liveBook · Manning

Mpz_invert

As explained in Elliptic Curve Cryptography for Developers

mpz_invert is a GMP function that computes a modular multiplicative inverse when one exists.

mpz_invert computes the multiplicative inverse of c modulo n when one exists, providing the inverse needed for modular division. section 2.3

Use the inverse inside a modular division routine:

  • Initialize temporary storage so the result can safely overlap an input without clobbering it. section 2.3
  • Call mpz_invert(rslt, c, n) and test its return value; failure is treated as a division-by-zero error. section 2.3

Modular division

The routine computes a = b/c mod n by obtaining c's inverse, multiplying it by b, reducing the product modulo n, and aborting if inversion fails.

How Elliptic Curve Cryptography for Developers covers it

How deep it goes
Explains the API's operational role and error path, while deferring Euclid's algorithmic derivation.
Examples
Uses a C mod_div() routine that computes b/c modulo n and handles failed inversion as a fatal error.
What it assumes
Assumes modular arithmetic and GMP integer handling, while reinforcing initialization, alias safety, error checks, and cleanup.
What you can do after
Apply it via GMP to implement modular division with temporary storage, failure checks, reduction, and cleanup.
How it connects
Connects modular inversion with modular division, Euclid's algorithm, finite-field arithmetic, and modulus management.
Cover of Elliptic Curve Cryptography for Developers
liveBookmanning.com
Read Elliptic Curve Cryptography for Developers on liveBook Get the book at manning.com

Related concepts

This explainer was generated by Manning's knowledge graph from the text of Elliptic Curve Cryptography for Developers. The section links point to the parts of the book it draws on.