gcs: update fp and modulus values based on recent optimality analysis

In this commit, we decrease the default fp rate to 19, or 1/2^19. We do
this as recent analysis by sipa on the bitcoin dev mailing list has
shown that optimally, we can use a value of 2^19 for the fp rate, while
use n=1.497137*2^P rather than n directly. As a result, we can shrink
the filter size by quite a bit, while still maintaining a sane false
positive value.

gcs/builder/builder.go

@@ -8,6 +8,8 @@ package builder
 import (
 	"crypto/rand"
 	"encoding/binary"
+	"fmt"
+	"math"
 
 	"github.com/btcsuite/btcd/chaincfg/chainhash"
 	"github.com/btcsuite/btcd/txscript"
@@ -15,13 +17,20 @@ import (
 	"github.com/btcsuite/btcutil/gcs"
 )
 
-// DefaultP is the default collision probability (2^-20)
+const (
-const DefaultP = 20
+	// DefaultP is the default collision probability (2^-19)
+	DefaultP = 19
+
+	// DefaultM is the default value used for the hash range.
+	DefaultM uint64 = 784931
+)
 
 // GCSBuilder is a utility class that makes building GCS filters convenient.
 type GCSBuilder struct {
 	p uint8
 
+	m uint64
+
 	key [gcs.KeySize]byte
 
 	// data is a set of entries represented as strings. This is done to
@@ -120,6 +129,23 @@ func (b *GCSBuilder) SetP(p uint8) *GCSBuilder {
 	return b
 }
 
+// SetM sets the filter's modulous value after calling Builder().
+func (b *GCSBuilder) SetM(m uint64) *GCSBuilder {
+	// Do nothing if the builder's already errored out.
+	if b.err != nil {
+		return b
+	}
+
+	// Basic sanity check.
+	if m > uint64(math.MaxUint32) {
+		b.err = gcs.ErrPTooBig
+		return b
+	}
+
+	b.m = m
+	return b
+}
+
 // Preallocate sets the estimated filter size after calling Builder() to reduce
 // the probability of memory reallocations. If the builder has already had data
 // added to it, Preallocate has no effect.
@@ -221,46 +247,57 @@ func (b *GCSBuilder) Build() (*gcs.Filter, error) {
 		return nil, b.err
 	}
 
+	// We'll ensure that all the parmaters we need to actually build the
+	// filter properly are set.
+	if b.p == 0 {
+		return nil, fmt.Errorf("p value is not set, cannot build")
+	}
+	if b.m == 0 {
+		return nil, fmt.Errorf("m value is not set, cannot build")
+	}
+
 	dataSlice := make([][]byte, 0, len(b.data))
 	for item := range b.data {
 		dataSlice = append(dataSlice, []byte(item))
 	}
 
-	return gcs.BuildGCSFilter(b.p, b.key, dataSlice)
+	return gcs.BuildGCSFilter(b.p, b.m, b.key, dataSlice)
 }
 
-// WithKeyPN creates a GCSBuilder with specified key and the passed probability
+// WithKeyPNM creates a GCSBuilder with specified key and the passed
-// and estimated filter size.
+// probability, modulus and estimated filter size.
-func WithKeyPN(key [gcs.KeySize]byte, p uint8, n uint32) *GCSBuilder {
+func WithKeyPNM(key [gcs.KeySize]byte, p uint8, n uint32, m uint64) *GCSBuilder {
 	b := GCSBuilder{}
-	return b.SetKey(key).SetP(p).Preallocate(n)
+	return b.SetKey(key).SetP(p).SetM(m).Preallocate(n)
 }
 
-// WithKeyP creates a GCSBuilder with specified key and the passed probability.
+// WithKeyPM creates a GCSBuilder with specified key and the passed
-// Estimated filter size is set to zero, which means more reallocations are
+// probability.  Estimated filter size is set to zero, which means more
-// done when building the filter.
+// reallocations are done when building the filter.
-func WithKeyP(key [gcs.KeySize]byte, p uint8) *GCSBuilder {
+func WithKeyPM(key [gcs.KeySize]byte, p uint8, m uint64) *GCSBuilder {
-	return WithKeyPN(key, p, 0)
+	return WithKeyPNM(key, p, 0, m)
 }
 
