# Key encapsulation

> Cryptographic protocol for key transport over an insecure channel

**Wikidata**: [Q6398156](https://www.wikidata.org/wiki/Q6398156)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Key_encapsulation_mechanism)  
**Source**: https://4ort.xyz/entity/key-encapsulation

## Summary
Key encapsulation is a cryptographic primitive used to securely transport keys over an insecure channel. Functioning as a fundamental building block in public-key cryptography, it allows two parties to establish a shared secret key without exposing the key itself during transmission. It is often referred to as a Key Encapsulation Mechanism (KEM).

## Key Facts
*   **Definition:** A cryptographic protocol designed specifically for key transport over insecure channels.
*   **Classification:** It is a subclass of a **cryptographic primitive**, serving as a basic algorithm used to construct more complex cryptosystems.
*   **Primary Use:** Utilized within **public-key cryptography** to securely exchange symmetric keys.
*   **Aliases:** Also known as **KEM**, key encapsulation mechanism, *Schlüsselkapselungsverfahren* (German), and *密鑰封裝* (Chinese).
*   **RSA Association:** In the context of RSA, the mechanism uses the defining formula $c \equiv m^e \pmod{n}$.
*   **Post-Quantum Implementations:** Notable specific mechanisms include **Kyber** (a quantum-safe mechanism) and **SABER**.
*   **Maintenance:** The topic is maintained by **WikiProject Mathematics**.

## FAQs
### Q: What is the primary purpose of Key encapsulation?
A: The primary purpose is to facilitate secure key transport over an insecure channel. It allows a sender to generate a random session key and send it to a receiver using the receiver's public key.

### Q: How does Key encapsulation relate to Post-Quantum Cryptography?
A: Key encapsulation is a standard method for implementing post-quantum cryptosystems. Specific examples include **Kyber** (quantum-safe) and **Supersingular Isogeny Key Encapsulation**, which are designed to resist attacks from quantum computers.

### Q: What is the mathematical basis for Key encapsulation in RSA?
A: According to source data, the defining formula applicable to the RSA part of the mechanism is $c \equiv m^e \pmod{n}$, where $c$ is the ciphertext, $m$ is the message, $e$ is the exponent, and $n$ is the modulus.

## Why It Matters
Key encapsulation matters because it addresses the critical challenge of secure key distribution in digital communications. In modern cryptography, while symmetric encryption is efficient for bulk data, the keys used for that encryption must be shared securely. Key encapsulation mechanisms (KEMs) provide the standardized algorithmic structure to do this.

As a subclass of cryptographic primitives, KEMs are essential building blocks for complex security systems. Their relevance has increased with the rise of quantum computing threats; the cryptographic community actively develops and standardizes quantum-safe KEMs like **Kyber** and **SABER** to ensure future data privacy. By encapsulating a key rather than encrypting arbitrary data, these mechanisms provide a defined interface for establishing secure sessions, making them indispensable in internet protocols and secure messaging applications.

## Notable For
*   **Fundamental Building Block:** Being a standardized cryptographic primitive used to construct complex cryptosystems.
*   **Quantum Resistance:** Hosting advanced implementations like **Kyber** and **SABER**, which are leading candidates for post-quantum cryptography standards.
*   **Diverse Nomenclature:** Being known by various names globally, including the German term *Schlüsselkapselungsverfahren*.
*   **Mathematical Foundation:** Relying on specific mathematical properties, such as the RSA formula $c \equiv m^e \pmod{n}$, for its operation in certain contexts.

## Body
### Definition and Classification
Key encapsulation is defined as a cryptographic protocol used for key transport over an insecure channel. In the hierarchy of cryptographic concepts, it is classified as a **cryptographic primitive**. This means it is an established, low-level algorithm that serves as a component for higher-level security protocols. It is strictly associated with **public-key cryptography**.

### Key Encapsulation Mechanisms (KEMs)
The mechanism is frequently abbreviated as **KEM**. A KEM allows a sender to encapsulate a symmetric key (often randomly generated) using the receiver's public key, resulting in an encapsulated key (ciphertext) that can only be decapsulated by the receiver using their private key.

### Associated Algorithms
The concept of Key encapsulation serves as the parent or related class for several specific, notable algorithms:
*   **Kyber:** Described as a quantum-safe key encapsulation mechanism.
*   **SABER:** Listed as a cryptographic key encapsulation mechanism.
*   **Supersingular Isogeny Key Encapsulation:** A class of post-quantum cryptographic algorithm.
*   **Indistinguishability obfuscation:** A related cryptographic algorithm class.

### Technical Specifications
For the RSA implementation of key encapsulation, the source data specifies the mathematical formula:
$$c \equiv m^e \pmod{n}$$
This formula defines the relationship between the ciphertext ($c$), the message/key material ($m$), the public exponent ($e$), and the modulus ($n$).

### Administrative Data
*   **Wikipedia Title:** Key encapsulation mechanism
*   **Site Links:** The entity has sitelinks across 5 language wikis (ca, de, en, fr, it).
*   **Freebase ID:** /m/0279d3k

## Schema Markup
```json
{
  "@context": "https://schema.org",
  "@type": "Thing",
  "name": "Key encapsulation",
  "description": "Cryptographic protocol for key transport over an insecure channel.",
  "alternateName": [
    "KEM",
    "Key encapsulation mechanism",
    "Schlüsselkapselungsverfahren",
    "密鑰封裝"
  ],
  "sameAs": [
    "https://en.wikipedia.org/wiki/Key_encapsulation_mechanism"
  ],
  "additionalType": "Cryptographic Primitive"
}

## References

1. [OpenAlex](https://docs.openalex.org/download-snapshot/snapshot-data-format)