← ACARA Digital Technologies Years 5–6

Longer means harder to guess

The number of possible guesses for a secret. Each extra character multiplies them, so longer passwords take much longer to guess, even for fast computers.

Part of: ACARA Digital Technologies Years 5–6 — Staying Safe Online — Module 7

Understanding Longer means harder to guess in ACARA Digital Technologies Years 5–6

What it does: A long passphrase has so many combinations that even a fast computer needs a very long time to guess it. With only 5 characters there are far fewer combinations, so it can be guessed quickly. Each extra digit multiplies the possibilities by 10. So 1,000 becomes 10,000, not just one more. A 4-digit code has ten times more combinations than a 3-digit code, so it takes much longer to guess. More random words means more characters and many more combinations for a guesser to try. Because computers try millions of guesses quickly, a longer password is needed to be safe.

Common mistakes: To see how many times more codes a 4-digit code has, divide: codes4 // codes3 gives 10. Subtracting only gives the gap between the two numbers, not how many times bigger it is. Each extra digit multiplies the combinations by 10, so we need the power operator: 10 ** length. Using * only gives 40, not 10000.

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This module's key terms are also in a printable crossword (Modules 137–153) and word search (Modules 137–225).

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Learning

Duo

A 3-digit code (000 to 999) has 1,000 possible combinations. How many does a 4-digit code have?

1,001 combinations10,000 combinations

Matches

A 4-digit code is only a little harder to guess than a 3-digit code.

↓

Each extra digit multiplies the combinations by 10, so it is 10 times harder, not just a little harder.

Applying

Meanings

Term

combinations

Meaning

The number of possible guesses for a secret. Each extra character multiplies them, so longer passwords take much longer to guess, even for fast computers.

Practice

3-digit code: 10 * 10 * 10 = 1000 guesses

Testing

Gaps

combos = ** 3

Check Answer

Spots

2codes4 = 10 ** 4

3extra = codes4 - codes3

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Quick Questions

1. A 3-digit code (000 to 999) has 1,000 possible combinations. How many does a 4-digit code have?

A. 10,000 combinations ✓

B. 1,001 combinations

Each extra digit multiplies the possibilities by 10. So 1,000 becomes 10,000, not just one more.

2. Which secret is harder to guess?

A. A 3-digit code

B. A 4-digit code ✓

A 4-digit code has ten times more combinations than a 3-digit code, so it takes much longer to guess.

3. What happens to the number of combinations each time you add one more character?

A. It multiplies, so there are many more combinations ✓

B. It only goes up by one

Each extra character multiplies the possible guesses. That is why long passwords are so much harder to guess.

4. Which password would take a guesser longer to crack?

A. cat7

B. purple-tiger-bike-cloud ✓

The long passphrase has far more combinations than a short password with only a few characters.

5. A computer can try thousands of guesses every second. Which is the safer choice?

A. A long passphrase ✓

B. A short password

Computers guess very fast, so a short password can be cracked quickly. Length gives more combinations to try.

Match the Pairs

3-digit code: 000 to 999 → There are 1000 possible codes. A guesser has 1000 combinations to try.

4-digit code: 0000 to 9999 → There are 10000 possible codes. That is 10 times more combinations than a 3-digit code.

A longer password has many more combinations, so it takes a computer much longer to guess. → blue-tiger-jumps-high-87

A short password has few combinations, so a fast computer can guess it very quickly. → cat12

A 4-digit code is only a little harder to guess than a 3-digit code. → Each extra digit multiplies the combinations by 10, so it is 10 times harder, not just a little harder.

Computers guess slowly, so a short password is safe enough. → Computers can guess very fast, so a short password with few combinations can be found quickly.

Key Term

combinations

The number of possible guesses for a secret. Each extra character multiplies them, so longer passwords take much longer to guess, even for fast computers.

Fill in the Blanks

1. combos = 10 ** 3 print(combos)

Hint: Type how many different digits can be chosen for each place in a 3-digit code.

2. small = 10 ** 3 big = small * 10 print(big)

Hint: Type the maths operator that multiplies the combinations when one extra digit is added.

3. small = 10 ** 3 big = 10 ** 4 print(big > small)

Hint: Type the comparison operator that checks if the 4-digit code has more combinations than the 3-digit code.

4. length = 8 combos = 26 ** length print(combos)

Hint: Type the variable that holds how many characters are in the password.

5. combos = 26 ** 8 speed = 1000000 seconds = combos / speed

Hint: Type the variable that stores how many guesses the computer can make each second.

Spot the Error

Question 1

A codes3 = 10 ** 3

B codes4 = 10 ** 4

C extra = codes4 - codes3

D print(extra)

Line C — To see how many times more codes a 4-digit code has, divide: codes4 // codes3 gives 10. Subtracting only gives the gap between the two numbers, not how many times bigger it is.

Question 2

A length = 4

B combos = 10 * length

C print(combos)

Line B — Each extra digit multiplies the combinations by 10, so we need the power operator: 10 ** length. Using * only gives 40, not 10000.

Question 3

A short = 26 ** 4

B long = 26 ** 8

C print(long < short)

Line C — A longer password has more combinations than a shorter one, so long > short should be True. The < sign checks the wrong way round and would print False.

Question 4

A for length in range(3, 6):

B combos = length ** 10

C print(length, combos)

Line B — The base (10 digits to choose from) stays the same and the length is the power: 10 ** length. Swapping them gives the wrong numbers and hides how fast combinations grow.

Question 5

A password = 'cat'

B total = 26 ** password

C print(total)

Line B — The power must be the number of characters, which is len(password). A word cannot be used as a power, so this causes an error.

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