safe_prime_generator_test.go

@@ -60,7 +60,7 @@ func TestAsyncGenerator(t *testing.T) {
 					t.Fatal(err)
 				}
 
-				AreSafePrimes(p, q, test.bitLen, t)
+				IsSafePrime(p, q, test.bitLen, t)
 			}
 		})
 	}

thresholdkey_generator.go

@@ -2,6 +2,7 @@ package paillier
 
 import (
 	"crypto/rand"
+	"errors"
 	"io"
 	"math/big"
 	"time"
@@ -19,18 +20,18 @@ import (
 //               with Applications to Electronic Voting
 //               Aarhus University, Dept. of Computer Science, BRICS
 type ThresholdKeyGenerator struct {
-	nbits                          int
+	PublicKeyBitLength             int
 	TotalNumberOfDecryptionServers int
 	Threshold                      int
-	Random                         io.Reader
+	random                         io.Reader
 
-	// Both p1 and q1 are primes of length nbits - 1
-	p1 *big.Int
-	q1 *big.Int
+	p *big.Int // p is prime of `PublicKeyBitLength/2` bits and `p = 2*p1 + 1`
+	q *big.Int // q is prime of `PublicKeyBitLength/2` bits and `q = 2*q1 + 1`
 
-	p       *big.Int // p is prime and p=2*p1+1
-	q       *big.Int // q is prime and q=2*q1+1
-	n       *big.Int // n=p*q
+	p1 *big.Int // p1 is prime of `PublicKeyBitLength/2 - 1` bits
+	q1 *big.Int // q1 is prime of `PublicKeyBitLength/2 - 1` bits
+
+	n       *big.Int // n=p*q and is of `PublicKeyBitLength` bits
 	m       *big.Int // m = p1*q1
 	nSquare *big.Int // nSquare = n*n
 	nm      *big.Int // nm = n*m
@@ -45,23 +46,44 @@ type ThresholdKeyGenerator struct {
 	polynomialCoefficients []*big.Int
 }
 
-// Preferable way to construct the ThresholdKeyGenerator. No verification
-// is done on the input values.  You need to be sure that nbits is big enough
-// and that Threshold > TotalNumberOfDecryptionServers / 2.
-// The plaintext space for the key will be Z_n.
-func GetThresholdKeyGenerator(nbits, TotalNumberOfDecryptionServers, Threshold int, random io.Reader) *ThresholdKeyGenerator {
-	ret := new(ThresholdKeyGenerator)
-	ret.nbits = nbits
-	ret.TotalNumberOfDecryptionServers = TotalNumberOfDecryptionServers
-	ret.Threshold = Threshold
-	ret.Random = random
-	return ret
+// GetThresholdKeyGenerator is a preferable way to construct the
+// ThresholdKeyGenerator.
+// Due to the various properties that must be met for the threshold key to be
+// considered valid, the minimum public key `N` bit length is 18 bits and the
+// public key bit length should be an even number.
+// The plaintext space for the key will be `Z_N`.
+func GetThresholdKeyGenerator(
+	publicKeyBitLength int,
+	totalNumberOfDecryptionServers int,
+	threshold int,
+	random io.Reader,
+) (*ThresholdKeyGenerator, error) {
+	if publicKeyBitLength%2 == 1 {
+		// For an odd n-bit number, we can't find two n/2-bit numbers with two
+		// the most significant bits set on which multiplied gives an n-bit
+		// number.
+		return nil, errors.New("Public key bit length must be an even number")
+	}
+	if publicKeyBitLength < 18 {
+		// We need to find two n/2-bit safe primes, P and Q which are not equal.
+		// This is not possible for n<18.
+		return nil, errors.New("Public key bit length must be at least 18 bits")
+	}
+
+	return &ThresholdKeyGenerator{
+		PublicKeyBitLength:             publicKeyBitLength,
+		TotalNumberOfDecryptionServers: totalNumberOfDecryptionServers,
+		Threshold:                      threshold,
+		random:                         random,
+	}, nil
 }
 
