1,3,13,15,3
          .byte 8,19,1,24,17,24
          .byte 13,10,14,2,13,9
          .byte 7,8,8,21,22,23
          .byte 24,20,9,1,2,3
          .byte 24,6,10,21,7,22

; notch positions (i-viii)
notch1    .byte 16,4,21,9,25
          .byte 25,25,25
; second notch ($ff = none)
notch2    .byte $ff,$ff,$ff,$ff,$ff
          .byte 12,12,12

; address tables (rotors i-viii)
fwdlo    .byte <rot1f,<rot2f
          .byte <rot3f,<rot4f
          .byte <rot5f,<rot6f
          .byte <rot7f,<rot8f
fwdhi    .byte >rot1f,>rot2f
          .byte >rot3f,>rot4f
          .byte >rot5f,>rot6f
          .byte >rot7f,>rot8f
invlo    .byte <rot1i,<rot2i
          .byte <rot3i,<rot4i
          .byte <rot5i,<rot6i
          .byte <rot7i,<rot8i
invhi    .byte >rot1i,>rot2i
          .byte >rot3i,>rot4i
          .byte >rot5i,>rot6i
          .byte >rot7i,>rot8i

; === rotor wiring ===

; i: ekmflgdqvzntowyhxuspaibrcj
rot1f    .byte 4,10,12,5,11,6
          .byte 3,16,21,25,13,19
          .byte 14,22,24,7,23,20
          .byte 18,15,0,8,1,17
          .byte 2,9

; ii: ajdksiruxblhwtmcqgznpyfvoe
rot2f    .byte 0,9,3,10,18,8
          .byte 17,20,23,1,11,7
          .byte 22,19,12,2,16,6
          .byte 25,13,15,24,5,21
          .byte 14,4

; iii: bdfhjlcprtxvznyeiwgakmusqo
rot3f    .byte 1,3,5,7,9,11
          .byte 2,15,17,19,23,21
          .byte 25,13,24,4,8,22
          .byte 6,0,10,12,20,18
          .byte 16,14

; iv: esovpzjayquirhxlnftgkdcmwb
rot4f    .byte 4,18,14,21,15,25
          .byte 9,0,24,16,20,8
          .byte 17,7,23,11,13,5
          .byte 19,6,10,3,2,12
          .byte 22,1

; v: vzbrgityupsdnhlxawmjqofeck
rot5f    .byte 21,25,1,17,6,8
          .byte 19,24,20,15,18,3
          .byte 13,7,11,23,0,22
          .byte 12,9,16,14,5,4
          .byte 2,10

; vi: jpgvoumfyqbenhzrdkasxlictw
rot6f    .byte 9,15,6,21,14,20
          .byte 12,5,24,16,1,4
          .byte 13,7,25,17,3,10
          .byte 0,18,23,11,8,2
          .byte 19,22

; vii: nzjhgrcxmyswboufaivlpekqdt
rot7f    .byte 13,25,9,7,6,17
          .byte 2,23,12,24,18,22
          .byte 1,14,20,5,0,8
          .byte 21,11,15,4,10,16
          .byte 3,19

; viii: fkqhtlxocbjspdzramewniuygv
rot8f    .byte 5,10,16,7,19,11
          .byte 23,14,2,1,9,18
          .byte 15,3,25,17,0,12
          .byte 4,22,13,8,20,24
          .byte 6,21

