OpenCyber AcademyLesson map
Lesson 01 published. Map, example, EX001.
flowchart TD
N0["Learning outcomes"]
N1["1.1 The case"]
N2["1.2 Rates of sign-in"]
N3["1.3 Derivatives and capacity"]
N4["1.4 Why this matters for security"]
N5["Synthesis"]
N0 --> N1 --> N2 --> N3 --> N4 --> N5
N5 --> EX["Worked example"]
EX --> Q["Exercise EX001"]
Logical drawing
flowchart LR
N0["Learning outcomes"]
N1["1.1 The case"]
N2["1.2 Rates of sign-in"]
N3["1.3 Derivatives and capacity"]
N4["1.4 Why this matters for security"]
N5["Synthesis"]
N0 --> N1 --> N2 --> N3 --> N4 --> N5 --> Q["EX001"]
[Learning outcomes]
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[1.1 The case]
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[1.2 Rates of sign-in]
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[1.3 Derivatives and capacity]
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[1.4 Why this matters for security]
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[Synthesis]
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[Worked example] --> [Exercise EX001]
Learning outcomes
You will (1) use rates of change to describe sign-in load; (2) relate derivatives to capacity; (3) estimate peaks from smooth curves.
1.1 The case
Sana Malik is a five-year engineering student at the fictional Brackenford Institute of Technology, supervised by Dr Owen Hale. Her long project is with the fictional Linmouth Borough Council, whose 2,400 staff use about 140 applications, most with their own local accounts and passwords. Nobody removes accounts reliably when people leave, and auditors found former staff still able to sign in to several systems. The council wants a central identity provider with single sign-on, multi-factor authentication, role-based access and automated joiner, mover and leaver processes. This book follows Sana from foundations to a defended engineering thesis.
1.2 Rates of sign-in
Identity systems handle quantities that change over time: sign-in requests, token issuances and password checks. If the cumulative count of sign-ins during a morning is a smooth curve, its derivative is the sign-in rate at each moment. At Linmouth, the curve rises steeply between 08:30 and 09:00 as staff arrive. The slope at its steepest point tells Sana the peak rate the identity provider must handle, which matters far more for capacity than the daily total, because a provider that copes on average can still fail at the morning rush.
1.3 Derivatives and capacity
If the identity provider can process a fixed number of sign-ins per second, any period where the arrival rate exceeds that capacity creates a backlog. The backlog grows at a rate equal to the difference between arrivals and capacity, which is itself a derivative. When the rush ends, the backlog drains. Sana uses this reasoning to explain why staff experience slow sign-in for a few minutes each morning even though the system is idle most of the day, and why capacity planning must start from peak rates, not averages.
1.4 Why this matters for security
Capacity is a security property as well as a performance one. If sign-in slows badly, staff and administrators look for shortcuts, such as shared accounts or disabling multi-factor prompts. A provider that fails under load also blocks access to every federated application at once. Understanding rates lets Sana size the system so that strong controls remain usable at peak. It also helps her recognise abnormal patterns, such as a sudden rise in failed sign-ins at night, which can indicate password-guessing attempts that monitoring should flag for review.
Worked example
Sana estimates the steepest slope of a synthetic cumulative sign-in curve at about 14 sign-ins per second between 08:40 and 08:50, and sizes the identity provider for at least twice that.
Synthetic case. Sana Malik, Brackenford Institute of Technology, Linmouth Borough Council and all figures are synthetic.
Errors and limits
Sizing an identity provider from daily averages ignores the morning peak, when failure would block every application at once.
Exercises
- EX001 — Peak rate. Why does peak rate matter more than the daily total for sizing?
Show marking criteria
Rubric: 3 = provider must cope at the rush or block all apps;; 2 = peak;; 1 = total;; 0 = none. - EX002 — Backlog growth. At what rate does a sign-in backlog grow?
Show marking criteria
Rubric: 3 = arrivals minus capacity;; 2 = difference;; 1 = capacity;; 0 = none. - EX003 — Night failures. What might a sudden night-time rise in failed sign-ins indicate?
Show marking criteria
Rubric: 3 = password-guessing attempts to flag;; 2 = attack;; 1 = vague;; 0 = none.
Synthesis
Rates and derivatives turn sign-in curves into capacity requirements that keep strong controls usable at peak.