 // WithKey creates a GCSBuilder with specified key. Probability is set to 19
 // (2^-19 collision probability). Estimated filter size is set to zero, which
 // means more reallocations are done when building the filter.
 func WithKey(key [gcs.KeySize]byte) *GCSBuilder {
-	return WithKeyPN(key, DefaultP, 0)
+	return WithKeyPNM(key, DefaultP, 0, DefaultM)
 }
 
-// WithKeyHashPN creates a GCSBuilder with key derived from the specified
+// WithKeyHashPNM creates a GCSBuilder with key derived from the specified
 // chainhash.Hash and the passed probability and estimated filter size.
-func WithKeyHashPN(keyHash *chainhash.Hash, p uint8, n uint32) *GCSBuilder {
+func WithKeyHashPNM(keyHash *chainhash.Hash, p uint8, n uint32,
-	return WithKeyPN(DeriveKey(keyHash), p, n)
+	m uint64) *GCSBuilder {
+
+	return WithKeyPNM(DeriveKey(keyHash), p, n, m)
 }
 
-// WithKeyHashP creates a GCSBuilder with key derived from the specified
+// WithKeyHashPM creates a GCSBuilder with key derived from the specified
 // chainhash.Hash and the passed probability. Estimated filter size is set to
 // zero, which means more reallocations are done when building the filter.
-func WithKeyHashP(keyHash *chainhash.Hash, p uint8) *GCSBuilder {
+func WithKeyHashPM(keyHash *chainhash.Hash, p uint8, m uint64) *GCSBuilder {
-	return WithKeyHashPN(keyHash, p, 0)
+	return WithKeyHashPNM(keyHash, p, 0, m)
 }
 
 // WithKeyHash creates a GCSBuilder with key derived from the specified
@@ -268,25 +305,25 @@ func WithKeyHashP(keyHash *chainhash.Hash, p uint8) *GCSBuilder {
 // Estimated filter size is set to zero, which means more reallocations are
 // done when building the filter.
 func WithKeyHash(keyHash *chainhash.Hash) *GCSBuilder {
-	return WithKeyHashPN(keyHash, DefaultP, 0)
+	return WithKeyHashPNM(keyHash, DefaultP, 0, DefaultM)
 }
 
-// WithRandomKeyPN creates a GCSBuilder with a cryptographically random key and
+// WithRandomKeyPNM creates a GCSBuilder with a cryptographically random key and
 // the passed probability and estimated filter size.
-func WithRandomKeyPN(p uint8, n uint32) *GCSBuilder {
+func WithRandomKeyPNM(p uint8, n uint32, m uint64) *GCSBuilder {
 	key, err := RandomKey()
 	if err != nil {
 		b := GCSBuilder{err: err}
 		return &b
 	}
-	return WithKeyPN(key, p, n)
+	return WithKeyPNM(key, p, n, m)
 }
 
-// WithRandomKeyP creates a GCSBuilder with a cryptographically random key and
+// WithRandomKeyPM creates a GCSBuilder with a cryptographically random key and
 // the passed probability. Estimated filter size is set to zero, which means
 // more reallocations are done when building the filter.
-func WithRandomKeyP(p uint8) *GCSBuilder {
+func WithRandomKeyPM(p uint8, m uint64) *GCSBuilder {
-	return WithRandomKeyPN(p, 0)
+	return WithRandomKeyPNM(p, 0, m)
 }
 
 // WithRandomKey creates a GCSBuilder with a cryptographically random key.
@@ -294,7 +331,7 @@ func WithRandomKeyP(p uint8) *GCSBuilder {
 // size is set to zero, which means more reallocations are done when
 // building the filter.
 func WithRandomKey() *GCSBuilder {
-	return WithRandomKeyPN(DefaultP, 0)
+	return WithRandomKeyPNM(DefaultP, 0, DefaultM)
 }
 
 // BuildBasicFilter builds a basic GCS filter from a block. A basic GCS filter

gcs/builder/builder_test.go

@@ -105,7 +105,7 @@ func TestUseBlockHash(t *testing.T) {
 	BuilderTest(b, hash, builder.DefaultP, outPoint, addrBytes, witness, t)
 
 	// Create a GCSBuilder with a key hash and non-default P and test it.
-	b = builder.WithKeyHashP(hash, 30)
+	b = builder.WithKeyHashPM(hash, 30, 90)
 	BuilderTest(b, hash, 30, outPoint, addrBytes, witness, t)
 
 	// Create a GCSBuilder with a random key, set the key from a hash
@@ -135,7 +135,7 @@ func TestUseBlockHash(t *testing.T) {
 	BuilderTest(b, hash, builder.DefaultP, outPoint, addrBytes, witness, t)
 
