00 · IN THREE MINUTES

The answer in three steps

  1. 1A public key can be distributed; the private key must remain controlled by its owner.
  2. 2Many real protocols use public-key operations to agree on a temporary symmetric key.
  3. 3Encryption and digital signatures use the key pair for different purposes and should not be conflated.

01 · A ONE-WAY PROBLEM CREATES ASYMMETRY

A one-way problem creates asymmetry

The construction makes one direction easy with public information and the inverse infeasible without a secret, under stated mathematical assumptions. “Infeasible” means beyond practical resources, not logically impossible.

02 · KEY AGREEMENT AVOIDS SENDING THE KEY

Key agreement avoids sending the key

In Diffie–Hellman-style exchange, both parties publish contributions and independently compute the same shared secret. An eavesdropper sees the public values but lacks the private exponents needed for the practical attack assumed hard.

FIG. 02How the system changes state
A conceptual mechanism map. Geometry, scale and timing are explanatory unless labelled otherwise.

03 · FAST ENCRYPTION IS SYMMETRIC

Fast encryption is symmetric

After authentication and agreement, protocols generally use the shared with efficient symmetric encryption. Public-key mathematics establishes and authenticates that key rather than carrying every byte of a long conversation.

04 · SIGNATURES ANSWER A DIFFERENT QUESTION

Signatures answer a different question

A private signing key produces a value that anyone with the public key can verify. This supports integrity and origin, but it does not by itself hide the message.

05 · IMPLEMENTATION COMPLETES THE SECURITY CLAIM

Implementation completes the security claim

Randomness, certificate validation, key storage, parameter choices and side-channel resistance matter. Sound mathematics can be defeated by reused secrets, compromised endpoints or incorrect protocol composition.

06 · SOURCES AND EVIDENCE

Sources and evidence

Claims are linked to foundational papers, standards or the primary study behind the update.

  1. 01
    New Directions in Cryptography

    Supports a defined mechanism, measurement or evidence boundary in this article.

    PRIMARY STUDY ↗
  2. 02
    Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography

    Supports a defined mechanism, measurement or evidence boundary in this article.

    TECHNICAL STANDARD ↗
CHANGE LOG29 Aug 2026 · First five-language edition; mechanisms, limits, diagrams and sources checked.