backport of commit ed08e45069 (#19527)

Co-authored-by: Rachel Culpepper <84159930+rculpepper@users.noreply.github.com>

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
+	var r uint8 = 0
+	var i uint8 = 8
 
-	ret := int(expTable[sum])
+	for i > 0 {
+		i--
+		r = (-(b >> i & 1) & a) ^ (-(r >> 7) & 0x1B) ^ (r + r)
+	}
 
-	// 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)
-
-	return uint8(ret)
+	return r
 }
 
 // add combines two numbers in GF(2^8)

shamir/tables.go

@@ -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,
-	}
-)

shamir/tables_test.go

@@ -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)
-		}
-	}
-}