; inverse tables

rot1i    .byte 20,22,24,6,0,3
          .byte 5,15,21,25,1,4
          .byte 2,10,12,19,7,23
          .byte 18,11,17,8,13,16
          .byte 14,9

rot2i    .byte 0,9,15,2,25,22
          .byte 17,11,5,1,3,10
          .byte 14,19,24,20,16,6
          .byte 4,13,7,23,12,8
          .byte 21,18

rot3i    .byte 19,0,6,1,15,2
          .byte 18,3,16,4,20,5
          .byte 21,13,25,7,24,8
          .byte 23,9,22,11,17,10
          .byte 14,12

rot4i    .byte 7,25,22,21,0,17
          .byte 19,13,11,6,20,15
          .byte 23,16,2,4,9,12
          .byte 1,18,10,3,24,14
          .byte 8,5

rot5i    .byte 16,2,24,11,23,22
          .byte 4,13,5,19,25,14
          .byte 18,12,21,9,20,3
          .byte 10,6,8,0,17,15
          .byte 7,1

rot6i    .byte 18,10,23,16,11,7
          .byte 2,13,22,0,17,21
          .byte 6,12,4,1,9,15
          .byte 19,24,5,3,25,20
          .byte 8,14

rot7i    .byte 16,12,6,24,21,15
          .byte 4,3,17,2,22,19
          .byte 8,0,13,20,23,5
          .byte 10,25,14,18,11,7
          .byte 9,1

rot8i    .byte 16,9,8,13,18,0
          .byte 24,3,21,10,1,5
          .byte 17,20,7,12,2,15
          .byte 11,4,22,25,19,6
          .byte 23,14

; ukw-b reflector
reflector .byte 24,17,20,7,16,18
          .byte 11,3,15,23,13,6
          .byte 14,10,12,8,4,1
          .byte 5,25,2,22,21,9
          .byte 0,19

; === strings (petscii) ===

; "  enigma ic attack"
stitle   .byte 32,32,69,78,73,71
          .byte 77,65,32,73,67,32
          .byte 65,84,84,65,67,75
          .byte 0
; "  no crib needed"
ssub     .byte 32,32,78,79,32,67
          .byte 82,73,66,32,78,69
          .byte 69,68,69,68,0
; "  searching..."
ssearch  .byte 32,32,83,69,65,82
          .byte 67,72,73,78,71,46
          .byte 46,46,0
; "  total: "
stotal   .byte 32,32,84,79,84,65
          .byte 76,58,32,0
; " candidates"
scands   .byte 32,67,65,78,68,73
          .byte 68,65,84,69,83,0
; "  time: "
stime    .byte 32,32,84,73,77,69
          .byte 58,32,0
; " seconds"
ssec     .byte 32,83,69,67,79,78
          .byte 68,83,0

; rotor names (petscii)
rn1       .byte 73,0
rn2       .byte 73,73,0
rn3       .byte 73,73,73,0
rn4       .byte 73,86,0
rn5       .byte 86,0
rn6       .byte 86,73,0
rn7       .byte 86,73,73,0
rn8       .byte 86,73,73,73,0
rnlo     .byte <rn1,<rn2,<rn3
          .byte <rn4,<rn5,<rn6
          .byte <rn7,<rn8
rnhi     .byte >rn1,>rn2,>rn3
          .byte >rn4,>rn5,>rn6
          .byte >rn7,>rn8

Timing

The IC attack is slower per candidate than the brute-force cracker. Each candidate requires decrypting all 60 characters (60 encrypt calls) plus the frequency counting and IC sum computation. The cracker averaged about 1.04 encryptions per candidate thanks to early exit on the first crib character.

On a stock NTSC C64, the full IC search through all 5.9 million candidates takes 82 hours (about 3.4 days), producing 18,165 candidates at the 194 threshold.

The Jiffy Clock Problem

The C64’s jiffy clock at $a0-$a2 is 24 bits, which can count up to 16,777,216 jiffies (about 77.7 hours at 60 Hz). But the KERNAL never lets it get that high. The UDTIM routine at $f69b, called 60 times per second by the IRQ handler, resets the clock to zero when it reaches 5,184,000 jiffies (24 hours). It’s a time-of-day clock, not a free-running counter. From the original Commodore source:

; here we check for roll-over 23:59:59
; and reset the clock to zero if true
ud30    sec
        lda time+2
        sbc #$01
        lda time+1
        sbc #$1a
        lda time
        sbc #$4f
        bcc ud60
; time has rolled--zero register
        stx time
        stx time+1
        stx time+2

An 82-hour search hits this reset three times. If you just read the clock at the end, you get the time since the last midnight reset, not the total elapsed time. I learned this the hard way after a four-day run reported ten hours. The fix: at each rotor ordering (every ~15 minutes), read the jiffy clock, add it to a 32-bit accumulator, and zero the clock. The KERNAL reset never fires because the clock never reaches 24 hours.

