technologybriefs
12:36in productionCh. 1 · The First Usable Public Key/ 12:36 · ceiling 15 min
Security · Tech history

RSA cryptosystem

Ron Rivest, Adi Shamir and Leonard Adleman · 1977

RSA didn’t invent public-key crypto—but it made it usable, public, and real.

RSA is the first publicly described, usable public-key cryptosystem. It works by exploiting the asymmetry between modular exponentiation and root extraction modulo a composite number whose factorisation is secret. Its security depends on factoring difficulty—but that dependence is not proven equivalent. No published attack breaks it with large keys. It changed cryptography by enabling open protocols, trustless key exchange, and standardised role names like Alice and Bob.

SecurityTech historyCryptographyMathematicsAlgorithmsCryptography across the network →
Chapters & takeaways6
  1. 1:01
    The First Usable Public Key

    RSA was the first usable and publicly described method for public-key cryptography.

  2. 2:32
    A Year and One Night

    It emerged from a year of failed attempts, then one overnight formalisation by Rivest.

  3. 3:41
    Two Hard Problems

    Security rests on the infeasibility of computing eth roots modulo n—and the difficulty of factoring n.

  4. 5:26
    An Open Question

    We still do not know whether breaking RSA is equivalent to factoring.

  5. 6:57
    Still Unbroken

    No published attack defeats RSA when large enough keys are used.

  6. 8:54
    Alice and Bob Begin Here

    The same paper introduced Alice and Bob—now universal shorthand for cryptographic participants.

Worth your time?

Yes. Study the whole thing.

4.5/ 5
What works
  • enabling public-key infrastructure
  • securing early internet protocols
  • standardising cryptographic narrative roles
What does not
  • prove equivalence between RSA and factoring
  • eliminate implementation risk
  • guarantee resistance to quantum computation
Study it if
  • cryptographic engineers
  • protocol designers
  • historians of computing
Skip it if
  • developers seeking lightweight signing
  • post-quantum migration planners
The written brief1 min read

What it is and the problem it solves

RSA is a public-key cryptosystem that solves the problem of secure key exchange and digital signatures without pre-shared secrets. It enables two parties to communicate securely over an insecure channel using mathematically linked public and private keys.

How it works

RSA uses modular exponentiation with three large integers: a public exponent e, a public modulus n (the product of two large primes), and a private exponent d. It relies on the infeasibility of computing eth roots modulo n when only e and n are known.

What works

The core mechanism works: given large enough keys, no published method breaks RSA. Its reliance on modular exponentiation and the hardness of root-finding modulo n remains computationally infeasible with only public parameters.

What does not

RSA does not prove that breaking it is as hard as factoring large primes—the equivalence remains an open question. It also does not eliminate side-channel risks, implementation flaws, or poor key management.

What it changes

RSA established public-key cryptography as usable and publicly describable. It shifted cryptographic practice from shared-secret secrecy to asymmetric trust models—and introduced Alice and Bob as standard protocol actors.

Is it worth your time

Yes—if you work with digital trust, key exchange, or long-term data confidentiality. Its mechanism is still sound for sufficiently large keys, but it demands careful implementation and has been superseded in many new systems by elliptic-curve alternatives.

Same field · Security4 of 29
10:41
Diffie–Hellman key exchangeDiffie–Hellman key exchange is a foundational cryptographic protocol that enables two parties to derive a shared secret over an insecure channel using modular exponentiation in a finite group. Published in 1976, it introduced the first publicly known private–public key concept and remains embedded in internet infrastructure. But it provides no authentication—making it vulnerable to man-in-the-middle attacks unless combined with digital signatures or certificates.
9:26
Zero-knowledge proofZero-knowledge proof redefines verification: truth without exposure. Its 1985 formulation was precise, narrow, and assumption-bound. It works—but only where assumptions hold, only where implementation avoids side channels, and only after significant computational cost.
10:46
Elliptic-curve cryptographyVictor S. Miller and Neal KoblitzECC is a public-key method based on elliptic curves over finite fields. Proposed independently by Koblitz and Miller in 1985. Delivers equivalent security to RSA and ElGamal with smaller keys. Security rests on the hardness of the elliptic curve discrete logarithm problem — specifically, recovering scalar k from points P and Q = kP — and on efficient yet irreversible point multiplication for appropriate parameters.
8:52
Cryptocurrency walletA cryptocurrency wallet manages cryptographic keys — not funds — and enables transaction signing. Its strength lies in user-controlled key generation and offline derivation. Its weakness is that it offers no recovery, no insurance, and no abstraction from cryptographic risk. It changes who bears responsibility for asset security — from institution to individual — but does not change the cost of bearing it.
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