 	// Create a GCSBuilder with a random key and non-default P and test it.
-	b = builder.WithRandomKeyP(30)
+	b = builder.WithRandomKeyPM(30, 90)
 	key2, err := b.Key()
 	if err != nil {
 		t.Fatalf("Builder instantiation with random key failed: %s",
@@ -162,7 +162,7 @@ func TestUseBlockHash(t *testing.T) {
 	BuilderTest(b, hash, builder.DefaultP, outPoint, addrBytes, witness, t)
 
 	// Create a GCSBuilder with a known key and non-default P and test it.
-	b = builder.WithKeyP(testKey, 30)
+	b = builder.WithKeyPM(testKey, 30, 90)
 	key, err = b.Key()
 	if err != nil {
 		t.Fatalf("Builder instantiation with known key failed: %s",
@@ -177,7 +177,7 @@ func TestUseBlockHash(t *testing.T) {
 
 	// Create a GCSBuilder with a known key and too-high P and ensure error
 	// works throughout all functions that use it.
-	b = builder.WithRandomKeyP(33).SetKeyFromHash(hash).SetKey(testKey)
+	b = builder.WithRandomKeyPM(33, 99).SetKeyFromHash(hash).SetKey(testKey)
 	b.SetP(30).AddEntry(hash.CloneBytes()).AddEntries(contents)
 	b.AddOutPoint(outPoint).AddHash(hash).AddScript(addrBytes)
 	_, err = b.Key()

gcs/gcs.go

@@ -52,7 +52,6 @@ const (
 // number to reduce, and our modulus N divided into its high 32-bits and lower
 // 32-bits.
 func fastReduction(v, nHi, nLo uint64) uint64 {
-
 	// First, we'll spit the item we need to reduce into its higher and
 	// lower bits.
 	vhi := v >> 32
@@ -85,13 +84,14 @@ type Filter struct {
 	n         uint32
 	p         uint8
 	modulusNP uint64
+
 	filterData []byte
 }
 
 // BuildGCSFilter builds a new GCS filter with the collision probability of
 // `1/(2**P)`, key `key`, and including every `[]byte` in `data` as a member of
 // the set.
-func BuildGCSFilter(P uint8, key [KeySize]byte, data [][]byte) (*Filter, error) {
+func BuildGCSFilter(P uint8, M uint64, key [KeySize]byte, data [][]byte) (*Filter, error) {
 	// Some initial parameter checks: make sure we have data from which to
 	// build the filter, and make sure our parameters will fit the hash
 	// function we're using.
@@ -107,7 +107,11 @@ func BuildGCSFilter(P uint8, key [KeySize]byte, data [][]byte) (*Filter, error)
 		n: uint32(len(data)),
 		p: P,
 	}
-	f.modulusNP = uint64(f.n) << P
+
+	// First we'll compute the value of m, which is the modulus we use
+	// within our finite field. We want to compute: mScalar * 2^P. We use
+	// math.Round in order to round the value up, rather than down.
+	f.modulusNP = uint64(f.n) * M
 
 	// Shortcut if the filter is empty.
 	if f.n == 0 {
@@ -142,7 +146,7 @@ func BuildGCSFilter(P uint8, key [KeySize]byte, data [][]byte) (*Filter, error)
 	for _, v := range values {
 		// Calculate the difference between this value and the last,
 		// modulo P.
-		remainder = (v - lastValue) & ((uint64(1) << P) - 1)
+		remainder = (v - lastValue) & ((uint64(1) << f.p) - 1)
 
 		// Calculate the difference between this value and the last,
 		// divided by P.
@@ -170,7 +174,7 @@ func BuildGCSFilter(P uint8, key [KeySize]byte, data [][]byte) (*Filter, error)
 
 // FromBytes deserializes a GCS filter from a known N, P, and serialized filter
 // as returned by Bytes().
-func FromBytes(N uint32, P uint8, d []byte) (*Filter, error) {
+func FromBytes(N uint32, P uint8, M uint64, d []byte) (*Filter, error) {
 
 	// Basic sanity check.
 	if P > 32 {
@@ -182,7 +186,11 @@ func FromBytes(N uint32, P uint8, d []byte) (*Filter, error) {
 		n: N,
 		p: P,
 	}
-	f.modulusNP = uint64(f.n) << P
+
+	// First we'll compute the value of m, which is the modulus we use
+	// within our finite field. We want to compute: mScalar * 2^P. We use
+	// math.Round in order to round the value up, rather than down.
+	f.modulusNP = uint64(f.n) * M
 
