Quoting form the draft of OpenSSL upstream advisory:

Memory corruption in the ASN.1 encoder (CVE-2016-2108)
======================================================

Severity: High

This issue affected versions of OpenSSL prior to April 2015. The bug
causing the vulnerability was fixed on April 18th 2015, and released
as part of the June 11th 2015 security releases. The security impact
of the bug was not known at the time.

In previous versions of OpenSSL, ASN.1 encoding the value zero
represented as a negative integer can cause a buffer underflow
with an out-of-bounds write in i2c_ASN1_INTEGER. The ASN.1 parser does
not normally create "negative zeroes" when parsing ASN.1 input, and
therefore, an attacker cannot trigger this bug.

However, a second, independent bug revealed that the ASN.1 parser
(specifically, d2i_ASN1_TYPE) can misinterpret a large universal tag
as a negative zero value. Large universal tags are not present in any
common ASN.1 structures (such as X509) but are accepted as part of ANY
structures.

Therefore, if an application deserializes untrusted ASN.1 structures
containing an ANY field, and later reserializes them, an attacker may
be able to trigger an out-of-bounds write. This has been shown to
cause memory corruption that is potentially exploitable with some
malloc implementations.

Applications that parse and re-encode X509 certificates are known to
be vulnerable. Applications that verify RSA signatures on X509
certificates may also be vulnerable; however, only certificates with
valid signatures trigger ASN.1 re-encoding and hence the
bug. Specifically, since OpenSSL's default TLS X509 chain verification
code verifies the certificate chain from root to leaf, TLS handshakes
could only be targeted with valid certificates issued by trusted
Certification Authorities.

OpenSSL 1.0.2 users should upgrade to 1.0.2c
OpenSSL 1.0.1 users should upgrade to 1.0.1o

This vulnerability is a combination of two bugs, neither of which
individually has security impact. The first bug (mishandling of
negative zero integers) was reported to OpenSSL by Huzaifa Sidhpurwala
(Red Hat) and independently by Hanno Böck in April 2015. The second
issue (mishandling of large universal tags) was found using libFuzzer,
and reported on the public issue tracker on March 1st 2016. The fact
that these two issues combined present a security vulnerability was
reported by David Benjamin (Google) on March 31st 2016. The fixes were
developed by Steve Henson of the OpenSSL development team, and David
Benjamin.  The OpenSSL team would also like to thank Mark Brand and
Ian Beer from the Google Project Zero team for their careful analysis
of the impact.

The fix for the "negative zero" memory corruption bug can be
identified by commits

3661bb4e7934668bd99ca777ea8b30eedfafa871 (1.0.2)
and
32d3b0f52f77ce86d53f38685336668d47c5bdfe (1.0.1)

End of quote.


Links to the mentioned commits correcting the "negative zero" memory corruption bug:

1.0.2: https://git.openssl.org/gitweb/?p=openssl.git;a=commitdiff;h=3661bb4e7934668bd99ca777ea8b30eedfafa871
1.0.1: https://git.openssl.org/gitweb/?p=openssl.git;a=commitdiff;h=32d3b0f52f77ce86d53f38685336668d47c5bdfe

The report of the additional problem - mishandling of large universal tags:

https://rt.openssl.org/Ticket/Display.html?id=4364&user=guest&pass=guest

Includes proposed fix and the matching fix that was applied to BoringSSL:

https://boringssl.googlesource.com/boringssl/+/fb2c6f8c8565e1e2d85c24408050c96521acbcdc%5E!/