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Mpz_t

As explained in Elliptic Curve Cryptography for Developers

mpz_t is GMP's type for representing arbitrary-precision integers.

mpz_t is GMP’s type for arbitrary-precision integers. Finite-field routines use it for operands, results, and moduli, combining GMP operations such as addition, multiplication, division, inversion, and mpz_mod(). section 2.3

Use mpz_t with an explicit lifecycle and alias-safe intermediate storage:

  • Initialize variables with mpz_init() or mpz_init_set() before computation. section 2.3
  • Place output before input arguments, matching the a = b op c convention. section 2.3
  • Use a temporary mpz_t when calculations could overwrite an input, then release it with mpz_clear(). section 2.3

Modular addition

A modular addition routine initializes rslt, computes mpz_add(rslt, b, c), reduces it with mpz_mod(a, rslt, n), and clears rslt.

How Elliptic Curve Cryptography for Developers covers it

How deep it goes
Defines the type and demonstrates initialization, temporary storage, argument ordering, arithmetic, reduction, inversion, and cleanup.
Examples
Uses modular addition, modular division, shared modulus state, and a header containing explicit and implicit-modulus APIs.
What it assumes
Assumes C function calls and modular arithmetic, while defining GMP’s integer type and its basic lifecycle from the implementation context.
What you can do after
Build modular arithmetic routines with GMP while preserving inputs through temporaries and managing mpz_t storage explicitly.
How it connects
Connects arbitrary-precision integers with GMP, modular arithmetic, finite fields, and embedded-system arithmetic implementations.
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Related concepts

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