crypto/elliptic: split up P-256 field and group ops

This makes Gerrit recognize the rename of the field implementation and
facilitates the review. No code changes.

For #52182

Change-Id: I827004e175db1ae2fcdf17d0f586ff21503d27e3
Reviewed-on: https://go-review.googlesource.com/c/go/+/390754
Reviewed-by: Ian Lance Taylor <iant@google.com>
Reviewed-by: Russ Cox <rsc@golang.org>
Reviewed-by: Roland Shoemaker <roland@golang.org>
Run-TryBot: Filippo Valsorda <filippo@golang.org>
Auto-Submit: Filippo Valsorda <filippo@golang.org>
TryBot-Result: Gopher Robot <gobot@golang.org>

2 files changed, 705 insertions, 696 deletions

diff --git a/src/crypto/elliptic/p256_generic.go b/src/crypto/elliptic/p256_generic.go
index fc105c547c..22dde23109 100644
--- a/src/crypto/elliptic/p256_generic.go
+++ b/src/crypto/elliptic/p256_generic.go
@@ -57,38 +57,6 @@ func (p256Curve) ScalarMult(bigX, bigY *big.Int, scalar []byte) (x, y *big.Int)
 	return p256ToAffine(&x1, &y1, &z1)
 }
 
-// Field elements are represented as nine, unsigned 32-bit words.
-//
-// The value of a field element is:
-//   x[0] + (x[1] * 2**29) + (x[2] * 2**57) + ... + (x[8] * 2**228)
-//
-// That is, each limb is alternately 29 or 28-bits wide in little-endian
-// order.
-//
-// This means that a field element hits 2**257, rather than 2**256 as we would
-// like. A 28, 29, ... pattern would cause us to hit 2**256, but that causes
-// problems when multiplying as terms end up one bit short of a limb which
-// would require much bit-shifting to correct.
-//
-// Finally, the values stored in a field element are in Montgomery form. So the
-// value |y| is stored as (y*R) mod p, where p is the P-256 prime and R is
-// 2**257.
-
-const (
-	p256Limbs    = 9
-	bottom29Bits = 0x1fffffff
-)
-
-var (
-	// p256One is the number 1 as a field element.
-	p256One  = [p256Limbs]uint32{2, 0, 0, 0xffff800, 0x1fffffff, 0xfffffff, 0x1fbfffff, 0x1ffffff, 0}
-	p256Zero = [p256Limbs]uint32{0, 0, 0, 0, 0, 0, 0, 0, 0}
-	// p256P is the prime modulus as a field element.
-	p256P = [p256Limbs]uint32{0x1fffffff, 0xfffffff, 0x1fffffff, 0x3ff, 0, 0, 0x200000, 0xf000000, 0xfffffff}
-	// p2562P is the twice prime modulus as a field element.
-	p2562P = [p256Limbs]uint32{0x1ffffffe, 0xfffffff, 0x1fffffff, 0x7ff, 0, 0, 0x400000, 0xe000000, 0x1fffffff}
-)
-
 // p256Precomputed contains precomputed values to aid the calculation of scalar
 // multiples of the base point, G. It's actually two, equal length, tables
 // concatenated.
@@ -181,613 +149,6 @@ var p256Precomputed = [p256Limbs * 2 * 15 * 2]uint32{
 	0xbe73d6f, 0xaa88141, 0xd976c81, 0x7e7a9cc, 0x18beb771, 0xd773cbd, 0x13f51951, 0x9d0c177, 0x1c49a78,
 }
 
-// Field element operations:
-
-const bottom28Bits = 0xfffffff
-
-// nonZeroToAllOnes returns:
-//
-//	0xffffffff for 0 < x <= 2**31
-//	0 for x == 0 or x > 2**31.
-func nonZeroToAllOnes(x uint32) uint32 {
-	return ((x - 1) >> 31) - 1
-}
-
-// p256ReduceCarry adds a multiple of p in order to cancel |carry|,
-// which is a term at 2**257.
-//
-// On entry: carry < 2**3, inout[0,2,...] < 2**29, inout[1,3,...] < 2**28.
-// On exit: inout[0,2,..] < 2**30, inout[1,3,...] < 2**29.
-func p256ReduceCarry(inout *[p256Limbs]uint32, carry uint32) {
-	carry_mask := nonZeroToAllOnes(carry)
-
-	inout[0] += carry << 1
-	inout[3] += 0x10000000 & carry_mask
-	// carry < 2**3 thus (carry << 11) < 2**14 and we added 2**28 in the
-	// previous line therefore this doesn't underflow.
-	inout[3] -= carry << 11
-	inout[4] += (0x20000000 - 1) & carry_mask
-	inout[5] += (0x10000000 - 1) & carry_mask
-	inout[6] += (0x20000000 - 1) & carry_mask
-	inout[6] -= carry << 22
-	// This may underflow if carry is non-zero but, if so, we'll fix it in the
-	// next line.
-	inout[7] -= 1 & carry_mask
-	inout[7] += carry << 25
-}
-
-// p256Sum sets out = in+in2.
-//
-// On entry: in[i]+in2[i] must not overflow a 32-bit word.
-// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
-func p256Sum(out, in, in2 *[p256Limbs]uint32) {
-	carry := uint32(0)
-	for i := 0; ; i++ {
-		out[i] = in[i] + in2[i]
-		out[i] += carry
-		carry = out[i] >> 29
-		out[i] &= bottom29Bits
-
-		i++
-		if i == p256Limbs {
-			break
-		}
-
-		out[i] = in[i] + in2[i]
-		out[i] += carry
-		carry = out[i] >> 28
-		out[i] &= bottom28Bits
-	}
-
-	p256ReduceCarry(out, carry)
-}
-
-const (
-	two30m2    = 1<<30 - 1<<2
-	two30p13m2 = 1<<30 + 1<<13 - 1<<2
-	two31m2    = 1<<31 - 1<<2
-	two31m3    = 1<<31 - 1<<3
-	two31p24m2 = 1<<31 + 1<<24 - 1<<2
-	two30m27m2 = 1<<30 - 1<<27 - 1<<2
-)
-
-// p256Zero31 is 0 mod p.
-var p256Zero31 = [p256Limbs]uint32{two31m3, two30m2, two31m2, two30p13m2, two31m2, two30m2, two31p24m2, two30m27m2, two31m2}
-
-// p256Diff sets out = in-in2.
-//
-// On entry: in[0,2,...] < 2**30, in[1,3,...] < 2**29 and
-// in2[0,2,...] < 2**30, in2[1,3,...] < 2**29.
-// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
-func p256Diff(out, in, in2 *[p256Limbs]uint32) {
-	var carry uint32
-
-	for i := 0; ; i++ {
-		out[i] = in[i] - in2[i]
-		out[i] += p256Zero31[i]
-		out[i] += carry
-		carry = out[i] >> 29
-		out[i] &= bottom29Bits
-
-		i++
-		if i == p256Limbs {
-			break
-		}
-
-		out[i] = in[i] - in2[i]
-		out[i] += p256Zero31[i]
-		out[i] += carry
-		carry = out[i] >> 28
-		out[i] &= bottom28Bits
-	}
-
-	p256ReduceCarry(out, carry)
-}
-
-// p256ReduceDegree sets out = tmp/R mod p where tmp contains 64-bit words with
-// the same 29,28,... bit positions as a field element.
-//
-// The values in field elements are in Montgomery form: x*R mod p where R =
-// 2**257. Since we just multiplied two Montgomery values together, the result
-// is x*y*R*R mod p. We wish to divide by R in order for the result also to be
-// in Montgomery form.
