Bignum: Add the new modulus and the residue structures with low level I/O operations

[yanesca]

Add the modulus and the residue structures with low level I/O operations.

Residue structure:

typedef struct
{
    size_t n;
    mbedtls_mpi_uint *p;
} mbedtls_mpi_mod_residue;

Modulus structure:

typedef struct {
    mbedtls_mpi_uint *p;
    size_t n; // number of limbs
    size_t plen; // bitlen of p
    int ext_rep; // signals external representation (eg. byte order)
    int int_rep; // selector to signal the active member of the union
    union rep
    {
        mbedtls_mpi_mont_struct mont;
        mbedtls_mpi_opt_red_struct ored;
    };
} mbedtls_mpi_mod_modulus;

(The latter is different from the one in the design document and this is intentional as there were changes based on Gilles's feedback.)

mbedtls_mpi_mont_struct and mbedtls_mpi_opt_red_struct are dummy structs for now (eg aliasing to void*).

The task is to add life cycle functions and low level I/O:

• Standard init and free functions for the modulus. The residue doesn't own its memory, it only needs a release function, that releases the pointer set in setup (sets the p to NULL and n to 0). (The modulus doesn't own the memory pointed by p either, but will need to allocate memory for mbedtls_mpi_opt_red_struct later). Setup for residue takes a modulus and a raw pointer (mbedtls_mpi_uint*). It takes n from there and fails if the value defined by the raw pointer and n is greater than or equal to the modulus. Setup for the modulus takes p, n, ext_rep, int_rep and calculates plen. All of these have mbedtls_mpi_mod prefix and are declared in library/bignum_mod.h.
• One set of I/O functions (mbedtls_mpi_core_read_le(),mbedtls_mpi_core_write_le(), mbedtls_mpi_core_read_be(),mbedtls_mpi_core_write_be()). These should work exactly like their legacy counterparts (eg. mbedtls_mpi_read_binary()), but should take a raw pointer (mbedtls_mpi_uint*) and a length instead of an mbedtls_mpi*. The legacy functions should call these new mpi_core_ functions instead of duplicating code. The function declarations go into library/bignum_core.h.
• Another set of I/O functions (mbedtls_mpi_mod_raw_read() and mbedtls_mpi_mod_raw_write()) should take a raw pointer (mbedtls_mpi_uint*) and a modulus. The length and the external representation should be taken from the modulus. The function declarations go into library/bignum_mod_raw.h.

All new function implementations should go into bignum_new.c.

This task is done when the following changes are merged on development:

• The two structures and their life cycle functions have been added
• The core I/O functions have been added with extensive unit tests
• The raw I/O functions have been added with extensive unit tests