You don’t have to wait for the full search, though. The correct answer (III-I-V at M-C-Q) is ordering #87 out of 336. It shows up on the printer about 21 hours in, less than a day. The remaining 61 hours just confirm there’s nothing better hiding in the other orderings.

Where the Cycles Go

The rotorpass routine is where the CPU spends most of its time. It runs 2.1 billion times across the full search. Here’s every instruction with its cycle count:

rotorpass
          stx temp       ; 3  save position offset
          clc            ; 2
          adc temp       ; 3  add position to letter
          jsr mod26      ; 17 reduce mod 26
          tay            ; 2  use as table index
          lda (ptr),y    ; 5  look up rotor wiring
          sec            ; 2
          sbc temp       ; 3  subtract position
          clc            ; 2
          adc #26        ; 2  keep positive
          jsr mod26      ; 17 reduce mod 26
          rts            ; 6
                         ; total: 64 cycles

Each jsr mod26 costs 6 cycles for the call, then a compare, a conditional subtract, and a return. About 17 cycles total depending on whether the value needs reducing.

Each encrypt call does 6 of these (3 forward through the rotors, 3 inverse), plus table pointer setup (setfwd/setinv at 26 cycles each), stepping, and the reflector lookup. One full encrypt comes to about 720 cycles.

The inner loop does that 60 times per candidate (once per ciphertext character), then counts frequencies and computes the IC sum. Across 5.9 million candidates on an NTSC C64 at 1,022,727 Hz, the whole search takes 82 hours.

The tradeoff: the IC attack trades speed for generality. It’s slower than a crib-based attack, but it doesn’t need known plaintext. When you have a crib, use it. When you don’t, IC is your best option.

IC vs. Crib Attack

The IC attack was never used operationally against Enigma during the war. Bletchley Park had enough cribs from weather reports, re-sends, and formulaic messages that the Bombe was the practical choice. IC analysis was well understood (Friedman published it in 1922), but the computational cost of decrypting entire messages for every candidate setting made it impractical with 1940s technology.

On a C64, the cost is steep but possible. Three and a half days to search every ordering, but the answer lands on the printer in about 21 hours. No known plaintext required. Just plug in a printer, type sys 49152, and go live your life for a while. On modern hardware, the same search finishes in seconds. The math existed in 1922. The computation to make it useful against Enigma didn’t arrive for decades.

A few ways to take this further:

• Pre-filter with IC: Use IC as a first pass to narrow down rotor orderings. For each ordering, compute IC for a sample of positions. If no position scores well, skip the ordering entirely. This reduces the search space for any follow-up attack.

• Bigram scoring: IC uses single-letter frequencies. Bigram frequencies (pairs like TH, ER, EN in German) are an even stronger signal. Count all 676 bigram frequencies and compare to expected German bigrams. Higher accuracy, but the frequency table grows from 26 bytes to 676 bytes.

• Solve the plugboard: Once IC identifies the correct rotor settings, the plugboard can be deduced using frequency analysis. Compare the letter frequencies of the rotor-only decryption to expected German frequencies. The mapping from observed frequencies to expected frequencies reveals the plugboard swaps.

• Variable threshold: Use a sliding threshold based on message length. Shorter messages need a lower threshold (more false positives) because the IC is noisier. Longer messages allow a higher threshold (fewer false positives). Pre-compute the threshold for the specific message length.

• Code
• How-To
• Retro
• Programming
• Tutorial
• Enigma
• Cryptography
• C64