-//
-// On entry: tmp[i] < 2**64.
-// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
-func p256ReduceDegree(out *[p256Limbs]uint32, tmp [17]uint64) {
-	// The following table may be helpful when reading this code:
-	//
-	// Limb number:   0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10...
-	// Width (bits):  29| 28| 29| 28| 29| 28| 29| 28| 29| 28| 29
-	// Start bit:     0 | 29| 57| 86|114|143|171|200|228|257|285
-	//   (odd phase): 0 | 28| 57| 85|114|142|171|199|228|256|285
-	var tmp2 [18]uint32
-	var carry, x, xMask uint32
-
-	// tmp contains 64-bit words with the same 29,28,29-bit positions as a
-	// field element. So the top of an element of tmp might overlap with
-	// another element two positions down. The following loop eliminates
-	// this overlap.
-	tmp2[0] = uint32(tmp[0]) & bottom29Bits
-
-	tmp2[1] = uint32(tmp[0]) >> 29
-	tmp2[1] |= (uint32(tmp[0]>>32) << 3) & bottom28Bits
-	tmp2[1] += uint32(tmp[1]) & bottom28Bits
-	carry = tmp2[1] >> 28
-	tmp2[1] &= bottom28Bits
-
-	for i := 2; i < 17; i++ {
-		tmp2[i] = (uint32(tmp[i-2] >> 32)) >> 25
-		tmp2[i] += (uint32(tmp[i-1])) >> 28
-		tmp2[i] += (uint32(tmp[i-1]>>32) << 4) & bottom29Bits
-		tmp2[i] += uint32(tmp[i]) & bottom29Bits
-		tmp2[i] += carry
-		carry = tmp2[i] >> 29
-		tmp2[i] &= bottom29Bits
-
-		i++
-		if i == 17 {
-			break
-		}
-		tmp2[i] = uint32(tmp[i-2]>>32) >> 25
-		tmp2[i] += uint32(tmp[i-1]) >> 29
-		tmp2[i] += ((uint32(tmp[i-1] >> 32)) << 3) & bottom28Bits
-		tmp2[i] += uint32(tmp[i]) & bottom28Bits
-		tmp2[i] += carry
-		carry = tmp2[i] >> 28
-		tmp2[i] &= bottom28Bits
-	}
-
-	tmp2[17] = uint32(tmp[15]>>32) >> 25
-	tmp2[17] += uint32(tmp[16]) >> 29
-	tmp2[17] += uint32(tmp[16]>>32) << 3
-	tmp2[17] += carry
-
-	// Montgomery elimination of terms:
-	//
-	// Since R is 2**257, we can divide by R with a bitwise shift if we can
-	// ensure that the right-most 257 bits are all zero. We can make that true
-	// by adding multiplies of p without affecting the value.
-	//
-	// So we eliminate limbs from right to left. Since the bottom 29 bits of p
-	// are all ones, then by adding tmp2[0]*p to tmp2 we'll make tmp2[0] == 0.
-	// We can do that for 8 further limbs and then right shift to eliminate the
-	// extra factor of R.
-	for i := 0; ; i += 2 {
-		tmp2[i+1] += tmp2[i] >> 29
-		x = tmp2[i] & bottom29Bits
-		xMask = nonZeroToAllOnes(x)
-		tmp2[i] = 0
-
-		// The bounds calculations for this loop are tricky. Each iteration of
-		// the loop eliminates two words by adding values to words to their
-		// right.
-		//
-		// The following table contains the amounts added to each word (as an
-		// offset from the value of i at the top of the loop). The amounts are
-		// accounted for from the first and second half of the loop separately
-		// and are written as, for example, 28 to mean a value <2**28.
-		//
-		// Word:                   3   4   5   6   7   8   9   10
-		// Added in top half:     28  11      29  21  29  28
-		//                                        28  29
-		//                                            29
-		// Added in bottom half:      29  10      28  21  28   28
-		//                                            29
-		//
-		// The value that is currently offset 7 will be offset 5 for the next
-		// iteration and then offset 3 for the iteration after that. Therefore
-		// the total value added will be the values added at 7, 5 and 3.
-		//
-		// The following table accumulates these values. The sums at the bottom
-		// are written as, for example, 29+28, to mean a value < 2**29+2**28.
-		//
-		// Word:                   3   4   5   6   7   8   9  10  11  12  13
-		//                        28  11  10  29  21  29  28  28  28  28  28
-		//                            29  28  11  28  29  28  29  28  29  28
-		//                                    29  28  21  21  29  21  29  21
-		//                                        10  29  28  21  28  21  28
-		//                                        28  29  28  29  28  29  28
-		//                                            11  10  29  10  29  10
-		//                                            29  28  11  28  11
-		//                                                    29      29
-		//                        --------------------------------------------
-		//                                                30+ 31+ 30+ 31+ 30+
-		//                                                28+ 29+ 28+ 29+ 21+
-		//                                                21+ 28+ 21+ 28+ 10
-		//                                                10  21+ 10  21+
-		//                                                    11      11
-		//
-		// So the greatest amount is added to tmp2[10] and tmp2[12]. If
-		// tmp2[10/12] has an initial value of <2**29, then the maximum value
-		// will be < 2**31 + 2**30 + 2**28 + 2**21 + 2**11, which is < 2**32,
-		// as required.
-		tmp2[i+3] += (x << 10) & bottom28Bits
-		tmp2[i+4] += (x >> 18)
-
-		tmp2[i+6] += (x << 21) & bottom29Bits
-		tmp2[i+7] += x >> 8
-
-		// At position 200, which is the starting bit position for word 7, we
-		// have a factor of 0xf000000 = 2**28 - 2**24.
-		tmp2[i+7] += 0x10000000 & xMask
-		tmp2[i+8] += (x - 1) & xMask
-		tmp2[i+7] -= (x << 24) & bottom28Bits
-		tmp2[i+8] -= x >> 4
-
-		tmp2[i+8] += 0x20000000 & xMask
-		tmp2[i+8] -= x
-		tmp2[i+8] += (x << 28) & bottom29Bits
-		tmp2[i+9] += ((x >> 1) - 1) & xMask
-
-		if i+1 == p256Limbs {
-			break
-		}
-		tmp2[i+2] += tmp2[i+1] >> 28
-		x = tmp2[i+1] & bottom28Bits
-		xMask = nonZeroToAllOnes(x)
-		tmp2[i+1] = 0
-
-		tmp2[i+4] += (x << 11) & bottom29Bits
-		tmp2[i+5] += (x >> 18)
-
-		tmp2[i+7] += (x << 21) & bottom28Bits
-		tmp2[i+8] += x >> 7
-
-		// At position 199, which is the starting bit of the 8th word when
-		// dealing with a context starting on an odd word, we have a factor of
-		// 0x1e000000 = 2**29 - 2**25. Since we have not updated i, the 8th
-		// word from i+1 is i+8.
-		tmp2[i+8] += 0x20000000 & xMask
-		tmp2[i+9] += (x - 1) & xMask
-		tmp2[i+8] -= (x << 25) & bottom29Bits
-		tmp2[i+9] -= x >> 4
-
-		tmp2[i+9] += 0x10000000 & xMask
-		tmp2[i+9] -= x
-		tmp2[i+10] += (x - 1) & xMask
-	}
-
-	// We merge the right shift with a carry chain. The words above 2**257 have
-	// widths of 28,29,... which we need to correct when copying them down.