 func (tkg *ThresholdKeyGenerator) generateSafePrimes() (*big.Int, *big.Int, error) {
 	concurrencyLevel := 4
 	timeout := 120 * time.Second
-	return GenerateSafePrime(tkg.nbits, concurrencyLevel, timeout, tkg.Random)
+	safePrimeBitLength := tkg.PublicKeyBitLength / 2
+
+	return GenerateSafePrime(safePrimeBitLength, concurrencyLevel, timeout, tkg.random)
 }
 
 func (tkg *ThresholdKeyGenerator) initPandP1() error {
@@ -112,7 +134,7 @@ func (tkg *ThresholdKeyGenerator) initPsAndQs() error {
 // v generates a cyclic group of squares in Zn^2.
 func (tkg *ThresholdKeyGenerator) computeV() error {
 	var err error
-	tkg.v, err = GetRandomGeneratorOfTheQuadraticResidue(tkg.nSquare, tkg.Random)
+	tkg.v, err = GetRandomGeneratorOfTheQuadraticResidue(tkg.nSquare, tkg.random)
 	return err
 }
 
@@ -165,7 +187,7 @@ func (tkg *ThresholdKeyGenerator) generateHidingPolynomial() error {
 	tkg.polynomialCoefficients[0] = tkg.d
 	var err error
 	for i := 1; i < tkg.Threshold; i++ {
-		tkg.polynomialCoefficients[i], err = rand.Int(tkg.Random, tkg.nm)
+		tkg.polynomialCoefficients[i], err = rand.Int(tkg.random, tkg.nm)
 		if err != nil {
 			return err
 		}

thresholdkey_generator_test.go

@@ -2,6 +2,7 @@ package paillier
 
 import (
 	"crypto/rand"
+	"errors"
 	"math/big"
 	"reflect"
 	"testing"
@@ -11,44 +12,183 @@ var MockGenerateSafePrimes = func() (*big.Int, *big.Int, error) {
 	return big.NewInt(887), big.NewInt(443), nil
 }
 