 	// Copy the filter.
 	f.filterData = make([]byte, len(d))
@@ -193,7 +201,7 @@ func FromBytes(N uint32, P uint8, d []byte) (*Filter, error) {
 
 // FromNBytes deserializes a GCS filter from a known P, and serialized N and
 // filter as returned by NBytes().
-func FromNBytes(P uint8, d []byte) (*Filter, error) {
+func FromNBytes(P uint8, M uint64, d []byte) (*Filter, error) {
 	buffer := bytes.NewBuffer(d)
 	N, err := wire.ReadVarInt(buffer, varIntProtoVer)
 	if err != nil {
@@ -202,34 +210,7 @@ func FromNBytes(P uint8, d []byte) (*Filter, error) {
 	if N >= (1 << 32) {
 		return nil, ErrNTooBig
 	}
-	return FromBytes(uint32(N), P, buffer.Bytes())
+	return FromBytes(uint32(N), P, M, buffer.Bytes())
-}
-
-// FromPBytes deserializes a GCS filter from a known N, and serialized P and
-// filter as returned by NBytes().
-func FromPBytes(N uint32, d []byte) (*Filter, error) {
-	return FromBytes(N, d[0], d[1:])
-}
-
-// FromNPBytes deserializes a GCS filter from a serialized N, P, and filter as
-// returned by NPBytes().
-func FromNPBytes(d []byte) (*Filter, error) {
-	buffer := bytes.NewBuffer(d)
-
-	N, err := wire.ReadVarInt(buffer, varIntProtoVer)
-	if err != nil {
-		return nil, err
-	}
-	if N >= (1 << 32) {
-		return nil, ErrNTooBig
-	}
-
-	P, err := buffer.ReadByte()
-	if err != nil {
-		return nil, err
-	}
-
-	return FromBytes(uint32(N), P, buffer.Bytes())
 }
 
 // Bytes returns the serialized format of the GCS filter, which does not

gcs/gcs_test.go

@@ -18,8 +18,11 @@ var (
 	// No need to allocate an err variable in every test
 	err error
 
-	// Collision probability for the tests (1/2**20)
+	// Collision probability for the tests (1/2**19)
-	P = uint8(20)
+	P = uint8(19)
+
+	// Modulus value for the tests.
+	M uint64 = 784931
 
 	// Filters are conserved between tests but we must define with an
 	// interface which functions we're testing because the gcsFilter type
@@ -79,7 +82,7 @@ func TestGCSFilterBuild(t *testing.T) {
 	for i := 0; i < gcs.KeySize; i += 4 {
 		binary.BigEndian.PutUint32(key[i:], rand.Uint32())
 	}
-	filter, err = gcs.BuildGCSFilter(P, key, contents)
+	filter, err = gcs.BuildGCSFilter(P, M, key, contents)
 	if err != nil {
 		t.Fatalf("Filter build failed: %s", err.Error())
 	}
@@ -91,7 +94,7 @@ func TestGCSFilterCopy(t *testing.T) {
 	if err != nil {
 		t.Fatalf("Filter Bytes() failed: %v", err)
 	}
-	filter2, err = gcs.FromBytes(filter.N(), P, serialized2)
+	filter2, err = gcs.FromBytes(filter.N(), P, M, serialized2)
 	if err != nil {
 		t.Fatalf("Filter copy failed: %s", err.Error())
 	}
@@ -99,23 +102,7 @@ func TestGCSFilterCopy(t *testing.T) {
 	if err != nil {
 		t.Fatalf("Filter NBytes() failed: %v", err)
 	}
-	filter3, err = gcs.FromNBytes(filter.P(), serialized3)
+	filter3, err = gcs.FromNBytes(filter.P(), M, serialized3)
-	if err != nil {
-		t.Fatalf("Filter copy failed: %s", err.Error())
-	}
-	serialized4, err := filter.PBytes()
-	if err != nil {
-		t.Fatalf("Filter PBytes() failed: %v", err)
-	}
-	filter4, err = gcs.FromPBytes(filter.N(), serialized4)
-	if err != nil {
-		t.Fatalf("Filter copy failed: %s", err.Error())
-	}
-	serialized5, err := filter.NPBytes()
-	if err != nil {
-		t.Fatalf("Filter NPBytes() failed: %v", err)
-	}
-	filter5, err = gcs.FromNPBytes(serialized5)
 	if err != nil {
 		t.Fatalf("Filter copy failed: %s", err.Error())
 	}
@@ -136,24 +123,12 @@ func TestGCSFilterMetadata(t *testing.T) {
 	if filter.P() != filter3.P() {
 		t.Fatal("P doesn't match between copied filters")
 	}
-	if filter.P() != filter4.P() {
-		t.Fatal("P doesn't match between copied filters")
-	}
-	if filter.P() != filter5.P() {
-		t.Fatal("P doesn't match between copied filters")
-	}
 	if filter.N() != filter2.N() {
 		t.Fatal("N doesn't match between copied filters")
 	}
 	if filter.N() != filter3.N() {
 		t.Fatal("N doesn't match between copied filters")
 	}
-	if filter.N() != filter4.N() {
-		t.Fatal("N doesn't match between copied filters")
-	}
-	if filter.N() != filter5.N() {
-		t.Fatal("N doesn't match between copied filters")
-	}
 	serialized, err := filter.Bytes()
 	if err != nil {
 		t.Fatalf("Filter Bytes() failed: %v", err)
@@ -179,13 +154,6 @@ func TestGCSFilterMetadata(t *testing.T) {
 	if !bytes.Equal(serialized, serialized4) {
 		t.Fatal("Bytes don't match between copied filters")
 	}
-	serialized5, err := filter5.Bytes()
-	if err != nil {
-		t.Fatalf("Filter Bytes() failed: %v", err)
-	}
-	if !bytes.Equal(serialized, serialized5) {
-		t.Fatal("Bytes don't match between copied filters")
-	}
 }
 