-	carry = 0
-	for i := 0; i < 8; i++ {
-		// The maximum value of tmp2[i + 9] occurs on the first iteration and
-		// is < 2**30+2**29+2**28. Adding 2**29 (from tmp2[i + 10]) is
-		// therefore safe.
-		out[i] = tmp2[i+9]
-		out[i] += carry
-		out[i] += (tmp2[i+10] << 28) & bottom29Bits
-		carry = out[i] >> 29
-		out[i] &= bottom29Bits
-
-		i++
-		out[i] = tmp2[i+9] >> 1
-		out[i] += carry
-		carry = out[i] >> 28
-		out[i] &= bottom28Bits
-	}
-
-	out[8] = tmp2[17]
-	out[8] += carry
-	carry = out[8] >> 29
-	out[8] &= bottom29Bits
-
-	p256ReduceCarry(out, carry)
-}
-
-// p256Square sets out=in*in.
-//
-// On entry: in[0,2,...] < 2**30, in[1,3,...] < 2**29.
-// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
-func p256Square(out, in *[p256Limbs]uint32) {
-	var tmp [17]uint64
-
-	tmp[0] = uint64(in[0]) * uint64(in[0])
-	tmp[1] = uint64(in[0]) * (uint64(in[1]) << 1)
-	tmp[2] = uint64(in[0])*(uint64(in[2])<<1) +
-		uint64(in[1])*(uint64(in[1])<<1)
-	tmp[3] = uint64(in[0])*(uint64(in[3])<<1) +
-		uint64(in[1])*(uint64(in[2])<<1)
-	tmp[4] = uint64(in[0])*(uint64(in[4])<<1) +
-		uint64(in[1])*(uint64(in[3])<<2) +
-		uint64(in[2])*uint64(in[2])
-	tmp[5] = uint64(in[0])*(uint64(in[5])<<1) +
-		uint64(in[1])*(uint64(in[4])<<1) +
-		uint64(in[2])*(uint64(in[3])<<1)
-	tmp[6] = uint64(in[0])*(uint64(in[6])<<1) +
-		uint64(in[1])*(uint64(in[5])<<2) +
-		uint64(in[2])*(uint64(in[4])<<1) +
-		uint64(in[3])*(uint64(in[3])<<1)
-	tmp[7] = uint64(in[0])*(uint64(in[7])<<1) +
-		uint64(in[1])*(uint64(in[6])<<1) +
-		uint64(in[2])*(uint64(in[5])<<1) +
-		uint64(in[3])*(uint64(in[4])<<1)
-	// tmp[8] has the greatest value of 2**61 + 2**60 + 2**61 + 2**60 + 2**60,
-	// which is < 2**64 as required.
-	tmp[8] = uint64(in[0])*(uint64(in[8])<<1) +
-		uint64(in[1])*(uint64(in[7])<<2) +
-		uint64(in[2])*(uint64(in[6])<<1) +
-		uint64(in[3])*(uint64(in[5])<<2) +
-		uint64(in[4])*uint64(in[4])
-	tmp[9] = uint64(in[1])*(uint64(in[8])<<1) +
-		uint64(in[2])*(uint64(in[7])<<1) +
-		uint64(in[3])*(uint64(in[6])<<1) +
-		uint64(in[4])*(uint64(in[5])<<1)
-	tmp[10] = uint64(in[2])*(uint64(in[8])<<1) +
-		uint64(in[3])*(uint64(in[7])<<2) +
-		uint64(in[4])*(uint64(in[6])<<1) +
-		uint64(in[5])*(uint64(in[5])<<1)
-	tmp[11] = uint64(in[3])*(uint64(in[8])<<1) +
-		uint64(in[4])*(uint64(in[7])<<1) +
-		uint64(in[5])*(uint64(in[6])<<1)
-	tmp[12] = uint64(in[4])*(uint64(in[8])<<1) +
-		uint64(in[5])*(uint64(in[7])<<2) +
-		uint64(in[6])*uint64(in[6])
-	tmp[13] = uint64(in[5])*(uint64(in[8])<<1) +
-		uint64(in[6])*(uint64(in[7])<<1)
-	tmp[14] = uint64(in[6])*(uint64(in[8])<<1) +
-		uint64(in[7])*(uint64(in[7])<<1)
-	tmp[15] = uint64(in[7]) * (uint64(in[8]) << 1)
-	tmp[16] = uint64(in[8]) * uint64(in[8])
-
-	p256ReduceDegree(out, tmp)
-}
-
-// p256Mul sets out=in*in2.
-//
-// On entry: in[0,2,...] < 2**30, in[1,3,...] < 2**29 and
-// in2[0,2,...] < 2**30, in2[1,3,...] < 2**29.
-// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
-func p256Mul(out, in, in2 *[p256Limbs]uint32) {
-	var tmp [17]uint64
-
-	tmp[0] = uint64(in[0]) * uint64(in2[0])
-	tmp[1] = uint64(in[0])*(uint64(in2[1])<<0) +
-		uint64(in[1])*(uint64(in2[0])<<0)
-	tmp[2] = uint64(in[0])*(uint64(in2[2])<<0) +
-		uint64(in[1])*(uint64(in2[1])<<1) +
-		uint64(in[2])*(uint64(in2[0])<<0)
-	tmp[3] = uint64(in[0])*(uint64(in2[3])<<0) +
-		uint64(in[1])*(uint64(in2[2])<<0) +
-		uint64(in[2])*(uint64(in2[1])<<0) +
-		uint64(in[3])*(uint64(in2[0])<<0)
-	tmp[4] = uint64(in[0])*(uint64(in2[4])<<0) +
-		uint64(in[1])*(uint64(in2[3])<<1) +
-		uint64(in[2])*(uint64(in2[2])<<0) +
-		uint64(in[3])*(uint64(in2[1])<<1) +
-		uint64(in[4])*(uint64(in2[0])<<0)
-	tmp[5] = uint64(in[0])*(uint64(in2[5])<<0) +
-		uint64(in[1])*(uint64(in2[4])<<0) +
-		uint64(in[2])*(uint64(in2[3])<<0) +
-		uint64(in[3])*(uint64(in2[2])<<0) +
-		uint64(in[4])*(uint64(in2[1])<<0) +
-		uint64(in[5])*(uint64(in2[0])<<0)
-	tmp[6] = uint64(in[0])*(uint64(in2[6])<<0) +
-		uint64(in[1])*(uint64(in2[5])<<1) +
-		uint64(in[2])*(uint64(in2[4])<<0) +
-		uint64(in[3])*(uint64(in2[3])<<1) +
-		uint64(in[4])*(uint64(in2[2])<<0) +
-		uint64(in[5])*(uint64(in2[1])<<1) +
-		uint64(in[6])*(uint64(in2[0])<<0)
-	tmp[7] = uint64(in[0])*(uint64(in2[7])<<0) +
-		uint64(in[1])*(uint64(in2[6])<<0) +
-		uint64(in[2])*(uint64(in2[5])<<0) +
-		uint64(in[3])*(uint64(in2[4])<<0) +
-		uint64(in[4])*(uint64(in2[3])<<0) +
-		uint64(in[5])*(uint64(in2[2])<<0) +
-		uint64(in[6])*(uint64(in2[1])<<0) +
-		uint64(in[7])*(uint64(in2[0])<<0)
-	// tmp[8] has the greatest value but doesn't overflow. See logic in
-	// p256Square.
