Move common code between two branches.

Some follow-up cleanup to bd30f8e34a38d04bf34df51ea0a2ce159e8ab273.

Change-Id: Id996c6c43f42f4db410e1e612ee1e5e8e0233356
Reviewed-on: https://boringssl-review.googlesource.com/1569
Reviewed-by: Adam Langley <agl@google.com>