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Extended Euclidean AlgorithmAll functions are free

Extended Euclidean Algorithm

finds the greatest common divisor, Bézout coefficient, and modular inverse when they exist.

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is an exact integer; the modular inverse only exists when the two numbers are relatively prime.

Extended Euclidean Algorithm: uses and methods

finds the greatest common divisor, Bézout coefficient, and modular inverse when they exist.

Applicable scope and calculation boundary

is an exact integer; the modular inverse only exists when the two numbers are relatively prime.

model and reference method

ax+by=gcd(a,b)

model version: 1.1.0. The results are used for scientific research, exploration and teaching, please interpret according to the model conditions.

input parameters

integer a
Value range: 1 – 1000000000
integer b / modulus
Value range: 2 – 1000000000

How to use

  1. Load the example or enter data that matches the field description.
  2. Confirm units and models, run calculations and check diagnostics.
  3. Export charts, tables or results packages and record model versions.

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FROM SCIENCE TO PRACTICE

commercial application case

Industry Application · Independent Reproduction Example

Extended Euclidean Algorithm

algorithm engineer verifies modular inversion and key mathematical parameters.

Public industry reference: Stanford · Applied Cryptography Group

The institution’s public research directions include: applied cryptography, proof systems and security protocols. This link serves as a portal for field background and extended learning.

View product or organization original information

on this site

  1. Load the default example of Extended Euclidean Algorithm and check integer a、integer b / modulus and its units.
  2. is calculated using ax+by=gcd(a,b), and the results are compared after adjusting a single parameter.
  3. checks applicable conditions and diagnostics, and exports numerical tables, charts, and model versions for review.

Deliverables

finds the greatest common divisor, Bézout coefficient, and modular inverse when they exist. delivers parameter records, calculation charts, and reproducible JSON result packages.

needs to be checked before landing

is an exact integer; the modular inverse only exists when the two numbers are relatively prime.。

case is compiled for public industry purposes, and the reproduction steps are independent examples of this site; it does not mean that the above-mentioned institutions use or endorse this site, nor does it cite customer benefits that have not been publicly verified. The

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recommended by universities and research institutions

Cryptography

The following is the recommended reading order of this website organized by direction relevance, public research resources and learning portals. The number is the serial number recommended by the editor, not QS, THE or paper measurement ranking; it does not represent the overall strength of the institution.

  1. 01

    Stanford · Applied Cryptography Group

    United States The

    applied cryptography, proof systems and security protocols。

    official website link accessibility check: 2026-10-03
  2. 02

    KU Leuven · COSIC

    Belgium

    cryptographic algorithms, hardware security and post-quantum cryptography。

    official website link accessibility check: 2026-10-03
  3. 03

    NIST · Computer Security Resource Center

    United States The

    cryptographic standards, algorithm verification and post-quantum standardization。

    official website link accessibility check: 2026-10-03

catalog compiled on 2026-10-03. Link accessibility does not equate to verification of the latest papers, admissions, or program status; please check the institution's official website for specific research teams and opportunities.

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