-	tmp[8] = uint64(in[0])*(uint64(in2[8])<<0) +
-		uint64(in[1])*(uint64(in2[7])<<1) +
-		uint64(in[2])*(uint64(in2[6])<<0) +
-		uint64(in[3])*(uint64(in2[5])<<1) +
-		uint64(in[4])*(uint64(in2[4])<<0) +
-		uint64(in[5])*(uint64(in2[3])<<1) +
-		uint64(in[6])*(uint64(in2[2])<<0) +
-		uint64(in[7])*(uint64(in2[1])<<1) +
-		uint64(in[8])*(uint64(in2[0])<<0)
-	tmp[9] = uint64(in[1])*(uint64(in2[8])<<0) +
-		uint64(in[2])*(uint64(in2[7])<<0) +
-		uint64(in[3])*(uint64(in2[6])<<0) +
-		uint64(in[4])*(uint64(in2[5])<<0) +
-		uint64(in[5])*(uint64(in2[4])<<0) +
-		uint64(in[6])*(uint64(in2[3])<<0) +
-		uint64(in[7])*(uint64(in2[2])<<0) +
-		uint64(in[8])*(uint64(in2[1])<<0)
-	tmp[10] = uint64(in[2])*(uint64(in2[8])<<0) +
-		uint64(in[3])*(uint64(in2[7])<<1) +
-		uint64(in[4])*(uint64(in2[6])<<0) +
-		uint64(in[5])*(uint64(in2[5])<<1) +
-		uint64(in[6])*(uint64(in2[4])<<0) +
-		uint64(in[7])*(uint64(in2[3])<<1) +
-		uint64(in[8])*(uint64(in2[2])<<0)
-	tmp[11] = uint64(in[3])*(uint64(in2[8])<<0) +
-		uint64(in[4])*(uint64(in2[7])<<0) +
-		uint64(in[5])*(uint64(in2[6])<<0) +
-		uint64(in[6])*(uint64(in2[5])<<0) +
-		uint64(in[7])*(uint64(in2[4])<<0) +
-		uint64(in[8])*(uint64(in2[3])<<0)
-	tmp[12] = uint64(in[4])*(uint64(in2[8])<<0) +
-		uint64(in[5])*(uint64(in2[7])<<1) +
-		uint64(in[6])*(uint64(in2[6])<<0) +
-		uint64(in[7])*(uint64(in2[5])<<1) +
-		uint64(in[8])*(uint64(in2[4])<<0)
-	tmp[13] = uint64(in[5])*(uint64(in2[8])<<0) +
-		uint64(in[6])*(uint64(in2[7])<<0) +
-		uint64(in[7])*(uint64(in2[6])<<0) +
-		uint64(in[8])*(uint64(in2[5])<<0)
-	tmp[14] = uint64(in[6])*(uint64(in2[8])<<0) +
-		uint64(in[7])*(uint64(in2[7])<<1) +
-		uint64(in[8])*(uint64(in2[6])<<0)
-	tmp[15] = uint64(in[7])*(uint64(in2[8])<<0) +
-		uint64(in[8])*(uint64(in2[7])<<0)
-	tmp[16] = uint64(in[8]) * (uint64(in2[8]) << 0)
-
-	p256ReduceDegree(out, tmp)
-}
-
-func p256Assign(out, in *[p256Limbs]uint32) {
-	*out = *in
-}
-
-// p256Invert calculates |out| = |in|^{-1}
-//
-// Based on Fermat's Little Theorem:
-//
-//	a^p = a (mod p)
-//	a^{p-1} = 1 (mod p)
-//	a^{p-2} = a^{-1} (mod p)
-func p256Invert(out, in *[p256Limbs]uint32) {
-	var ftmp, ftmp2 [p256Limbs]uint32
-
-	// each e_I will hold |in|^{2^I - 1}
-	var e2, e4, e8, e16, e32, e64 [p256Limbs]uint32
-
-	p256Square(&ftmp, in)     // 2^1
-	p256Mul(&ftmp, in, &ftmp) // 2^2 - 2^0
-	p256Assign(&e2, &ftmp)
-	p256Square(&ftmp, &ftmp)   // 2^3 - 2^1
-	p256Square(&ftmp, &ftmp)   // 2^4 - 2^2
-	p256Mul(&ftmp, &ftmp, &e2) // 2^4 - 2^0
-	p256Assign(&e4, &ftmp)
-	p256Square(&ftmp, &ftmp)   // 2^5 - 2^1
-	p256Square(&ftmp, &ftmp)   // 2^6 - 2^2
-	p256Square(&ftmp, &ftmp)   // 2^7 - 2^3
-	p256Square(&ftmp, &ftmp)   // 2^8 - 2^4
-	p256Mul(&ftmp, &ftmp, &e4) // 2^8 - 2^0
-	p256Assign(&e8, &ftmp)
-	for i := 0; i < 8; i++ {
-		p256Square(&ftmp, &ftmp)
-	} // 2^16 - 2^8
-	p256Mul(&ftmp, &ftmp, &e8) // 2^16 - 2^0
-	p256Assign(&e16, &ftmp)
-	for i := 0; i < 16; i++ {
-		p256Square(&ftmp, &ftmp)
-	} // 2^32 - 2^16
-	p256Mul(&ftmp, &ftmp, &e16) // 2^32 - 2^0
-	p256Assign(&e32, &ftmp)
-	for i := 0; i < 32; i++ {
-		p256Square(&ftmp, &ftmp)
-	} // 2^64 - 2^32
-	p256Assign(&e64, &ftmp)
-	p256Mul(&ftmp, &ftmp, in) // 2^64 - 2^32 + 2^0
-	for i := 0; i < 192; i++ {
-		p256Square(&ftmp, &ftmp)
-	} // 2^256 - 2^224 + 2^192
-
-	p256Mul(&ftmp2, &e64, &e32) // 2^64 - 2^0
-	for i := 0; i < 16; i++ {
-		p256Square(&ftmp2, &ftmp2)
-	} // 2^80 - 2^16
-	p256Mul(&ftmp2, &ftmp2, &e16) // 2^80 - 2^0
-	for i := 0; i < 8; i++ {
-		p256Square(&ftmp2, &ftmp2)
-	} // 2^88 - 2^8
-	p256Mul(&ftmp2, &ftmp2, &e8) // 2^88 - 2^0
-	for i := 0; i < 4; i++ {
-		p256Square(&ftmp2, &ftmp2)
-	} // 2^92 - 2^4
-	p256Mul(&ftmp2, &ftmp2, &e4) // 2^92 - 2^0
-	p256Square(&ftmp2, &ftmp2)   // 2^93 - 2^1
-	p256Square(&ftmp2, &ftmp2)   // 2^94 - 2^2
-	p256Mul(&ftmp2, &ftmp2, &e2) // 2^94 - 2^0
-	p256Square(&ftmp2, &ftmp2)   // 2^95 - 2^1
-	p256Square(&ftmp2, &ftmp2)   // 2^96 - 2^2
-	p256Mul(&ftmp2, &ftmp2, in)  // 2^96 - 3
-
-	p256Mul(out, &ftmp2, &ftmp) // 2^256 - 2^224 + 2^192 + 2^96 - 3
-}
-
-// p256Scalar3 sets out=3*out.
-//
-// On entry: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
-// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
-func p256Scalar3(out *[p256Limbs]uint32) {
-	var carry uint32
-
-	for i := 0; ; i++ {
-		out[i] *= 3
-		out[i] += carry
-		carry = out[i] >> 29
-		out[i] &= bottom29Bits
-
-		i++
-		if i == p256Limbs {
-			break
-		}
-
-		out[i] *= 3
-		out[i] += carry
-		carry = out[i] >> 28
-		out[i] &= bottom28Bits
-	}
-
-	p256ReduceCarry(out, carry)
-}
-
-// p256Scalar4 sets out=4*out.
-//
-// On entry: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
-// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
-func p256Scalar4(out *[p256Limbs]uint32) {
-	var carry, nextCarry uint32
-
-	for i := 0; ; i++ {
-		nextCarry = out[i] >> 27
-		out[i] <<= 2
-		out[i] &= bottom29Bits
-		out[i] += carry
-		carry = nextCarry + (out[i] >> 29)
-		out[i] &= bottom29Bits
-
-		i++
-		if i == p256Limbs {
-			break
-		}
-		nextCarry = out[i] >> 26
-		out[i] <<= 2
-		out[i] &= bottom28Bits
-		out[i] += carry
-		carry = nextCarry + (out[i] >> 28)
-		out[i] &= bottom28Bits
-	}
-
-	p256ReduceCarry(out, carry)
-}
-
-// p256Scalar8 sets out=8*out.
-//
-// On entry: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
-// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
-func p256Scalar8(out *[p256Limbs]uint32) {
-	var carry, nextCarry uint32
-
-	for i := 0; ; i++ {
-		nextCarry = out[i] >> 26
-		out[i] <<= 3
-		out[i] &= bottom29Bits
-		out[i] += carry
-		carry = nextCarry + (out[i] >> 29)
-		out[i] &= bottom29Bits
-
-		i++
-		if i == p256Limbs {
-			break
-		}
-		nextCarry = out[i] >> 25
-		out[i] <<= 3
-		out[i] &= bottom28Bits
-		out[i] += carry
-		carry = nextCarry + (out[i] >> 28)
-		out[i] &= bottom28Bits
-	}
-
-	p256ReduceCarry(out, carry)
-}
-
 // Group operations:
 //
 // Elements of the elliptic curve group are represented in Jacobian
@@ -908,16 +269,6 @@ func p256PointAdd(xOut, yOut, zOut, x1, y1, z1, x2, y2, z2 *[p256Limbs]uint32) {
 	p256Diff(yOut, yOut, &tmp)
 }
 
-// p256CopyConditional sets out=in if mask = 0xffffffff in constant time.
-//
-// On entry: mask is either 0 or 0xffffffff.
-func p256CopyConditional(out, in *[p256Limbs]uint32, mask uint32) {
-	for i := 0; i < p256Limbs; i++ {
-		tmp := mask & (in[i] ^ out[i])
-		out[i] ^= tmp
-	}
-}
-
 // p256SelectAffinePoint sets {out_x,out_y} to the index'th entry of table.
 //
 // On entry: index < 16, table[0] must be zero.
@@ -1124,50 +475,3 @@ func p256ScalarMult(xOut, yOut, zOut, x, y *[p256Limbs]uint32, scalar *[32]uint8
 		nIsInfinityMask &^= pIsNoninfiniteMask
 	}
 }
-
-// p256FromBig sets out = R*in.
-func p256FromBig(out *[p256Limbs]uint32, in *big.Int) {
-	tmp := new(big.Int).Lsh(in, 257)
-	tmp.Mod(tmp, p256Params.P)
-
-	for i := 0; i < p256Limbs; i++ {
-		if bits := tmp.Bits(); len(bits) > 0 {
-			out[i] = uint32(bits[0]) & bottom29Bits
-		} else {
-			out[i] = 0
-		}
-		tmp.Rsh(tmp, 29)
-
-		i++
-		if i == p256Limbs {
-			break
-		}
-
-		if bits := tmp.Bits(); len(bits) > 0 {
-			out[i] = uint32(bits[0]) & bottom28Bits
-		} else {
-			out[i] = 0
-		}
-		tmp.Rsh(tmp, 28)
-	}
-}
-
-// p256ToBig returns a *big.Int containing the value of in.
-func p256ToBig(in *[p256Limbs]uint32) *big.Int {
-	result, tmp := new(big.Int), new(big.Int)
-
-	result.SetInt64(int64(in[p256Limbs-1]))
-	for i := p256Limbs - 2; i >= 0; i-- {
-		if (i & 1) == 0 {
-			result.Lsh(result, 29)
-		} else {
-			result.Lsh(result, 28)
-		}
-		tmp.SetInt64(int64(in[i]))
-		result.Add(result, tmp)
-	}
-
-	result.Mul(result, p256RInverse)
-	result.Mod(result, p256Params.P)
-	return result
-}
diff --git a/src/crypto/elliptic/p256_generic_field.go b/src/crypto/elliptic/p256_generic_field.go
new file mode 100644
index 0000000000..5824946ba4
--- /dev/null
+++ b/src/crypto/elliptic/p256_generic_field.go
@@ -0,0 +1,705 @@
+// Copyright 2013 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+//go:build !amd64 && !arm64
+
+package elliptic
+
+import "math/big"
+
+// Field elements are represented as nine, unsigned 32-bit words.
+//
+// The value of a field element is:
+//   x[0] + (x[1] * 2**29) + (x[2] * 2**57) + ... + (x[8] * 2**228)
+//
+// That is, each limb is alternately 29 or 28-bits wide in little-endian
+// order.
+//
+// This means that a field element hits 2**257, rather than 2**256 as we would
+// like. A 28, 29, ... pattern would cause us to hit 2**256, but that causes
+// problems when multiplying as terms end up one bit short of a limb which
+// would require much bit-shifting to correct.
+//
+// Finally, the values stored in a field element are in Montgomery form. So the
+// value |y| is stored as (y*R) mod p, where p is the P-256 prime and R is
+// 2**257.
+
+const (
+	p256Limbs    = 9
+	bottom29Bits = 0x1fffffff
+)
+
+var (
+	// p256One is the number 1 as a field element.
+	p256One  = [p256Limbs]uint32{2, 0, 0, 0xffff800, 0x1fffffff, 0xfffffff, 0x1fbfffff, 0x1ffffff, 0}
+	p256Zero = [p256Limbs]uint32{0, 0, 0, 0, 0, 0, 0, 0, 0}
+	// p256P is the prime modulus as a field element.
+	p256P = [p256Limbs]uint32{0x1fffffff, 0xfffffff, 0x1fffffff, 0x3ff, 0, 0, 0x200000, 0xf000000, 0xfffffff}
+	// p2562P is the twice prime modulus as a field element.
+	p2562P = [p256Limbs]uint32{0x1ffffffe, 0xfffffff, 0x1fffffff, 0x7ff, 0, 0, 0x400000, 0xe000000, 0x1fffffff}
+)
+
+// Field element operations:
+
+const bottom28Bits = 0xfffffff
+
+// nonZeroToAllOnes returns:
+//
+//	0xffffffff for 0 < x <= 2**31
+//	0 for x == 0 or x > 2**31.
+func nonZeroToAllOnes(x uint32) uint32 {
+	return ((x - 1) >> 31) - 1
+}
+
+// p256ReduceCarry adds a multiple of p in order to cancel |carry|,
+// which is a term at 2**257.
+//
+// On entry: carry < 2**3, inout[0,2,...] < 2**29, inout[1,3,...] < 2**28.
+// On exit: inout[0,2,..] < 2**30, inout[1,3,...] < 2**29.
+func p256ReduceCarry(inout *[p256Limbs]uint32, carry uint32) {
+	carry_mask := nonZeroToAllOnes(carry)
+
+	inout[0] += carry << 1
+	inout[3] += 0x10000000 & carry_mask
+	// carry < 2**3 thus (carry << 11) < 2**14 and we added 2**28 in the
+	// previous line therefore this doesn't underflow.
