From ed08e45069d60fc4452fad7d44bcfd3b2e4c8236 Mon Sep 17 00:00:00 2001 From: Rachel Culpepper <84159930+rculpepper@users.noreply.github.com> Date: Mon, 13 Mar 2023 15:52:55 -0400 Subject: [PATCH] change mul and div functions (#19495) --- shamir/shamir.go | 39 +++++++++++++-------- shamir/tables.go | 79 ------------------------------------------- shamir/tables_test.go | 13 ------- 3 files changed, 24 insertions(+), 107 deletions(-) delete mode 100644 shamir/tables.go delete mode 100644 shamir/tables_test.go diff --git a/shamir/shamir.go b/shamir/shamir.go index e311f501d9bc..22e3c337dcb1 100644 --- a/shamir/shamir.go +++ b/shamir/shamir.go @@ -86,31 +86,40 @@ func div(a, b uint8) uint8 { panic("divide by zero") } - log_a := logTable[a] - log_b := logTable[b] - diff := ((int(log_a) - int(log_b)) + 255) % 255 - - ret := int(expTable[diff]) + ret := int(mult(a, inverse(b))) // Ensure we return zero if a is zero but aren't subject to timing attacks ret = subtle.ConstantTimeSelect(subtle.ConstantTimeByteEq(a, 0), 0, ret) return uint8(ret) } +// inverse calculates the inverse of a number in GF(2^8) +func inverse(a uint8) uint8 { + b := mult(a, a) + c := mult(a, b) + b = mult(c, c) + b = mult(b, b) + c = mult(b, c) + b = mult(b, b) + b = mult(b, b) + b = mult(b, c) + b = mult(b, b) + b = mult(a, b) + + return mult(b, b) +} + // mult multiplies two numbers in GF(2^8) func mult(a, b uint8) (out uint8) { - log_a := logTable[a] - log_b := logTable[b] - sum := (int(log_a) + int(log_b)) % 255 - - ret := int(expTable[sum]) + var r uint8 = 0 + var i uint8 = 8 - // Ensure we return zero if either a or b are zero but aren't subject to - // timing attacks - ret = subtle.ConstantTimeSelect(subtle.ConstantTimeByteEq(a, 0), 0, ret) - ret = subtle.ConstantTimeSelect(subtle.ConstantTimeByteEq(b, 0), 0, ret) + for i > 0 { + i-- + r = (-(b >> i & 1) & a) ^ (-(r >> 7) & 0x1B) ^ (r + r) + } - return uint8(ret) + return r } // add combines two numbers in GF(2^8) diff --git a/shamir/tables.go b/shamir/tables.go deleted file mode 100644 index 07ec4e5283fc..000000000000 --- a/shamir/tables.go +++ /dev/null @@ -1,79 +0,0 @@ -package shamir - -// Tables taken from http://www.samiam.org/galois.html -// They use 0xe5 (229) as the generator - -var ( - // logTable provides the log(X)/log(g) at each index X - logTable = [256]uint8{ - 0x00, 0xff, 0xc8, 0x08, 0x91, 0x10, 0xd0, 0x36, - 0x5a, 0x3e, 0xd8, 0x43, 0x99, 0x77, 0xfe, 0x18, - 0x23, 0x20, 0x07, 0x70, 0xa1, 0x6c, 0x0c, 0x7f, - 0x62, 0x8b, 0x40, 0x46, 0xc7, 0x4b, 0xe0, 0x0e, - 0xeb, 0x16, 0xe8, 0xad, 0xcf, 0xcd, 0x39, 0x53, - 0x6a, 0x27, 0x35, 0x93, 0xd4, 0x4e, 0x48, 0xc3, - 0x2b, 0x79, 0x54, 0x28, 0x09, 0x78, 0x0f, 0x21, - 0x90, 0x87, 0x14, 0x2a, 0xa9, 0x9c, 0xd6, 0x74, - 0xb4, 0x7c, 0xde, 0xed, 0xb1, 0x86, 0x76, 0xa4, - 0x98, 0xe2, 0x96, 0x8f, 0x02, 0x32, 0x1c, 0xc1, - 0x33, 0xee, 0xef, 0x81, 0xfd, 0x30, 0x5c, 0x13, - 0x9d, 0x29, 0x17, 0xc4, 0x11, 0x44, 0x8c, 0x80, - 0xf3, 0x73, 0x42, 0x1e, 0x1d, 0xb5, 0xf0, 0x12, - 0xd1, 0x5b, 0x41, 0xa2, 0xd7, 0x2c, 0xe9, 0xd5, - 