← ACARA Digital Technologies Years 9–10

The XOR cipher

Encrypts by XOR-ing (^ in Python) each character code with a key number. XOR-ing the result with the same key again restores the original, so one key encrypts and decrypts.

Part of: ACARA Digital Technologies Years 9–10 — Cyber Security Threats and Vulnerabilities — Module 128, QCE Digital Solutions Unit 4 — Prototype Digital Data Exchanges — Module 116

Understanding The XOR cipher in ACARA Digital Technologies Years 9–10

What it does: The first XOR scrambles 72 into 65. XOR-ing with 9 again restores 72, so the same key encrypts and decrypts. The loop visits each character in the message and adds its XOR-scrambled version to the output. In Python, ^ is the XOR operator. ** means 'to the power of'. XOR means 'exclusive or'. 0 ^ 1 and 1 ^ 0 give 1, but 1 ^ 1 and 0 ^ 0 give 0. Both bits are the same, so XOR gives 0. XOR each pair of bits: 01000001 ^ 00000101 = 01000100, which is 68. XOR-ing with the same key twice cancels out, so you get the original number back.

Common mistakes: A for loop header must end with a colon. It should be: for ch in text:. & is the AND operator, not XOR. The XOR cipher uses ^, so it should be: code = ord("A") ^ key.

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This module's key terms are also in a printable crossword (Modules 876–944) and word search (Modules 860–944).

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Learning

Duo

Which Python operator performs XOR on two numbers?

**^

Matches

chr("A" ^ 5)

↓

The ^ operator needs numbers, but "A" is a string. The letter must be converted first with ord(), as in chr(ord("A") ^ 5).

Applying

Meanings

Term

XOR cipher

Meaning

Encrypts by XOR-ing (^ in Python) each character code with a key number. XOR-ing the result with the same key again restores the original, so one key encrypts and decrypts.

Practice

key = 5

Testing

Gaps

print(5 3)

Check Answer

Spots

3out = ""

4for ch in text

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Quick Questions

1. Which Python operator performs XOR on two numbers?

A. ^ ✓

B. **

In Python, ^ is the XOR operator. ** means 'to the power of'.

2. When does XOR give an output bit of 1?

A. When the two input bits are different ✓

B. When both input bits are 1

XOR means 'exclusive or'. 0 ^ 1 and 1 ^ 0 give 1, but 1 ^ 1 and 0 ^ 0 give 0.

3. What is the result of 1 ^ 1 in Python?

A. 1

B. 0 ✓

Both bits are the same, so XOR gives 0.

4. What is 65 ^ 5? (65 is 01000001 in binary and 5 is 00000101.)

A. 68 ✓

B. 70

XOR each pair of bits: 01000001 ^ 00000101 = 01000100, which is 68.

5. What does 65 ^ 20 ^ 20 equal?

A. 20

B. 65 ✓

XOR-ing with the same key twice cancels out, so you get the original number back.

Match the Pairs

65 ^ 5 → XORs the numbers 65 and 5 to give 68, the character code for D

chr(ord(ch) ^ key) → Turns a letter into its code, XORs it with the key, then turns the result back into a character

XOR-ing a number with the same key twice gives back the original number → (72 ^ 9) ^ 9

To encrypt a whole message, XOR every character code in it with the key → for c in msg: out += chr(ord(c) ^ key)

chr("A" ^ 5) → The ^ operator needs numbers, but "A" is a string. The letter must be converted first with ord(), as in chr(ord("A") ^ 5).

plain = chr(ord(c) ^ 7) # key was 5 → Decrypting with a different key (7) does not restore the original. XOR cipher needs the same key (5) for both steps.

Key Term

XOR cipher

Encrypts by XOR-ing (^ in Python) each character code with a key number. XOR-ing the result with the same key again restores the original, so one key encrypts and decrypts.

Fill in the Blanks

1. print(5 ^ 3)

Hint: Type the Python operator that performs XOR on two numbers.

2. scrambled = ord("A") ^ 7

Hint: Type the function that turns a character into its numeric code.

3. key = 7 scrambled = ord("H") ^ key back = scrambled ^ key

Hint: Type the variable holding the same number used to encrypt, because one key reverses the scramble.

4. key = 7 letter = chr(72 ^ key)

Hint: Type the function that turns a character code back into a character.

5. key = 9 for ch in "HI": print(chr(ord(ch) ^ key))

Hint: Type the keyword that starts a loop over every character in the message.

Spot the Error

Question 1

A key = 42

B text = "Hi"

C out = ""

D for ch in text

E out += chr(ord(ch) ^ key)

Line D — A for loop header must end with a colon. It should be: for ch in text:

Question 2

A key = 7

B code = ord("A") & key

C print(code)

Line B — & is the AND operator, not XOR. The XOR cipher uses ^, so it should be: code = ord("A") ^ key

Question 3

A key = 5

B msg = "Hello"

C for ch in msg:

D n = ord(ch) ** key

E print(chr(n))

Line D — ** raises a number to a power, which is not XOR. The character code must be XOR-ed with the key using ^.

Question 4

A key = "42"

B msg = "Hi"

C for ch in msg:

D print(ord(ch) ^ key)

Line A — The key must be a number so ^ can XOR it with the character code. "42" is a string and causes an error. It should be: key = 42

Question 5

A def xor_text(text, key):

B out = 0

C for ch in text:

D out += chr(ord(ch) ^ key)

E return out

Line B — out collects characters, so it must start as an empty string. Adding a character to the number 0 causes an error. It should be: out = ""

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