-func TestGenerateSafePrimesOfThresholdKeyGenerator(t *testing.T) {
-	tkh := new(ThresholdKeyGenerator)
-	tkh.nbits = 10
-	tkh.Random = rand.Reader
-	p, q, err := tkh.generateSafePrimes()
-	if err != nil {
-		t.Error(err)
+func TestCreateThresholdKeyGenerator(t *testing.T) {
+	var tests = map[string]struct {
+		publicKeyBitLength             int
+		totalNumberOfDecryptionServers int
+		threshold                      int
+		expectedError                  error
+	}{
+		"generator successfully created for 20 bit key length": {
+			publicKeyBitLength:             20,
+			totalNumberOfDecryptionServers: 6,
+			threshold:                      5,
+		},
+		"generator can't be created for 19 bit key length": {
+			publicKeyBitLength:             19,
+			totalNumberOfDecryptionServers: 4,
+			threshold:                      3,
+			expectedError:                  errors.New("Public key bit length must be an even number"),
+		},
+		"generator successfully created for 18 bit key length": {
+			publicKeyBitLength:             18,
+			totalNumberOfDecryptionServers: 4,
+			threshold:                      3,
+		},
+		"generator can't be created for 17 bit key length": {
+			publicKeyBitLength:             17,
+			totalNumberOfDecryptionServers: 4,
+			threshold:                      3,
+			expectedError:                  errors.New("Public key bit length must be an even number"),
+		},
+		"generator can't be created for 16 bit key length": {
+			publicKeyBitLength:             16,
+			totalNumberOfDecryptionServers: 4,
+			threshold:                      3,
+			expectedError:                  errors.New("Public key bit length must be at least 18 bits"),
+		},
+	}
+
+	for testName, test := range tests {
+		t.Run(testName, func(t *testing.T) {
+			gen, err := GetThresholdKeyGenerator(
+				test.publicKeyBitLength,
+				test.totalNumberOfDecryptionServers,
+				test.threshold,
+				rand.Reader,
+			)
+
+			if !reflect.DeepEqual(test.expectedError, err) {
+				t.Fatalf(
+					"Unexpected error\nActual: %v\nExpected: %v",
+					err,
+					test.expectedError,
+				)
+			}
+
+			if test.expectedError == nil {
+				if gen == nil {
+					t.Fatal(
+						"Got nil generator, it should be successfully created",
+					)
+				}
+
+				if test.publicKeyBitLength != gen.PublicKeyBitLength {
+					t.Fatalf(
+						"Unexpected public key length\nExpected: %v\nActual: %v",
+						test.publicKeyBitLength,
+						gen.PublicKeyBitLength,
+					)
+				}
+
+				if test.threshold != gen.Threshold {
+					t.Fatalf(
+						"Unexpected threshold\nExpected: %v\nActual: %v",
+						test.threshold,
+						gen.Threshold,
+					)
+				}
+
+				if test.totalNumberOfDecryptionServers != gen.TotalNumberOfDecryptionServers {
+					t.Fatalf(
+						"Unexpected number of decryption servers\nExpected: %v\nActual: %v",
+						test.totalNumberOfDecryptionServers,
+						gen.TotalNumberOfDecryptionServers,
+					)
+				}
+			}
+		})
+	}
+}
+
+func TestGenerateNumbersOfCorrectBitLength(t *testing.T) {
+	var tests = map[string]struct {
+		publicKeyLength     int
+		expectedPrimeLength int
+	}{
+		"public key bit length = 32, prime bit length = 16": {
+			publicKeyLength:     32,
+			expectedPrimeLength: 16,
+		},
+		"public key bit length = 64, prime bit length = 32": {
+			publicKeyLength:     64,
+			expectedPrimeLength: 32,
+		},
+	}
+
+	for testName, test := range tests {
+		t.Run(testName, func(t *testing.T) {
+			gen, err := GetThresholdKeyGenerator(test.publicKeyLength, 10, 6, rand.Reader)
+			if err != nil {
+				t.Fatal(err)
+			}
+
+			err = gen.initNumerialValues()
+			if err != nil {
+				t.Fatal(err)
+			}
+
+			if gen.p.BitLen() != test.expectedPrimeLength {
+				t.Fatalf(
+					"Unexpected prime bit length\nExpected %v\n Actual %v",
+					test.expectedPrimeLength,
+					gen.p.BitLen(),
+				)
+			}
+
+			if gen.q.BitLen() != test.expectedPrimeLength {
+				t.Fatalf(
+					"Unexpected prime bit length\nExpected %v\n Actual %v",
+					test.expectedPrimeLength,
+					gen.q.BitLen(),
+				)
+			}
+
+			if gen.n.BitLen() != test.publicKeyLength {
+				t.Fatalf(
+					"Unexpected modulus bit length\nExpected %v\n Actual %v",
+					test.publicKeyLength,
+					gen.n.BitLen(),
+				)
+			}
+
+			if new(big.Int).Mul(gen.p, gen.q).Cmp(gen.n) != 0 {
+				t.Fatal("n != pq")
+			}
+		})
 	}
-	AreSafePrimes(p, q, 10, t)
 }
 
 func TestInitPandP1(t *testing.T) {
-	tkh := new(ThresholdKeyGenerator)
-	tkh.nbits = 10
-	tkh.Random = rand.Reader
+	tkh, err := GetThresholdKeyGenerator(32, 4, 3, rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
 
 	tkh.initPandP1()
-	AreSafePrimes(tkh.p, tkh.p1, 10, t)
+	IsSafePrime(tkh.p, tkh.p1, 16, t)
 }
 
 func TestInitQandQ1(t *testing.T) {
-	tkh := new(ThresholdKeyGenerator)
-	tkh.nbits = 10
-	tkh.Random = rand.Reader
+	tkh, err := GetThresholdKeyGenerator(32, 4, 3, rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
 
 	tkh.initQandQ1()
-	AreSafePrimes(tkh.q, tkh.q1, 10, t)
+	IsSafePrime(tkh.q, tkh.q1, 16, t)
 }
 
 func TestInitPsAndQs(t *testing.T) {
-	tkh := new(ThresholdKeyGenerator)
-	tkh.nbits = 10
-	tkh.Random = rand.Reader
+	tkh, err := GetThresholdKeyGenerator(32, 4, 3, rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
 
 	tkh.initPsAndQs()
 
