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Simplify encoding of e in GF(1024) tables to (1,0)

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This follows PR 64 of the sipa/bech32 repo.
This commit is contained in:
Samuel Dobson 2021-11-30 11:49:06 +13:00
parent 14358a029d
commit 28d9c2857f
1 changed files with 9 additions and 9 deletions
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18
src/bech32.cpp
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@ -84,14 +84,16 @@ constexpr std::pair<std::array<int16_t, 1023>, std::array<int16_t, 1024>> Genera
// Each element v of GF(1024) is encoded as a 10 bit integer in the following way:
// v = v1 || v0 where v0, v1 are 5-bit integers (elements of GF(32)).
// The element (e) is encoded as 9 || 15. Given (v), we
// compute (e)*(v) by multiplying in the following way:
// The element (e) is encoded as 1 || 0, to represent 1*(e) + 0. Every other element
// a*(e) + b is represented as a || b (a and b are both GF(32) elements). Given (v),
// we compute (e)*(v) by multiplying in the following way:
//
// v0' = 27*v1 + 15*v0
// v1' = 6*v1 + 9*v0
// v0' = 23*v1
// v1' = 9*v1 + v0
// e*v = v1' || v0'
//
// Multiplication in GF(32) is done using the log/exp tables:
// Where 23, 9 are GF(32) elements encoded as described above. Multiplication in GF(32)
// is done using the log/exp tables:
// e^x * e^y = e^(x + y) so a * b = EXP[ LOG[a] + LOG [b] ]
// for non-zero a and b.
@ -100,10 +102,8 @@ constexpr std::pair<std::array<int16_t, 1023>, std::array<int16_t, 1024>> Genera
int v0 = v & 31;
int v1 = v >> 5;
int v0n = (v1 ? GF32_EXP.at((GF32_LOG.at(v1) + GF32_LOG.at(27)) % 31) : 0) ^
(v0 ? GF32_EXP.at((GF32_LOG.at(v0) + GF32_LOG.at(15)) % 31) : 0);
int v1n = (v1 ? GF32_EXP.at((GF32_LOG.at(v1) + GF32_LOG.at(6)) % 31) : 0) ^
(v0 ? GF32_EXP.at((GF32_LOG.at(v0) + GF32_LOG.at(9)) % 31) : 0);
int v0n = v1 ? GF32_EXP.at((GF32_LOG.at(v1) + GF32_LOG.at(23)) % 31) : 0;
int v1n = (v1 ? GF32_EXP.at((GF32_LOG.at(v1) + GF32_LOG.at(9)) % 31) : 0) ^ v0;
v = v1n << 5 | v0n;
GF1024_EXP[i] = v;