CVE-2023-24533 (Go, published 2023-03-08T20:15Z)
Description: value: Multiplication of certain unreduced P-256 scalars produce incorrect results. There are no protocols known at this time that can be attacked due to this.
Severity: nan (CVSS v3 base score: 7.5)
Weakness: CWE-682 \u2014 Incorrect Calculation
The product performs a calculation that generates incorrect or unintended results that are later used in security-critical decisions or resource management.
Repository: https://github.com/FiloSottile/nistec
Files changed:
nistec_test.go
p256_asm.go
p256_ordinv.go
Commit message: crypto/internal/nistec: reduce P-256 scalar

Unlike the rest of nistec, the P-256 assembly doesn't use complete
addition formulas, meaning that p256PointAdd[Affine]Asm won't return the
correct value if the two inputs are equal.

This was (undocumentedly) ignored in the scalar multiplication loops
because as long as the input point is not the identity and the scalar is
lower than the order of the group, the addition inputs can't be the same.

As part of the math/big rewrite, we went however from always reducing
the scalar to only checking its length, under the incorrect assumption
that the scalar multiplication loop didn't require reduction.

Added a reduction, and while at it added it in P256OrdInverse, too, to
enforce a universal reduction invariant on p256OrdElement values.

Note that if the input point is the infinity, the code currently still
relies on undefined behavior, but that's easily tested to behave
acceptably, and will be addressed in a future CL.

Fixes #58647
Fixes CVE-2023-24532

(Filed with the "safe APIs like complete addition formulas are good" dept.)

Change-Id: I7b2c75238440e6852be2710fad66ff1fdc4e2b24


Vulnerable code:

Fixed code:
	"fmt"
func TestScalarMult(t *testing.T) {
	t.Run("P224", func(t *testing.T) {
		testScalarMult(t, nistec.NewP224Point, elliptic.P224())
	})
	t.Run("P256", func(t *testing.T) {
		testScalarMult(t, nistec.NewP256Point, elliptic.P256())
	})
	t.Run("P384", func(t *testing.T) {
		testScalarMult(t, nistec.NewP384Point, elliptic.P384())
	})
	t.Run("P521", func(t *testing.T) {
		testScalarMult(t, nistec.NewP521Point, elliptic.P521())
	})
}

func testScalarMult[P nistPoint[P]](t *testing.T, newPoint func() P, c elliptic.Curve) {
	G := newPoint().SetGenerator()
	checkScalar := func(t *testing.T, scalar []byte) {
		p1, err := newPoint().ScalarBaseMult(scalar)
		fatalIfErr(t, err)
		p2, err := newPoint().ScalarMult(G, scalar)
		fatalIfErr(t, err)
		if !bytes.Equal(p1.Bytes(), p2.Bytes()) {
			t.Error("[k]G != ScalarBaseMult(k)")
		}

		d := new(big.Int).SetBytes(scalar)
		d.Sub(c.Params().N, d)
		d.Mod(d, c.Params().N)
		g1, err := newPoint().ScalarBaseMult(d.FillBytes(make([]byte, len(scalar))))
		fatalIfErr(t, err)
		g1.Add(g1, p1)
		if !bytes.Equal(g1.Bytes(), newPoint().Bytes()) {
			t.Error("[N - k]G + [k]G != ∞")
		}
	}

	byteLen := len(c.Params().N.Bytes())
	bitLen := c.Params().N.BitLen()
	t.Run("0", func(t *testing.T) { checkScalar(t, make([]byte, byteLen)) })
	t.Run("1", func(t *testing.T) {
		checkScalar(t, big.NewInt(1).FillBytes(make([]byte, byteLen)))
	})
	t.Run("N-1", func(t *testing.T) {
		checkScalar(t, new(big.Int).Sub(c.Params().N, big.NewInt(1)).Bytes())
	})
	t.Run("N", func(t *testing.T) { checkScalar(t, c.Params().N.Bytes()) })
	t.Run("N+1", func(t *testing.T) {
		checkScalar(t, new(big.Int).Add(c.Params().N, big.NewInt(1)).Bytes())
	})
	t.Run("all1s", func(t *testing.T) {
		s := new(big.Int).Lsh(big.NewInt(1), uint(bitLen))
		s.Sub(s, big.NewInt(1))
		checkScalar(t, s.Bytes())
	})
	if testing.Short() {
		return
	}
	for i := 0; i < bitLen; i++ {
		t.Run(fmt.Sprintf("1<<%d", i), func(t *testing.T) {
			s := new(big.Int).Lsh(big.NewInt(1), uint(i))
			checkScalar(t, s.FillBytes(make([]byte, byteLen)))
		})
	}
	// Test N+1...N+32 since they risk overlapping with precomputed table values
	// in the final additions.
	for i := int64(2); i <= 32; i++ {
		t.Run(fmt.Sprintf("N+%d", i), func(t *testing.T) {
			checkScalar(t, new(big.Int).Add(c.Params().N, big.NewInt(i)).Bytes())
		})
	}
}

func fatalIfErr(t *testing.T, err error) {
	t.Helper()
	if err != nil {
		t.Fatal(err)
	}
}

// p256OrdReduce ensures s is in the range [0, ord(G)-1].
func p256OrdReduce(s *p256OrdElement) {
	// Since 2 * ord(G) > 2²⁵⁶, we can just conditionally subtract ord(G),
	// keeping the result if it doesn't underflow.
	t0, b := bits.Sub64(s[0], 0xf3b9cac2fc632551, 0)
	t1, b := bits.Sub64(s[1], 0xbce6faada7179e84, b)
	t2, b := bits.Sub64(s[2], 0xffffffffffffffff, b)
	t3, b := bits.Sub64(s[3], 0xffffffff00000000, b)
	tMask := b - 1 // zero if subtraction underflowed
	s[0] ^= (t0 ^ s[0]) & tMask
	s[1] ^= (t1 ^ s[1]) & tMask
	s[2] ^= (t2 ^ s[2]) & tMask
	s[3] ^= (t3 ^ s[3]) & tMask
}

	p256OrdReduce(scalarReversed)
	p256OrdReduce(scalarReversed)
	p256OrdReduce(x)