RSA cryptosystem
A public-key cryptosystem whose security rests on the difficulty of factoring the product of two large primes.
At a glance
Key signals
50% cross fields · reaches 3 more
- Cryptography
- Explanation
- Examples
- Misconception
- Sourced relations
- Attribution
Dependencies
What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.
Foundations · builds on
RSA cryptosystemdepends onModular arithmeticEstablished
RSA operates in modular arithmetic.
Mechanism: Encryption and decryption are modular exponentiations mod n; correctness follows from Euler's theorem in the ring of integers modulo n.
RSA cryptosystemdepends onOne-way functionEstablished
RSA's security rests on a one-way (trapdoor) function.
Mechanism: Multiplying two large primes is easy but factoring their product is believed hard; the trapdoor (the private key) makes inversion feasible only for the key holder.
Enables · leads to
RSA cryptosystemenablesDigital signatureEstablished
RSA can be used to produce digital signatures.
Mechanism: Signing with the private exponent and verifying with the public exponent turns the RSA trapdoor permutation into a signature scheme.
System context
RSA cryptosystemis aPublic-key cryptographyEstablished
Open Public-key cryptography →
Security from factoring.
Mechanism: RSA is a public-key scheme safe because factoring a big semiprime is hard — until quantum computers.
Structural role & consequence
Interpreted from the current atlas graph — what the connections mean, not just how many there are.
50% of its relationships cross field boundaries, reaching 3 other disciplines — above the 42% median of 10 concepts in the same discipline.
structural · Structural graph analysis — not a claim of importance, causation or history.
Currently dark in the atlas: no verified source · no key date stored · 4 of 4 of its relations lack claim-level evidence.
atlas representation · Describes the current Thinking OS representation, not the state of the world.
Directly enables 1 concept; following enables/causes relations, 1 concept is downstream across 2 disciplines.
structural · Follows only enables/causes dependency edges — not general relatedness.
Builds on 2 foundations (requires / depends-on / derived-from / emerges-from).
structural · Structural graph analysis — not a claim of importance, causation or history.
cross-field
2 within-field, 2 cross-field
Strengths & constraints
Strengths
- Cross-disciplinary connector — 50% of its relationships cross field boundaries. structural
- Redundantly connected — removing it leaves the sampled cross-field routes unchanged. structural
Constraints
- Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
- No dated history stored — the atlas records no key date for this concept. atlas representation
Conditions
- Its dependency reading rests on 2 foundation relations. structural
- Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural
Dependency radial
What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.
Seen through each discipline
How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.
Through this lens it connects to One-way function and Digital signature.
Formula
Source: Wikidata
Related ideas to explore
Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.
This idea also appears in…
The same structure shows up in other disciplines. These are real recurrences drawn from the graph — a starting point for asking “what carries over, and what changes?”
Concepts
crosses a discipline boundary
- Public-key cryptographyComputer Science
crosses a discipline boundary
- Connects 4 other ideas across 1 discipline.
- A cross-disciplinary bridge — its connections reach into 3 other fields.
- Most of its connections are of the “Dependency” kind.
Derived from the graph’s real structure — observations, not a score.
Sources
No primary source is attached to this concept yet. In a real deployment this would be required before publication.