This commit adds a dedicated function in `EC_METHOD` to access a modular
field inversion implementation suitable for the specifics of the
implemented curve, featuring SCA countermeasures.
The new pointer is defined as:
`int (*field_inv)(const EC_GROUP*, BIGNUM *r, const BIGNUM *a, BN_CTX*)`
and computes the multiplicative inverse of `a` in the underlying field,
storing the result in `r`.
Three implementations are included, each including specific SCA
countermeasures:
- `ec_GFp_simple_field_inv()`, featuring SCA hardening through
blinding.
- `ec_GFp_mont_field_inv()`, featuring SCA hardening through Fermat's
Little Theorem (FLT) inversion.
- `ec_GF2m_simple_field_inv()`, that uses `BN_GF2m_mod_inv()` which
already features SCA hardening through blinding.
From a security point of view, this also helps addressing a leakage
previously affecting conversions from projective to affine coordinates.
This commit also adds a new error reason code (i.e.,
`EC_R_CANNOT_INVERT`) to improve consistency between the three
implementations as all of them could fail for the same reason but
through different code paths resulting in inconsistent error stack
states.
Co-authored-by: Nicola Tuveri <nic.tuv@gmail.com>
Reviewed-by: Matt Caswell <matt@openssl.org>
Reviewed-by: Nicola Tuveri <nic.tuv@gmail.com>
(Merged from https://github.com/openssl/openssl/pull/8254)
e0033efc30