Chapter 2 — Computing systems
Lesson map
Lesson 02 published. Map, example, EX003.
flowchart TD
N0["Learning outcomes"]
N1["2.1 Layers and where cryptography sits"]
N2["2.2 Bits, qubits and what quantum computers are"]
N3["2.4 Practical activity"]
N4["Synthesis"]
N0 --> N1 --> N2 --> N3 --> N4
N4 --> EX["Worked example"]
EX --> Q["Exercise EX003"]
Logical drawing
flowchart LR
N0["Learning outcomes"]
N1["2.1 Layers and where cryptography sits"]
N2["2.2 Bits, qubits and what quantum computers are"]
N3["2.4 Practical activity"]
N4["Synthesis"]
N0 --> N1 --> N2 --> N3 --> N4 --> Q["EX003"]
[Learning outcomes]
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[2.1 Layers and where cryptography sits]
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v
[2.2 Bits, qubits and what quantum computers are]
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v
[2.4 Practical activity]
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v
[Synthesis]
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v
[Worked example] --> [Exercise EX003]
Learning outcomes
You will (1) describe the layers of a computing system from hardware to application; (2) explain where cryptographic code and keys live in each layer; (3) contrast classical bits with qubits at a conceptual level; and (4) map one HCU service onto these layers.
2.1 Layers and where cryptography sits
A modern service is a stack. At the bottom are processors, memory, storage and network interfaces; above them firmware boots the machine, an operating system manages resources, libraries provide shared functions, and applications deliver features. Cryptography appears in almost every layer. Firmware verifies signatures on the next boot stage. The operating system stores keys and offers a cryptographic provider. Libraries such as TLS stacks negotiate algorithms with remote peers. Applications sign documents or encrypt fields. Hardware security modules (HSMs) and smart cards are small computers whose whole purpose is to keep keys inside a boundary.
This layering matters for migration. Replacing an algorithm in an application is a software release; replacing it in a card terminal's boot ROM may require replacing the device. Students who can locate each cryptographic use in the stack can estimate how hard it will be to change, and that estimate drives every later plan in this book.
2.2 Bits, qubits and what quantum computers are
A classical bit is 0 or 1. A qubit's state is described by two complex amplitudes; measuring it yields 0 or 1 with probabilities given by those amplitudes. Several qubits can be entangled, so their joint state is not a list of independent bits. Quantum algorithms arrange interference so that wrong answers cancel and right answers reinforce. That is a narrow capability: quantum computers are not faster general-purpose machines, and for most workloads — databases, web servers, spreadsheets — they offer nothing. Their security relevance comes from a few algorithms, above all Shor's period finding.
Today's devices are noisy. Running Shor against RSA-2048 needs error-corrected logical qubits, each built from many physical qubits. Public estimates have fallen over time — Gidney (2025) estimated under a million noisy qubits running for less than a week under stated hardware assumptions — but no such machine exists, and its arrival date is uncertain.
2.3 Worked example
Map HCU's mobile banking login. The phone's secure enclave holds a device key (hardware); the phone OS provides a keystore (operating system); the app's TLS library negotiates key exchange with the server (library); the server's load balancer terminates TLS using a certificate from HCU's CA (infrastructure); the core banking application checks a signed session token (application). Five layers, at least four quantum-relevant algorithms, three different owners.
Five layers each hold a key or a check, and each could need a different change in a migration. The device key and the TLS key exchange are both quantum-vulnerable if they use elliptic curves. The session token's signature may be checked only on the server, which is easier to change. Mapping the login this way shows the HCU team that the app is not one cryptographic decision but several, owned by different people.
2.4 Practical activity
Choose a device you own. List its layers and, for each, one cryptographic function you believe it performs. Mark each belief as observed (you saw configuration or documentation) or assumed. Keep the list; Chapter 22 turns such lists into an inventory.
Most students find more assumed entries than observed ones, especially in firmware and hardware. That gap is the point of the exercise: an organisation's knowledge of its own cryptography is usually incomplete, and the first job of a migration is to find out what is really there. Note where you would look to confirm each assumption, such as a settings screen or a vendor's documentation.
2.5 Common errors and limits
- Assuming "quantum computer" means a faster laptop.
- Forgetting firmware and hardware when listing cryptography.
- Quoting a qubit count without the error rate and run time it assumes.
A quantum computer is a different kind of machine that is faster only for certain problems; for most tasks it offers no advantage. Firmware and hardware are often missed because nobody configures them day to day, yet they verify signatures and hold keys. A qubit count alone says little, since useful algorithms need error-corrected qubits and long run times, and published estimates make those assumptions explicit.
Exercises
- EX003 — Layer map. Map HCU's ATM withdrawal across at least four layers and name one cryptographic function in each. Rubric: 3 = four correct layers with plausible functions and owners.
- EX004 — Myth check. Explain in three sentences why a quantum computer would not speed up HCU's monthly statement batch job. Rubric: 3 = refers to narrow algorithmic advantage and to the workload type.
Synthesis
Cryptography is spread across every layer of a system, and the layer determines how hard it is to change. Quantum computers are specialised machines whose security impact comes from a few algorithms, and their arrival depends on error correction at scale.
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