-	AreSafePrimes(tkh.p, tkh.p1, 10, t)
-	AreSafePrimes(tkh.q, tkh.q1, 10, t)
+	IsSafePrime(tkh.p, tkh.p1, 16, t)
+	IsSafePrime(tkh.q, tkh.q1, 16, t)
 }
 
 func TestArePsAndQsGood(t *testing.T) {
@@ -102,9 +242,10 @@ func TestInitD(t *testing.T) {
 }
 
 func TestInitNumerialValues(t *testing.T) {
-	tkh := new(ThresholdKeyGenerator)
-	tkh.nbits = 10
-	tkh.Random = rand.Reader
+	tkh, err := GetThresholdKeyGenerator(32, 4, 3, rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
 
 	if err := tkh.initNumerialValues(); err != nil {
 		t.Error(err)
@@ -112,10 +253,11 @@ func TestInitNumerialValues(t *testing.T) {
 }
 
 func TestGenerateHidingPolynomial(t *testing.T) {
-	tkh := new(ThresholdKeyGenerator)
-	tkh.nbits = 10
-	tkh.Threshold = 10
-	tkh.Random = rand.Reader
+	tkh, err := GetThresholdKeyGenerator(32, 15, 10, rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
+
 	if err := tkh.initNumerialValues(); err != nil {
 		t.Error(err)
 	}
@@ -137,10 +279,11 @@ func TestGenerateHidingPolynomial(t *testing.T) {
 }
 
 func TestComputeShare(t *testing.T) {
-	tkh := new(ThresholdKeyGenerator)
-	tkh.nbits = 10
-	tkh.Threshold = 3
-	tkh.TotalNumberOfDecryptionServers = 5
+	tkh, err := GetThresholdKeyGenerator(32, 5, 3, rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
+
 	tkh.nm = b(103)
 	tkh.polynomialCoefficients = []*big.Int{b(29), b(88), b(51)}
 	share := tkh.computeShare(2)
@@ -150,11 +293,11 @@ func TestComputeShare(t *testing.T) {
 }
 
 func TestCreateShares(t *testing.T) {
-	tkh := new(ThresholdKeyGenerator)
-	tkh.nbits = 10
-	tkh.Threshold = 10
-	tkh.TotalNumberOfDecryptionServers = 100
-	tkh.Random = rand.Reader
+	tkh, err := GetThresholdKeyGenerator(32, 100, 10, rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
+
 	if err := tkh.initNumerialValues(); err != nil {
 		t.Error(err)
 	}
@@ -180,14 +323,22 @@ func TestCreateViArray(t *testing.T) {
 }
 
 func TestGetThresholdKeyGenerator(t *testing.T) {
-	tkh := GetThresholdKeyGenerator(50, 10, 6, rand.Reader)
+	tkh, err := GetThresholdKeyGenerator(50, 10, 6, rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
+
 	if err := tkh.initNumerialValues(); err != nil {
 		t.Error(nil)
 	}
 }
 
 func TestGenerate(t *testing.T) {
-	tkh := GetThresholdKeyGenerator(32, 10, 6, rand.Reader)
+	tkh, err := GetThresholdKeyGenerator(32, 10, 6, rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
+
 	tpks, err := tkh.Generate()
 	if err != nil {
 		t.Error(err)
@@ -213,7 +364,11 @@ func TestGenerate(t *testing.T) {
 }
 
