Use a simpler process to compute n0

This seems to be a relatively common trick.
https://crypto.stackexchange.com/a/47496 and
https://bearssl.org/bigint.html#montgomery-reduction-and-multiplication
were the clearest citations I could find.

I modified it slightly. Normally you need n0 up to the precision of the
word size you can easily multiply. We actually need double-word (64-bit)
precision on 32-bit architectures, due to the x86 assembly. (32-bit x86
has 64-bit multiplication in SSE2. We currently compute a 64-bit n0 on
all 32-bit platforms but just ignore the upper half on the others.)

So we start by computing the 32-bit inverse, using uint32_t, then do one
extra iteration in 64-bit. The recurrence can also be modified for the
negative inverse, which lets us do the negation while we're still
single-precision.

This is also the technique described in
https://en.wikipedia.org/wiki/Montgomery_modular_multiplication#Arithmetic_in_Montgomery_form
as Hensel's lemma, but I'm having a hard time following the extremely
generalized description there.

Change-Id: I08580cdd09929cebca723570ef44068304d5ac43
Reviewed-on: https://boringssl-review.googlesource.com/c/boringssl/+/82027
Reviewed-by: Lily Chen <chlily@google.com>
Auto-Submit: David Benjamin <davidben@google.com>
Commit-Queue: David Benjamin <davidben@google.com>
1 file changed
tree: a43ac179294ebc1c19e0780bc427cf1fb3dd4e39
  1. .bcr/
  2. .github/
  3. cmake/
  4. crypto/
  5. decrepit/
  6. docs/
  7. fuzz/
  8. gen/
  9. include/
  10. infra/
  11. pki/
  12. rust/
  13. ssl/
  14. third_party/
  15. tool/
  16. util/
  17. .bazelignore
  18. .bazelrc
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  21. .gitignore
  22. API-CONVENTIONS.md
  23. AUTHORS
  24. BREAKING-CHANGES.md
  25. BUILD.bazel
  26. build.json
  27. BUILDING.md
  28. CMakeLists.txt
  29. codereview.settings
  30. CONTRIBUTING.md
  31. FUZZING.md
  32. go.mod
  33. go.sum
  34. INCORPORATING.md
  35. LICENSE
  36. MODULE.bazel
  37. MODULE.bazel.lock
  38. PORTING.md
  39. PrivacyInfo.xcprivacy
  40. README.md
  41. SANDBOXING.md
  42. STYLE.md
README.md

BoringSSL

BoringSSL is a fork of OpenSSL that is designed to meet Google's needs.

Although BoringSSL is an open source project, it is not intended for general use, as OpenSSL is. We don't recommend that third parties depend upon it. Doing so is likely to be frustrating because there are no guarantees of API or ABI stability.

Programs ship their own copies of BoringSSL when they use it and we update everything as needed when deciding to make API changes. This allows us to mostly avoid compromises in the name of compatibility. It works for us, but it may not work for you.

BoringSSL arose because Google used OpenSSL for many years in various ways and, over time, built up a large number of patches that were maintained while tracking upstream OpenSSL. As Google's product portfolio became more complex, more copies of OpenSSL sprung up and the effort involved in maintaining all these patches in multiple places was growing steadily.

Currently BoringSSL is the SSL library in Chrome/Chromium, Android (but it's not part of the NDK) and a number of other apps/programs.

Project links:

To file a security issue, use the Chromium process and mention in the report this is for BoringSSL. You can ignore the parts of the process that are specific to Chromium/Chrome.

There are other files in this directory which might be helpful: