The EFD database does not state that the "ladd-2002-it-3" algorithm
assumes X1 != 0.
Consequently the current implementation, based on it, fails to compute
correctly if the affine x coordinate of the scalar multiplication input
point is 0.
We replace this implementation using the alternative algorithm based on
Eq. (9) and (10) from the same paper, which being derived from the
additive relation of (6) does not incur in this problem, but costs one
extra field multiplication.
The EFD entry for this algorithm is at
https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-ladd-2002-it-4
and the code to implement it was generated with tooling.
Regression tests add one positive test for each named curve that has
such a point. The `SharedSecret` was generated independently from the
OpenSSL codebase with sage.
This bug was originally reported by Dmitry Belyavsky on the
openssl-users maling list:
https://mta.openssl.org/pipermail/openssl-users/2018-August/008540.html
Co-authored-by: Billy Brumley <bbrumley@gmail.com>
Reviewed-by: Andy Polyakov <appro@openssl.org>
Reviewed-by: Tim Hudson <tjh@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/7000)
1. For every named curve, two "golden" keypair positive tests.
2. Also two "golden" stock ECDH positive tests.
3. For named curves with non-trivial cofactors, additionally two "golden"
ECC CDH positive tests.
4. For named curves with non-trivial cofactors, additionally two negative
tests.
There is some overlap with existing EVP tests, especially for the NIST
curves (for example, positive testing ECC CDH KATs for NIST curves).
"Golden" here means all the values are independent from OpenSSL's ECC
code. I used sage to calculate them. What comes from OpenSSL is:
1. The OIDs (parsed by tooling)
2. The curve parameters (parsing ecparam output with tooling)
The values inside the PEMs (private keys, public keys) and shared keys
are from sage. The PEMs themselves are the output of asn1parse, with
input taken from sage.
Reviewed-by: Andy Polyakov <appro@openssl.org>
Reviewed-by: Rich Salz <rsalz@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/6608)
