Simplify HRSS mod3 circuits.

The multiplication and subtraction circuits were found by djb using GNU
Superoptimizer, and the addition circuit is derived from the subtraction
one by hand. They depend on a different representation: -1 is now (1, 1)
rather than (1, 0), and the latter becomes undefined.

The following Python program checks that the circuits work:

values = [0, 1, -1]

def toBits(v):
    if v == 0:
        return 0, 0
    elif v == 1:
        return 0, 1
    elif v == -1:
        return 1, 1
        raise ValueError(v)

def mul((s1, a1), (s2, a2)):
    return ((s1 ^ s2) & a1 & a2, a1 & a2)

def add((s1, a1), (s2, a2)):
    t = s1 ^ a2
    return (t & (s2 ^ a1), (a1 ^ a2) | (t ^ s2))

def sub((s1, a1), (s2, a2)):
    t = a1 ^ a2
    return ((s1 ^ a2) & (t ^ s2), t | (s1 ^ s2))

def fromBits((s, a)):
    if s == 0 and a == 0:
        return 0
    if s == 0 and a == 1:
        return 1
    if s == 1 and a == 1:
        return -1
        raise ValueError((s, a))

def wrap(v):
    if v == 2:
        return -1
    elif v == -2:
        return 1
        return v

for v1 in values:
    for v2 in values:
        print v1, v2

        result = fromBits(mul(toBits(v1), toBits(v2)))
        if result != v1 * v2:
            raise ValueError((v1, v2, result))

        result = fromBits(add(toBits(v1), toBits(v2)))
        if result != wrap(v1 + v2):
            raise ValueError((v1, v2, result))

        result = fromBits(sub(toBits(v1), toBits(v2)))
        if result != wrap(v1 - v2):
            raise ValueError((v1, v2, result))

Change-Id: Ie1a4ca5a82c2651057efc62330eca6fdd9878122
Reviewed-by: David Benjamin <>
2 files changed
tree: 9306bf94ffe191b2a3849e48f86e59b4a6b0b3a0
  1. .clang-format
  2. .github/
  3. .gitignore
  7. CMakeLists.txt
  15. codereview.settings
  16. crypto/
  17. decrepit/
  18. fipstools/
  19. fuzz/
  20. go.mod
  21. include/
  22. infra/
  23. sources.cmake
  24. ssl/
  25. third_party/
  26. tool/
  27. util/


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

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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.

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