How many times should an error review be done?

At least twice per chapter; the second round only revisits the item types you got wrong, with the reason written beside the answer.

It is only a rough baseline for converting seconds into years; if a question gives 365 days, always use the number given.

S6 ICT | Network Security and Encryption Practice Paper 4 (Error Review)

2026-11-04

Tutor Prep Guide · Secondary ICT

Redo the six calculation patterns most often missed in the first three papers: the exponent in keyspace, unit conversion in cracking time, phi(n) and d in RSA, length multiples, 62-character strength and backup RPO.

Attempt first, mark afterwards　Allow about thirty minutes; write the exponent or modular expression for each item before checking it, then use the explanation to find the step you missed.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10 items
Suggested time	About 30 minutes
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: S6 ICT \| Network Security and Encryption
Level	S6 (Secondary 6) ICT

02　Questions (10 items)

FoundationA password uses exactly 10 lowercase English letters. How many possible combinations are there?
FoundationContinuing from the previous item, an attacker tries 2 000 000 passwords per second and on average needs half the keyspace. Roughly how many hours does that take?
FoundationAn AES-192 key is 192 bits long. How many bytes is that?
FoundationWhat is the main purpose of adding a salt before storing a password hash?
IntermediateAn RSA system uses p = 47, q = 59 and public exponent e = 17. Find the modulus n, phi(n) and the private exponent d.
IntermediateA phone PIN uses 6 digits. If it is changed to 8 digits, how many times more combinations are there?
IntermediateA backup plan takes one full backup of 120 GB per week and one incremental backup of 5 GB on each of the other 6 days. What is the weekly backup total, and what is the longest RPO?
ChallengeIf a password may use 62 characters (26 lowercase, 26 uppercase and 10 digits) for the same 12 positions, how many times more combinations are there than lowercase letters alone?
ChallengeContinuing from the previous item, an attacker tries 1 000 000 000 guesses per second and needs half the keyspace on average. Roughly how many years is that for the 62-character, 12-position password? (Use 365.25 days per year.)
Error redoError review: a student claims that symmetric encryption is slower than asymmetric encryption because it has to manage two different keys. Is that correct?

03　Answers and one-line notes

#	Answer	One-line note
1	141,167,095,653,376	Each position offers 26 choices, so 10 positions give 26 to the power 10, which is 141,167,095,653,376; the length is an exponent, not a multiplier of 10.
2	About 9,803.3 hours	141,167,095,653,376 / 2 / 2,000,000 / 3 600 = 9,803.3 hours; only half the keyspace is needed on average, hence the division by 2.
3	24 bytes	192 / 8 = 24; converting bits to bytes always divides by 8.
4	It makes the same password hash differently in each account, which defeats precomputed rainbow tables	A salt only needs to be unique and random and need not be secret; it does not stop online guessing and does not replace a deliberately slow hash.
5	n = 2,773, phi(n) = 2,668, d = 157	n = 47 x 59 = 2,773; phi(n) = 46 x 58 = 2,668; e x d is congruent to 1 mod 2,668, and 17 x 157 = 2,669 = 2,668 x 1 + 1, so d = 157.
6	100 times (100,000,000 versus 1,000,000)	Each digit has 10 choices: 6 digits give 10 to the power 6, that is 1,000,000, and 8 digits give 10 to the power 8, that is 100,000,000, a factor of 10 squared, namely 100.
7	150 GB; the longest RPO is 24 hours	120 + 5 x 6 = 150 GB; with one backup per day, the worst case is an incident just before the next backup, so the RPO is 24 hours.
8	About 33,808.0 times	(62 / 26) to the power 12 = 33,808.0; an alphabet about 2.38 times larger becomes roughly 33,808.0 times more combinations after 12 positions.
9	About 51,117 years	3,226,266,762,397,899,821,056 / 2 / 1,000,000,000 / 3 600 / 8 766 = 51,117 years; exponential growth turns a modestly larger alphabet into an astronomical figure after 12 positions.
10	No; symmetric encryption uses one key, its operations are simple and it is much faster than asymmetric encryption	Asymmetric encryption relies on large-number modular arithmetic and is hundreds of times slower, so in practice it only exchanges a session key, after which the data itself travels under symmetric encryption.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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