 func TestComputeV(t *testing.T) {
-	tkh := GetThresholdKeyGenerator(32, 10, 6, rand.Reader)
+	tkh, err := GetThresholdKeyGenerator(32, 10, 6, rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
+
 	tkh.n = b(1907 * 1823)
 	tkh.nSquare = new(big.Int).Mul(tkh.n, tkh.n)
 	for i := 0; i < 100; i++ {

thresholdkey_test.go

@@ -8,7 +8,11 @@ import (
 )
 
 func getThresholdPrivateKey() *ThresholdPrivateKey {
-	tkh := GetThresholdKeyGenerator(32, 10, 6, rand.Reader)
+	tkh, err := GetThresholdKeyGenerator(32, 10, 6, rand.Reader)
+	if err != nil {
+		panic(err)
+	}
+
 	tpks, err := tkh.Generate()
 	if err != nil {
 		panic(err)
@@ -184,7 +188,11 @@ func TestupdateCprime(t *testing.T) {
 }
 
 func TestEncryptingDecryptingSimple(t *testing.T) {
-	tkh := GetThresholdKeyGenerator(10, 2, 1, rand.Reader)
+	tkh, err := GetThresholdKeyGenerator(32, 2, 1, rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
+
 	tpks, err := tkh.Generate()
 	if err != nil {
 		t.Error(err)
@@ -205,7 +213,11 @@ func TestEncryptingDecryptingSimple(t *testing.T) {
 }
 
 func TestEncryptingDecrypting(t *testing.T) {
-	tkh := GetThresholdKeyGenerator(10, 2, 2, rand.Reader)
+	tkh, err := GetThresholdKeyGenerator(32, 2, 2, rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
+
 	tpks, err := tkh.Generate()
 	if err != nil {
 		t.Error(err)
@@ -227,7 +239,11 @@ func TestEncryptingDecrypting(t *testing.T) {
 }
 
 func TestHomomorphicThresholdEncryption(t *testing.T) {
-	tkh := GetThresholdKeyGenerator(10, 2, 2, rand.Reader)
+	tkh, err := GetThresholdKeyGenerator(32, 2, 2, rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
+
 	tpks, _ := tkh.Generate()
 
 	plainText1 := b(13)
@@ -278,7 +294,11 @@ func TestValidate(t *testing.T) {
 }
 
 func TestCombinePartialDecryptionsZKP(t *testing.T) {
-	tkh := GetThresholdKeyGenerator(10, 2, 2, rand.Reader)
+	tkh, err := GetThresholdKeyGenerator(32, 2, 2, rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
+
 	tpks, err := tkh.Generate()
 	if err != nil {
 		t.Error(err)
@@ -311,7 +331,11 @@ func TestCombinePartialDecryptionsZKP(t *testing.T) {
 }
 
 func TestCombinePartialDecryptionsWith100Shares(t *testing.T) {
-	tkh := GetThresholdKeyGenerator(10, 100, 50, rand.Reader)
+	tkh, err := GetThresholdKeyGenerator(32, 100, 50, rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
+
 	tpks, err := tkh.Generate()
 	if err != nil {
 		t.Error(err)
@@ -338,7 +362,11 @@ func TestCombinePartialDecryptionsWith100Shares(t *testing.T) {
 }
 
 func TestVerifyDecryption(t *testing.T) {
-	tkh := GetThresholdKeyGenerator(10, 2, 2, rand.Reader)
+	tkh, err := GetThresholdKeyGenerator(32, 2, 2, rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
+
 	tpks, err := tkh.Generate()
 
 	pk := &tpks[0].ThresholdPublicKey

utils_test.go

@@ -59,7 +59,9 @@ func TestFactorial(t *testing.T) {
 	}
 }
 
-func AreSafePrimes(p, q *big.Int, expectedLength int, t *testing.T) {
+// IsSafePrime checks whether `p` is a safe prime. A safe prime is a prime
+// number of the form `2q + 1`, where `q` is also a prime.
+func IsSafePrime(p, q *big.Int, expectedLength int, t *testing.T) {
 	if l := p.BitLen(); l != expectedLength {
 		t.Error("p does not have the good length. ", l)
 	}