Caesar cipher wrap-around with MOD 26

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Quick Questions

Shade in the A or B circle for each question.

1. A Caesar cipher uses shift 5. What does the letter X (position 23) become?

A 28

B C

2. Which formula wraps a shifted letter back around the alphabet (A=0 to Z=25)?

A (position + shift) MOD 26

B (position + shift) MOD 25

3. Shift 3: what does Y (position 24) become?

A B

B A

4. True or false: 26 MOD 26 = 0, so a letter shifted from position 20 by 6 lands on A.

A True

B False

5. Why do we need MOD 26 in a Caesar cipher?

A So the shift is always 26

B So letters past Z loop back to A

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1(23 + 5) MOD 26		ADecrypts C with a shift of 5 by moving back 5 places, wrapping round to position 23, which is X
2(2 - 5 + 26) MOD 26		BnewPos = (pos - shift + 26) MOD 26
3To encrypt, add the shift to the letter's position, then use MOD 26 so the result stays between 0 and 25		CThe alphabet has 26 letters, so the wrap must use MOD 26, not MOD 25. With MOD 25, Z (25) would wrongly wrap to 0 and letters would be miscalculated.
4To decrypt with a negative shift, subtract the shift, add 26 so it is not negative, then wrap with MOD 26		DThere is no MOD 26, so X (23) shifted by 5 gives 28, which is not a letter. The result never wraps back to the start of the alphabet.
5newPos = (pos + shift) MOD 25		EnewPos = (pos + shift) MOD 26
6newPos = pos + shift		FEncrypts X with a shift of 5: 28 wraps around to 2, which is the letter C

Definitions

(position + shift) MOD 26

Fill in the Blanks

Complete each line of code by filling in the missing parts.

(23 + 5) ___ 26 = 2

(23 + 5) MOD __ = 2

newPos = (pos _ shift) MOD 26

=MOD(2+__,26)

X = 23 23 + 5 = 28 28 MOD 26 = _

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A pos = ord('X') - 97

B shift = 5

C new = (pos + shift) % 26

D print(chr(new + 65))

Question 2

A pos = 25

B new = (pos + 3) % 25

C print(new)

Question 3

A shift = 5

B pos = (23 * shift) % 26

C letter = chr(pos + 65)

D print(letter)

Question 4

A pos = 2

B shift = -5

C new = (pos - shift) % 26

D print(chr(new + 65))

Question 5

A letter = 'C'

B pos = ord(letter) - 65

C shift = -5

D new = pos + shift % 26

E print(chr(new + 65))

Answer Key

Caesar cipher wrap-around with MOD 26

Section A: Quick Questions

B — C

A — (position + shift) MOD 26

A — B

A — True

B — So letters past Z loop back to A

Section B: Match the Pairs

(23 + 5) MOD 26 → Encrypts X with a shift of 5: 28 wraps around to 2, which is the letter C

(2 - 5 + 26) MOD 26 → Decrypts C with a shift of 5 by moving back 5 places, wrapping round to position 23, which is X

To encrypt, add the shift to the letter's position, then use MOD 26 so the result stays between 0 and 25 → newPos = (pos + shift) MOD 26

To decrypt with a negative shift, subtract the shift, add 26 so it is not negative, then wrap with MOD 26 → newPos = (pos - shift + 26) MOD 26

newPos = (pos + shift) MOD 25 → The alphabet has 26 letters, so the wrap must use MOD 26, not MOD 25. With MOD 25, Z (25) would wrongly wrap to 0 and letters would be miscalculated.

newPos = pos + shift → There is no MOD 26, so X (23) shifted by 5 gives 28, which is not a letter. The result never wraps back to the start of the alphabet.

Section C: Definitions

(position + shift) MOD 26 — Caesar wrap-around rule: with A=0 to Z=25, add the shift then take MOD 26 so letters past Z loop back to A. Example: X (23) + 5 = 28, MOD 26 = 2, which is C.

Section D: Fill in the Blanks

(23 + 5) MOD 26 = 2

newPos = (pos + shift) MOD 26

=MOD(2+-5,26)

X = 23
23 + 5 = 28
28 MOD 26 = 2

Section E: Spot the Error

A — Capital letters start at ord 65, not 97 (that is for lowercase). Subtracting 97 gives a negative position. It should be ord('X') - 65 so that X = 23.

B — The alphabet has 26 letters, so the wrap-around uses MOD 26. MOD 25 gives the wrong result: Z (25) + 3 = 28, and 28 MOD 26 = 2 (C). It should be % 26.

B — A Caesar shift is added to the position, not multiplied. X (23) + 5 = 28, and 28 MOD 26 = 2 (C). It should be (23 + shift) % 26.

C — Decrypting uses a negative shift, so you add it: 2 + (-5) = -3, and -3 MOD 26 = 23 (X). Subtracting a negative shift adds 5 instead and gives the wrong letter. It should be (pos + shift) % 26.

D — MOD is worked out before the addition, so only shift is wrapped and the total can go outside 0-25. Brackets are needed: (pos + shift) % 26.