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ElGamal Encryption

ElGamal Encryption protects secrecy, integrity, or authenticity with a named cryptographic primitive.

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Quick Facts

Compact metadata for implementation and discovery.

Category: Cryptography
Difficulty: Intermediate
Family: Public-Key Encryption
Tier: Core
Status: Verified
Review: Source Checked
Sources: 1
Formulas: 1
Relationships: 1
Code example: Ready
Visualization: Ready

Overview

ElGamal Encryption is a cryptographic method that protects confidentiality, authenticity, or integrity with a defined primitive or protocol step. It should be used only as part of a well-defined protocol with correct parameters and key handling.

Core Concepts

key materialsecurity parameterverification ruleverification

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(n)

Average

O(n)

Worst

O(n)

Space

O(1)

When to Use

Use ElGamal Encryption only when the protocol calls for this specific primitive or construction.
Use it when a vetted implementation is available and parameter handling can be enforced.

When Not to Use

Avoid custom protocol combinations around this primitive.
Avoid when nonce, key, padding, or parameter requirements cannot be enforced.

What It Does

Computes public-key encryption within Public-Key Encryption workloads (O(n) time, O(1) space).
Works by It should be used only as part of a well-defined protocol with correct parameters and key handling.
Maintains key invariants across key material, security parameter, verification rule.

Use Cases

Secure communication
Authentication
Key management

Inputs

Message or secret
Key material
Nonce, salt, or public parameters

Outputs

Ciphertext, tag, key, signature, or proof
Verification result

Key Formulas (1)

ElGamal ciphertext

c₁ = g^k, c₂ = m · y^k

c1 = g^k, c2 = m * y^k

Uses an ephemeral exponent to hide the message under the recipient public key.

Pseudocode

1.Validate keys, nonces, and required parameters
2.Apply the primitive's block, group, hash, or verification operation
3.Combine intermediate values according to the construction
4.Return the ciphertext, tag, key, signature, proof, or verification result

Canonical Example

Input: message = 'pay 10', key material = provided, nonce or public parameters = provided
Output: protected value or verification result
Explanation: ElGamal Encryption applies its defined cryptographic operation without inventing extra protocol steps.

Implementation Notes

Use vetted implementations for low-level primitives.
Validate parameter lengths, nonce handling, and authentication failure behavior explicitly.

Common Pitfalls

Reusing nonces, salts, or ephemeral values can break security assumptions.
Treating a primitive as a full protocol invites key-management and authentication mistakes.

Interactive Mechanism Walkthrough

Graph Frontier & Edge Relaxation

Show messages, keys, nonces, and verification values moving through the cryptographic construction.

Step 1 of 4: Validate keys, nonces, and required parameters

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Notes

ElGamal Encryption operates in O(n) time and O(1) space within the Public-Key Encryption family. Key governing relation: c1 = g^k, c2 = m * y^k. Often compared with Diffie-Hellman Key Exchange and RSA.