0x59, 0xcb, 0x50, 0xa8, 0xdc, 0xfc, 0xf2, 0x56, - 0x72, 0xa6, 0x65, 0x2f, 0x9f, 0x9b, 0x3d, 0xba, - 0x7d, 0xc2, 0x45, 0x82, 0xa7, 0x57, 0xb6, 0xa3, - 0x7a, 0x75, 0x4f, 0xae, 0x3f, 0x37, 0x6d, 0x47, - 0x61, 0xbe, 0xab, 0xd3, 0x5f, 0xb0, 0x58, 0xaf, - 0xca, 0x5e, 0xfa, 0x85, 0xe4, 0x4d, 0x8a, 0x05, - 0xfb, 0x60, 0xb7, 0x7b, 0xb8, 0x26, 0x4a, 0x67, - 0xc6, 0x1a, 0xf8, 0x69, 0x25, 0xb3, 0xdb, 0xbd, - 0x66, 0xdd, 0xf1, 0xd2, 0xdf, 0x03, 0x8d, 0x34, - 0xd9, 0x92, 0x0d, 0x63, 0x55, 0xaa, 0x49, 0xec, - 0xbc, 0x95, 0x3c, 0x84, 0x0b, 0xf5, 0xe6, 0xe7, - 0xe5, 0xac, 0x7e, 0x6e, 0xb9, 0xf9, 0xda, 0x8e, - 0x9a, 0xc9, 0x24, 0xe1, 0x0a, 0x15, 0x6b, 0x3a, - 0xa0, 0x51, 0xf4, 0xea, 0xb2, 0x97, 0x9e, 0x5d, - 0x22, 0x88, 0x94, 0xce, 0x19, 0x01, 0x71, 0x4c, - 0xa5, 0xe3, 0xc5, 0x31, 0xbb, 0xcc, 0x1f, 0x2d, - 0x3b, 0x52, 0x6f, 0xf6, 0x2e, 0x89, 0xf7, 0xc0, - 0x68, 0x1b, 0x64, 0x04, 0x06, 0xbf, 0x83, 0x38, - } - - // expTable provides the anti-log or exponentiation value - // for the equivalent index - expTable = [256]uint8{ - 0x01, 0xe5, 0x4c, 0xb5, 0xfb, 0x9f, 0xfc, 0x12, - 0x03, 0x34, 0xd4, 0xc4, 0x16, 0xba, 0x1f, 0x36, - 0x05, 0x5c, 0x67, 0x57, 0x3a, 0xd5, 0x21, 0x5a, - 0x0f, 0xe4, 0xa9, 0xf9, 0x4e, 0x64, 0x63, 0xee, - 0x11, 0x37, 0xe0, 0x10, 0xd2, 0xac, 0xa5, 0x29, - 0x33, 0x59, 0x3b, 0x30, 0x6d, 0xef, 0xf4, 0x7b, - 0x55, 0xeb, 0x4d, 0x50, 0xb7, 0x2a, 0x07, 0x8d, - 0xff, 0x26, 0xd7, 0xf0, 0xc2, 0x7e, 0x09, 0x8c, - 0x1a, 0x6a, 0x62, 0x0b, 0x5d, 0x82, 0x1b, 0x8f, - 0x2e, 0xbe, 0xa6, 0x1d, 0xe7, 0x9d, 0x2d, 0x8a, - 0x72, 0xd9, 0xf1, 0x27, 0x32, 0xbc, 0x77, 0x85, - 0x96, 0x70, 0x08, 0x69, 0x56, 0xdf, 0x99, 0x94, - 0xa1, 0x90, 0x18, 0xbb, 0xfa, 0x7a, 0xb0, 0xa7, - 0xf8, 0xab, 0x28, 0xd6, 0x15, 0x8e, 0xcb, 0xf2, - 0x13, 0xe6, 0x78, 0x61, 0x3f, 0x89, 0x46, 0x0d, - 0x35, 0x31, 0x88, 0xa3, 0x41, 0x80, 0xca, 0x17, - 0x5f, 0x53, 0x83, 0xfe, 0xc3, 0x9b, 0x45, 0x39, - 0xe1, 0xf5, 0x9e, 0x19, 0x5e, 0xb6, 0xcf, 0x4b, - 0x38, 0x04, 0xb9, 0x2b, 0xe2, 0xc1, 0x4a, 0xdd, - 0x48, 0x0c, 0xd0, 0x7d, 0x3d, 0x58, 0xde, 0x7c, - 0xd8, 0x14, 0x6b, 0x87, 0x47, 0xe8, 0x79, 0x84, - 0x73, 0x3c, 0xbd, 0x92, 0xc9, 0x23, 0x8b, 0x97, - 0x95, 0x44, 0xdc, 0xad, 0x40, 0x65, 0x86, 0xa2, - 0xa4, 0xcc, 0x7f, 0xec, 0xc0, 0xaf, 0x91, 0xfd, - 0xf7, 0x4f, 0x81, 0x2f, 0x5b, 0xea, 0xa8, 0x1c, - 0x02, 0xd1, 0x98, 0x71, 0xed, 0x25, 0xe3, 0x24, - 0x06, 0x68, 0xb3, 0x93, 0x2c, 0x6f, 0x3e, 0x6c, - 0x0a, 0xb8, 0xce, 0xae, 0x74, 0xb1, 0x42, 0xb4, - 0x1e, 0xd3, 0x49, 0xe9, 0x9c, 0xc8, 0xc6, 0xc7, - 0x22, 0x6e, 0xdb, 0x20, 0xbf, 0x43, 0x51, 0x52, - 0x66, 0xb2, 0x76, 0x60, 0xda, 0xc5, 0xf3, 0xf6, - 0xaa, 0xcd, 0x9a, 0xa0, 0x75, 0x54, 0x0e, 0x01, - } -) diff --git a/shamir/tables_test.go b/shamir/tables_test.go deleted file mode 100644 index 81aa983b1087..000000000000 --- a/shamir/tables_test.go +++ /dev/null @@ -1,13 +0,0 @@ -package shamir - -import "testing" - -func TestTables(t *testing.T) { - for i := 1; i < 256; i++ { - logV := logTable[i] - expV := expTable[logV] - if expV != uint8(i) { - t.Fatalf("bad: %d log: %d exp: %d", i, logV, expV) - } - } -}