+	inout[3] -= carry << 11
+	inout[4] += (0x20000000 - 1) & carry_mask
+	inout[5] += (0x10000000 - 1) & carry_mask
+	inout[6] += (0x20000000 - 1) & carry_mask
+	inout[6] -= carry << 22
+	// This may underflow if carry is non-zero but, if so, we'll fix it in the
+	// next line.
+	inout[7] -= 1 & carry_mask
+	inout[7] += carry << 25
+}
+
+// p256Sum sets out = in+in2.
+//
+// On entry: in[i]+in2[i] must not overflow a 32-bit word.
+// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
+func p256Sum(out, in, in2 *[p256Limbs]uint32) {
+	carry := uint32(0)
+	for i := 0; ; i++ {
+		out[i] = in[i] + in2[i]
+		out[i] += carry
+		carry = out[i] >> 29
+		out[i] &= bottom29Bits
+
+		i++
+		if i == p256Limbs {
+			break
+		}
+
+		out[i] = in[i] + in2[i]
+		out[i] += carry
+		carry = out[i] >> 28
+		out[i] &= bottom28Bits
+	}
+
+	p256ReduceCarry(out, carry)
+}
+
+const (
+	two30m2    = 1<<30 - 1<<2
+	two30p13m2 = 1<<30 + 1<<13 - 1<<2
+	two31m2    = 1<<31 - 1<<2
+	two31m3    = 1<<31 - 1<<3
+	two31p24m2 = 1<<31 + 1<<24 - 1<<2
+	two30m27m2 = 1<<30 - 1<<27 - 1<<2
+)
+
+// p256Zero31 is 0 mod p.
+var p256Zero31 = [p256Limbs]uint32{two31m3, two30m2, two31m2, two30p13m2, two31m2, two30m2, two31p24m2, two30m27m2, two31m2}
+
+// p256Diff sets out = in-in2.
+//
+// On entry: in[0,2,...] < 2**30, in[1,3,...] < 2**29 and
+// in2[0,2,...] < 2**30, in2[1,3,...] < 2**29.
+// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
+func p256Diff(out, in, in2 *[p256Limbs]uint32) {
+	var carry uint32
+
+	for i := 0; ; i++ {
+		out[i] = in[i] - in2[i]
+		out[i] += p256Zero31[i]
+		out[i] += carry
+		carry = out[i] >> 29
+		out[i] &= bottom29Bits
+
+		i++
+		if i == p256Limbs {
+			break
+		}
+
+		out[i] = in[i] - in2[i]
+		out[i] += p256Zero31[i]
+		out[i] += carry
+		carry = out[i] >> 28
+		out[i] &= bottom28Bits
+	}
+
+	p256ReduceCarry(out, carry)
+}
+
+// p256ReduceDegree sets out = tmp/R mod p where tmp contains 64-bit words with
+// the same 29,28,... bit positions as a field element.
+//
+// The values in field elements are in Montgomery form: x*R mod p where R =
+// 2**257. Since we just multiplied two Montgomery values together, the result
+// is x*y*R*R mod p. We wish to divide by R in order for the result also to be
+// in Montgomery form.
+//
+// On entry: tmp[i] < 2**64.
+// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
+func p256ReduceDegree(out *[p256Limbs]uint32, tmp [17]uint64) {
+	// The following table may be helpful when reading this code:
+	//
+	// Limb number:   0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10...
+	// Width (bits):  29| 28| 29| 28| 29| 28| 29| 28| 29| 28| 29
+	// Start bit:     0 | 29| 57| 86|114|143|171|200|228|257|285
+	//   (odd phase): 0 | 28| 57| 85|114|142|171|199|228|256|285
+	var tmp2 [18]uint32
+	var carry, x, xMask uint32
+
+	// tmp contains 64-bit words with the same 29,28,29-bit positions as a
+	// field element. So the top of an element of tmp might overlap with
+	// another element two positions down. The following loop eliminates
+	// this overlap.
+	tmp2[0] = uint32(tmp[0]) & bottom29Bits
+
+	tmp2[1] = uint32(tmp[0]) >> 29
+	tmp2[1] |= (uint32(tmp[0]>>32) << 3) & bottom28Bits
+	tmp2[1] += uint32(tmp[1]) & bottom28Bits
+	carry = tmp2[1] >> 28
+	tmp2[1] &= bottom28Bits
+
+	for i := 2; i < 17; i++ {
+		tmp2[i] = (uint32(tmp[i-2] >> 32)) >> 25
+		tmp2[i] += (uint32(tmp[i-1])) >> 28
+		tmp2[i] += (uint32(tmp[i-1]>>32) << 4) & bottom29Bits
+		tmp2[i] += uint32(tmp[i]) & bottom29Bits
+		tmp2[i] += carry
+		carry = tmp2[i] >> 29
+		tmp2[i] &= bottom29Bits
+
+		i++
+		if i == 17 {
+			break
+		}
+		tmp2[i] = uint32(tmp[i-2]>>32) >> 25
+		tmp2[i] += uint32(tmp[i-1]) >> 29
+		tmp2[i] += ((uint32(tmp[i-1] >> 32)) << 3) & bottom28Bits
+		tmp2[i] += uint32(tmp[i]) & bottom28Bits
+		tmp2[i] += carry
+		carry = tmp2[i] >> 28
+		tmp2[i] &= bottom28Bits
+	}
+
+	tmp2[17] = uint32(tmp[15]>>32) >> 25
+	tmp2[17] += uint32(tmp[16]) >> 29
+	tmp2[17] += uint32(tmp[16]>>32) << 3
+	tmp2[17] += carry
+
+	// Montgomery elimination of terms:
+	//
+	// Since R is 2**257, we can divide by R with a bitwise shift if we can
+	// ensure that the right-most 257 bits are all zero. We can make that true
+	// by adding multiplies of p without affecting the value.
+	//
+	// So we eliminate limbs from right to left. Since the bottom 29 bits of p
+	// are all ones, then by adding tmp2[0]*p to tmp2 we'll make tmp2[0] == 0.
+	// We can do that for 8 further limbs and then right shift to eliminate the
+	// extra factor of R.
+	for i := 0; ; i += 2 {
+		tmp2[i+1] += tmp2[i] >> 29
+		x = tmp2[i] & bottom29Bits
+		xMask = nonZeroToAllOnes(x)
+		tmp2[i] = 0
+
+		// The bounds calculations for this loop are tricky. Each iteration of
+		// the loop eliminates two words by adding values to words to their
+		// right.
+		//
+		// The following table contains the amounts added to each word (as an
+		// offset from the value of i at the top of the loop). The amounts are
+		// accounted for from the first and second half of the loop separately
+		// and are written as, for example, 28 to mean a value <2**28.
+		//
+		// Word:                   3   4   5   6   7   8   9   10
+		// Added in top half:     28  11      29  21  29  28
+		//                                        28  29
+		//                                            29
+		// Added in bottom half:      29  10      28  21  28   28
+		//                                            29
+		//
+		// The value that is currently offset 7 will be offset 5 for the next
+		// iteration and then offset 3 for the iteration after that. Therefore
+		// the total value added will be the values added at 7, 5 and 3.
+		//
+		// The following table accumulates these values. The sums at the bottom
+		// are written as, for example, 29+28, to mean a value < 2**29+2**28.
