Including string.h in base.h causes any file that includes a BoringSSL
header to include string.h. Generally this wouldn't be a problem,
although string.h might slow down the compile if it wasn't otherwise
needed. However, it also causes problems for ipsec-tools in Android
because OpenSSL didn't have this behaviour.

This change removes string.h from base.h and, instead, adds it to each
.c file that requires it.

Change-Id: I5968e50b0e230fd3adf9b72dd2836e6f52d6fb37
Reviewed-on: https://boringssl-review.googlesource.com/3200
Reviewed-by: David Benjamin <davidben@chromium.org>
Reviewed-by: Adam Langley <agl@google.com>

Initial fork from f2d678e6e8 (1.0.2 beta).

(This change contains substantial changes from the original and
effectively starts a new history.)