Generate safe prime concurrently

How fast we generate a prime number is mostly a matter of luck. It
varies from miliseconds to seconds and depends how lucky we are with
drawing bytes.

With today's multicore processors, we can execute the process on
multiple cores concurrently, accept the first valid result and cancel
the rest of work. This way, with the same algorithm, we get the result
faster.

safe_prime_generator.go

@@ -5,9 +5,14 @@
 package paillier
 
 import (
+	"context"
+	"crypto/rand"
 	"errors"
+	"fmt"
 	"io"
 	"math/big"
+	"sync"
+	"time"
 )
 
 // smallPrimes is a list of small, prime numbers that allows us to rapidly
@@ -25,33 +30,87 @@ var smallPrimes = []uint8{
 // operations.
 var smallPrimesProduct = new(big.Int).SetUint64(16294579238595022365)
 
-// Prime returns a number, p, of the given size, such that p is prime
-// with high probability.
-// Prime will return error for any error returned by rand.Read or if bits < 2.
-func SafePrimes(rand io.Reader, bits int) (p *big.Int, q *big.Int, err error) {
-	qbits := bits - 1
-
-	if qbits < 2 {
-		err = errors.New("crypto/rand: prime size must be at least 2-bit")
-		return
+type safePrime struct {
+	p *big.Int
+	q *big.Int
 }
 
-	b := uint(qbits % 8)
+func GenerateSafePrime(
+	bitLen int,
+	concurrencyLevel int,
+	timeout time.Duration,
+) (*big.Int, *big.Int, error) {
+	if bitLen < 6 {
+		return nil, nil, errors.New("safe prime size must be at least 6 bits")
+	}
+
+	primeChan := make(chan safePrime, 1)
+	errChan := make(chan error, 1)
+
+	defer close(primeChan)
+	defer close(errChan)
+
+	mutex := &sync.Mutex{}
+
+	ctx, cancel := context.WithCancel(context.Background())
+
+	for i := 0; i < concurrencyLevel; i++ {
+		runGenPrimeRoutine(ctx, primeChan, errChan, mutex, rand.Reader, bitLen)
+	}
+
+	go func() {
+		time.Sleep(timeout)
+		mutex.Lock()
+		cancel()
+		mutex.Unlock()
+	}()
+
+	select {
+	case result := <-primeChan:
+		mutex.Lock()
+		cancel()
+		mutex.Unlock()
+		return result.p, result.q, nil
+	case err := <-errChan:
+		mutex.Lock()
+		cancel()
+		mutex.Unlock()
+		return nil, nil, err
+	case <-ctx.Done():
+		return nil, nil, fmt.Errorf("generator timed out after %v", timeout)
+	}
+}
+
+func runGenPrimeRoutine(
+	ctx context.Context,
+	primeChan chan safePrime,
+	errChan chan error,
+	mutex *sync.Mutex,
+	rand io.Reader,
+	pBitLen int,
+) {
+	qBitLen := pBitLen - 1
+	b := uint(qBitLen % 8)
 	if b == 0 {
 		b = 8
 	}
 
-	bytes := make([]byte, (qbits+7)/8)
-	p = new(big.Int)
-	q = new(big.Int)
+	bytes := make([]byte, (qBitLen+7)/8)
+	p := new(big.Int)
+	q := new(big.Int)
 
 	bigMod := new(big.Int)
 
-	//NextRand:
+	go func() {
 		for {
-		_, err = io.ReadFull(rand, bytes)
+			select {
+			case <-ctx.Done():
+				return
+			default:
+				_, err := io.ReadFull(rand, bytes)
 				if err != nil {
-			return nil, nil, err
+					errChan <- err
+					return
 				}
 
 				// Clear bits in the first byte to make sure the candidate has a size <= bits.
@@ -88,7 +147,7 @@ func SafePrimes(rand io.Reader, bits int) (p *big.Int, q *big.Int, err error) {
 				for delta := uint64(0); delta < 1<<20; delta += 2 {
 					m := mod + delta
 					for _, prime := range smallPrimes {
-				if m%uint64(prime) == 0 && (qbits > 6 || m != uint64(prime)) {
+						if m%uint64(prime) == 0 && (qBitLen > 6 || m != uint64(prime)) {
 							continue NextDelta
 						}
 					}
@@ -117,11 +176,20 @@ func SafePrimes(rand io.Reader, bits int) (p *big.Int, q *big.Int, err error) {
 				// here.
 				if q.ProbablyPrime(20) &&
 					isPocklingtonCriterionSatisfied(p) &&
-			q.BitLen() == qbits {
+					q.BitLen() == qBitLen {
+
+					mutex.Lock()
+					if ctx.Err() == nil {
+						primeChan <- safePrime{p, q}
+					}
+					mutex.Unlock()
+
 					return
 				}
 			}
 		}
+	}()
+}
 
 func isPocklingtonCriterionSatisfied(p *big.Int) bool {
 	return new(big.Int).Exp(

safe_prime_generator_test.go

@@ -0,0 +1,98 @@
+package paillier
+
+import (
+	"errors"
+	"fmt"
+	"math/big"
+	"reflect"
+	"testing"
+	"time"
+)
+
+func TestAsyncGenerator(t *testing.T) {
+	concurrencyLevel := 4
+
+	var tests = map[string]struct {
+		bitLen        int
+		timeout       time.Duration
+		expectedError error
+	}{
+		"primes successfully generated": {
+			bitLen:        512,
+			timeout:       60 * time.Second,
+			expectedError: nil,
+		},
+		"generator timed out": {
+			bitLen:        8192,
+			timeout:       1 * time.Second,
+			expectedError: errors.New("generator timed out after 1s"),
+		},
+		"bit length is 5": {
+			bitLen:        5,
+			timeout:       1 * time.Second,
+			expectedError: errors.New("safe prime size must be at least 6 bits"),
+		},
+		"bit length is 6": {
+			bitLen:        6,
+			timeout:       60 * time.Second,
+			expectedError: nil,
+		},
+	}
+
+	for testName, test := range tests {
+		t.Run(testName, func(t *testing.T) {
+			p, q, err := GenerateSafePrime(
+				test.bitLen,
+				concurrencyLevel,
+				test.timeout,
+			)
+
+			if test.expectedError != nil {
+				if !reflect.DeepEqual(test.expectedError, err) {
+					t.Fatalf(
+						"Unexpected error\nActual: %v\nExpected: %v",
+						err,
+						test.expectedError,
+					)
+				}
+			} else {
+				if err != nil {
+					t.Fatal(err)
+				}
+
+				if !p.ProbablyPrime(20) {
+					t.Errorf("p is not prime; p = %v", p)
+				}
+
+				if !q.ProbablyPrime(20) {
+					t.Errorf("q is not prime; q = %v", q)
+				}
+
+				// p = 2q + 1 ?
+				expectedP := new(big.Int)
+				expectedP.Mul(big.NewInt(2), q)
+				expectedP.Add(expectedP, big.NewInt(1))
+
+				if expectedP.Cmp(p) != 0 {
+					t.Errorf("2q + 1 != p")
+				}
+
+				if len(p.Bytes()) != test.bitLen {
+					fmt.Errorf(
+						"Unexpected p bit length\nActual: %v\nExpected: %v",
+						len(p.Bytes()),
+						test.bitLen,
+					)
+				}
+
+				if len(q.Bytes()) != test.bitLen-1 {
+					fmt.Errorf(
+						"Unexpected q bit length\nActual: %v\nExpected: %v",
+						len(q.Bytes()),
+						test.bitLen-1,
+					)
+				}
+			}
+		})
+	}
+}