 // TestGCSFilterMatch checks that both the built and copied filters match

gcs/gcsbench_test.go

@@ -38,16 +38,18 @@ func BenchmarkGCSFilterBuild50000(b *testing.B) {
 	for i := 0; i < gcs.KeySize; i += 4 {
 		binary.BigEndian.PutUint32(testKey[i:], rand.Uint32())
 	}
+
 	randFilterElems, genErr := genRandFilterElements(50000)
 	if err != nil {
 		b.Fatalf("unable to generate random item: %v", genErr)
 	}
+
 	b.StartTimer()
 
 	var localFilter *gcs.Filter
 	for i := 0; i < b.N; i++ {
 		localFilter, err = gcs.BuildGCSFilter(
-			P, key, randFilterElems,
+			P, M, key, randFilterElems,
 		)
 		if err != nil {
 			b.Fatalf("unable to generate filter: %v", err)
@@ -63,16 +65,19 @@ func BenchmarkGCSFilterBuild100000(b *testing.B) {
 	for i := 0; i < gcs.KeySize; i += 4 {
 		binary.BigEndian.PutUint32(testKey[i:], rand.Uint32())
 	}
+
 	randFilterElems, genErr := genRandFilterElements(100000)
 	if err != nil {
 		b.Fatalf("unable to generate random item: %v", genErr)
 	}
+
 	b.StartTimer()
 
 	var localFilter *gcs.Filter
 	for i := 0; i < b.N; i++ {
-		localFilter, err = gcs.BuildGCSFilter(P, key,
+		localFilter, err = gcs.BuildGCSFilter(
-			randFilterElems)
+			P, M, key, randFilterElems,
+		)
 		if err != nil {
 			b.Fatalf("unable to generate filter: %v", err)
 		}
@@ -87,7 +92,7 @@ var (
 // BenchmarkGCSFilterMatch benchmarks querying a filter for a single value.
 func BenchmarkGCSFilterMatch(b *testing.B) {
 	b.StopTimer()
-	filter, err := gcs.BuildGCSFilter(P, key, contents)
+	filter, err := gcs.BuildGCSFilter(P, M, key, contents)
 	if err != nil {
 		b.Fatalf("Failed to build filter")
 	}
@@ -114,7 +119,7 @@ func BenchmarkGCSFilterMatch(b *testing.B) {
 // values.
 func BenchmarkGCSFilterMatchAny(b *testing.B) {
 	b.StopTimer()
-	filter, err := gcs.BuildGCSFilter(P, key, contents)
+	filter, err := gcs.BuildGCSFilter(P, M, key, contents)
 	if err != nil {
 		b.Fatalf("Failed to build filter")
 	}