+		//
+		// Word:                   3   4   5   6   7   8   9  10  11  12  13
+		//                        28  11  10  29  21  29  28  28  28  28  28
+		//                            29  28  11  28  29  28  29  28  29  28
+		//                                    29  28  21  21  29  21  29  21
+		//                                        10  29  28  21  28  21  28
+		//                                        28  29  28  29  28  29  28
+		//                                            11  10  29  10  29  10
+		//                                            29  28  11  28  11
+		//                                                    29      29
+		//                        --------------------------------------------
+		//                                                30+ 31+ 30+ 31+ 30+
+		//                                                28+ 29+ 28+ 29+ 21+
+		//                                                21+ 28+ 21+ 28+ 10
+		//                                                10  21+ 10  21+
+		//                                                    11      11
+		//
+		// So the greatest amount is added to tmp2[10] and tmp2[12]. If
+		// tmp2[10/12] has an initial value of <2**29, then the maximum value
+		// will be < 2**31 + 2**30 + 2**28 + 2**21 + 2**11, which is < 2**32,
+		// as required.
+		tmp2[i+3] += (x << 10) & bottom28Bits
+		tmp2[i+4] += (x >> 18)
+
+		tmp2[i+6] += (x << 21) & bottom29Bits
+		tmp2[i+7] += x >> 8
+
+		// At position 200, which is the starting bit position for word 7, we
+		// have a factor of 0xf000000 = 2**28 - 2**24.
+		tmp2[i+7] += 0x10000000 & xMask
+		tmp2[i+8] += (x - 1) & xMask
+		tmp2[i+7] -= (x << 24) & bottom28Bits
+		tmp2[i+8] -= x >> 4
+
+		tmp2[i+8] += 0x20000000 & xMask
+		tmp2[i+8] -= x
+		tmp2[i+8] += (x << 28) & bottom29Bits
+		tmp2[i+9] += ((x >> 1) - 1) & xMask
+
+		if i+1 == p256Limbs {
+			break
+		}
+		tmp2[i+2] += tmp2[i+1] >> 28
+		x = tmp2[i+1] & bottom28Bits
+		xMask = nonZeroToAllOnes(x)
+		tmp2[i+1] = 0
+
+		tmp2[i+4] += (x << 11) & bottom29Bits
+		tmp2[i+5] += (x >> 18)
+
+		tmp2[i+7] += (x << 21) & bottom28Bits
+		tmp2[i+8] += x >> 7
+
+		// At position 199, which is the starting bit of the 8th word when
+		// dealing with a context starting on an odd word, we have a factor of
+		// 0x1e000000 = 2**29 - 2**25. Since we have not updated i, the 8th
+		// word from i+1 is i+8.
+		tmp2[i+8] += 0x20000000 & xMask
+		tmp2[i+9] += (x - 1) & xMask
+		tmp2[i+8] -= (x << 25) & bottom29Bits
+		tmp2[i+9] -= x >> 4
+
+		tmp2[i+9] += 0x10000000 & xMask
+		tmp2[i+9] -= x
+		tmp2[i+10] += (x - 1) & xMask
+	}
+
+	// We merge the right shift with a carry chain. The words above 2**257 have
+	// widths of 28,29,... which we need to correct when copying them down.
+	carry = 0
+	for i := 0; i < 8; i++ {
+		// The maximum value of tmp2[i + 9] occurs on the first iteration and
+		// is < 2**30+2**29+2**28. Adding 2**29 (from tmp2[i + 10]) is
+		// therefore safe.
+		out[i] = tmp2[i+9]
+		out[i] += carry
+		out[i] += (tmp2[i+10] << 28) & bottom29Bits
+		carry = out[i] >> 29
+		out[i] &= bottom29Bits
+
+		i++
+		out[i] = tmp2[i+9] >> 1
+		out[i] += carry
+		carry = out[i] >> 28
+		out[i] &= bottom28Bits
+	}
+
+	out[8] = tmp2[17]
+	out[8] += carry
+	carry = out[8] >> 29
+	out[8] &= bottom29Bits
+
+	p256ReduceCarry(out, carry)
+}
+
+// p256Square sets out=in*in.
+//
+// On entry: in[0,2,...] < 2**30, in[1,3,...] < 2**29.
+// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
+func p256Square(out, in *[p256Limbs]uint32) {
+	var tmp [17]uint64
+
+	tmp[0] = uint64(in[0]) * uint64(in[0])
+	tmp[1] = uint64(in[0]) * (uint64(in[1]) << 1)
+	tmp[2] = uint64(in[0])*(uint64(in[2])<<1) +
+		uint64(in[1])*(uint64(in[1])<<1)
+	tmp[3] = uint64(in[0])*(uint64(in[3])<<1) +
+		uint64(in[1])*(uint64(in[2])<<1)
+	tmp[4] = uint64(in[0])*(uint64(in[4])<<1) +
+		uint64(in[1])*(uint64(in[3])<<2) +
+		uint64(in[2])*uint64(in[2])
+	tmp[5] = uint64(in[0])*(uint64(in[5])<<1) +
+		uint64(in[1])*(uint64(in[4])<<1) +
+		uint64(in[2])*(uint64(in[3])<<1)
+	tmp[6] = uint64(in[0])*(uint64(in[6])<<1) +
+		uint64(in[1])*(uint64(in[5])<<2) +
+		uint64(in[2])*(uint64(in[4])<<1) +
+		uint64(in[3])*(uint64(in[3])<<1)
+	tmp[7] = uint64(in[0])*(uint64(in[7])<<1) +
+		uint64(in[1])*(uint64(in[6])<<1) +
+		uint64(in[2])*(uint64(in[5])<<1) +
+		uint64(in[3])*(uint64(in[4])<<1)
+	// tmp[8] has the greatest value of 2**61 + 2**60 + 2**61 + 2**60 + 2**60,
+	// which is < 2**64 as required.
+	tmp[8] = uint64(in[0])*(uint64(in[8])<<1) +
+		uint64(in[1])*(uint64(in[7])<<2) +
+		uint64(in[2])*(uint64(in[6])<<1) +
+		uint64(in[3])*(uint64(in[5])<<2) +
+		uint64(in[4])*uint64(in[4])
+	tmp[9] = uint64(in[1])*(uint64(in[8])<<1) +
+		uint64(in[2])*(uint64(in[7])<<1) +
+		uint64(in[3])*(uint64(in[6])<<1) +
+		uint64(in[4])*(uint64(in[5])<<1)
+	tmp[10] = uint64(in[2])*(uint64(in[8])<<1) +
+		uint64(in[3])*(uint64(in[7])<<2) +
+		uint64(in[4])*(uint64(in[6])<<1) +
+		uint64(in[5])*(uint64(in[5])<<1)
+	tmp[11] = uint64(in[3])*(uint64(in[8])<<1) +
+		uint64(in[4])*(uint64(in[7])<<1) +
+		uint64(in[5])*(uint64(in[6])<<1)
+	tmp[12] = uint64(in[4])*(uint64(in[8])<<1) +
+		uint64(in[5])*(uint64(in[7])<<2) +
+		uint64(in[6])*uint64(in[6])
+	tmp[13] = uint64(in[5])*(uint64(in[8])<<1) +
+		uint64(in[6])*(uint64(in[7])<<1)
+	tmp[14] = uint64(in[6])*(uint64(in[8])<<1) +
+		uint64(in[7])*(uint64(in[7])<<1)
+	tmp[15] = uint64(in[7]) * (uint64(in[8]) << 1)
+	tmp[16] = uint64(in[8]) * uint64(in[8])
+
+	p256ReduceDegree(out, tmp)
+}
+
+// p256Mul sets out=in*in2.
+//
+// On entry: in[0,2,...] < 2**30, in[1,3,...] < 2**29 and
+// in2[0,2,...] < 2**30, in2[1,3,...] < 2**29.
+// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
+func p256Mul(out, in, in2 *[p256Limbs]uint32) {
+	var tmp [17]uint64
+
+	tmp[0] = uint64(in[0]) * uint64(in2[0])
+	tmp[1] = uint64(in[0])*(uint64(in2[1])<<0) +
+		uint64(in[1])*(uint64(in2[0])<<0)
+	tmp[2] = uint64(in[0])*(uint64(in2[2])<<0) +
+		uint64(in[1])*(uint64(in2[1])<<1) +
+		uint64(in[2])*(uint64(in2[0])<<0)
+	tmp[3] = uint64(in[0])*(uint64(in2[3])<<0) +
+		uint64(in[1])*(uint64(in2[2])<<0) +
+		uint64(in[2])*(uint64(in2[1])<<0) +
+		uint64(in[3])*(uint64(in2[0])<<0)
+	tmp[4] = uint64(in[0])*(uint64(in2[4])<<0) +
+		uint64(in[1])*(uint64(in2[3])<<1) +
+		uint64(in[2])*(uint64(in2[2])<<0) +
+		uint64(in[3])*(uint64(in2[1])<<1) +
+		uint64(in[4])*(uint64(in2[0])<<0)
+	tmp[5] = uint64(in[0])*(uint64(in2[5])<<0) +
+		uint64(in[1])*(uint64(in2[4])<<0) +
+		uint64(in[2])*(uint64(in2[3])<<0) +
+		uint64(in[3])*(uint64(in2[2])<<0) +
+		uint64(in[4])*(uint64(in2[1])<<0) +
+		uint64(in[5])*(uint64(in2[0])<<0)
+	tmp[6] = uint64(in[0])*(uint64(in2[6])<<0) +
+		uint64(in[1])*(uint64(in2[5])<<1) +
+		uint64(in[2])*(uint64(in2[4])<<0) +
+		uint64(in[3])*(uint64(in2[3])<<1) +
+		uint64(in[4])*(uint64(in2[2])<<0) +
+		uint64(in[5])*(uint64(in2[1])<<1) +
+		uint64(in[6])*(uint64(in2[0])<<0)
+	tmp[7] = uint64(in[0])*(uint64(in2[7])<<0) +
+		uint64(in[1])*(uint64(in2[6])<<0) +
+		uint64(in[2])*(uint64(in2[5])<<0) +
+		uint64(in[3])*(uint64(in2[4])<<0) +
+		uint64(in[4])*(uint64(in2[3])<<0) +
+		uint64(in[5])*(uint64(in2[2])<<0) +
+		uint64(in[6])*(uint64(in2[1])<<0) +
+		uint64(in[7])*(uint64(in2[0])<<0)
+	// tmp[8] has the greatest value but doesn't overflow. See logic in
+	// p256Square.
+	tmp[8] = uint64(in[0])*(uint64(in2[8])<<0) +
+		uint64(in[1])*(uint64(in2[7])<<1) +
+		uint64(in[2])*(uint64(in2[6])<<0) +
+		uint64(in[3])*(uint64(in2[5])<<1) +
+		uint64(in[4])*(uint64(in2[4])<<0) +
+		uint64(in[5])*(uint64(in2[3])<<1) +
+		uint64(in[6])*(uint64(in2[2])<<0) +
+		uint64(in[7])*(uint64(in2[1])<<1) +
+		uint64(in[8])*(uint64(in2[0])<<0)
+	tmp[9] = uint64(in[1])*(uint64(in2[8])<<0) +
+		uint64(in[2])*(uint64(in2[7])<<0) +
+		uint64(in[3])*(uint64(in2[6])<<0) +
+		uint64(in[4])*(uint64(in2[5])<<0) +
+		uint64(in[5])*(uint64(in2[4])<<0) +
+		uint64(in[6])*(uint64(in2[3])<<0) +
+		uint64(in[7])*(uint64(in2[2])<<0) +
+		uint64(in[8])*(uint64(in2[1])<<0)
+	tmp[10] = uint64(in[2])*(uint64(in2[8])<<0) +
+		uint64(in[3])*(uint64(in2[7])<<1) +
+		uint64(in[4])*(uint64(in2[6])<<0) +
+		uint64(in[5])*(uint64(in2[5])<<1) +
+		uint64(in[6])*(uint64(in2[4])<<0) +
+		uint64(in[7])*(uint64(in2[3])<<1) +
+		uint64(in[8])*(uint64(in2[2])<<0)
+	tmp[11] = uint64(in[3])*(uint64(in2[8])<<0) +
+		uint64(in[4])*(uint64(in2[7])<<0) +
+		uint64(in[5])*(uint64(in2[6])<<0) +
+		uint64(in[6])*(uint64(in2[5])<<0) +
+		uint64(in[7])*(uint64(in2[4])<<0) +
+		uint64(in[8])*(uint64(in2[3])<<0)
+	tmp[12] = uint64(in[4])*(uint64(in2[8])<<0) +
+		uint64(in[5])*(uint64(in2[7])<<1) +
+		uint64(in[6])*(uint64(in2[6])<<0) +
+		uint64(in[7])*(uint64(in2[5])<<1) +
+		uint64(in[8])*(uint64(in2[4])<<0)
+	tmp[13] = uint64(in[5])*(uint64(in2[8])<<0) +
+		uint64(in[6])*(uint64(in2[7])<<0) +
+		uint64(in[7])*(uint64(in2[6])<<0) +
+		uint64(in[8])*(uint64(in2[5])<<0)
+	tmp[14] = uint64(in[6])*(uint64(in2[8])<<0) +
+		uint64(in[7])*(uint64(in2[7])<<1) +
+		uint64(in[8])*(uint64(in2[6])<<0)
+	tmp[15] = uint64(in[7])*(uint64(in2[8])<<0) +
+		uint64(in[8])*(uint64(in2[7])<<0)
+	tmp[16] = uint64(in[8]) * (uint64(in2[8]) << 0)
+
+	p256ReduceDegree(out, tmp)
+}
+
+func p256Assign(out, in *[p256Limbs]uint32) {
+	*out = *in
+}
+
+// p256Invert calculates |out| = |in|^{-1}
+//
+// Based on Fermat's Little Theorem:
+//
+//	a^p = a (mod p)
+//	a^{p-1} = 1 (mod p)
+//	a^{p-2} = a^{-1} (mod p)
+func p256Invert(out, in *[p256Limbs]uint32) {
+	var ftmp, ftmp2 [p256Limbs]uint32
+
+	// each e_I will hold |in|^{2^I - 1}
+	var e2, e4, e8, e16, e32, e64 [p256Limbs]uint32
+
+	p256Square(&ftmp, in)     // 2^1
+	p256Mul(&ftmp, in, &ftmp) // 2^2 - 2^0
+	p256Assign(&e2, &ftmp)
+	p256Square(&ftmp, &ftmp)   // 2^3 - 2^1
+	p256Square(&ftmp, &ftmp)   // 2^4 - 2^2
+	p256Mul(&ftmp, &ftmp, &e2) // 2^4 - 2^0
+	p256Assign(&e4, &ftmp)
+	p256Square(&ftmp, &ftmp)   // 2^5 - 2^1
+	p256Square(&ftmp, &ftmp)   // 2^6 - 2^2
+	p256Square(&ftmp, &ftmp)   // 2^7 - 2^3
+	p256Square(&ftmp, &ftmp)   // 2^8 - 2^4
+	p256Mul(&ftmp, &ftmp, &e4) // 2^8 - 2^0
+	p256Assign(&e8, &ftmp)
+	for i := 0; i < 8; i++ {
+		p256Square(&ftmp, &ftmp)
+	} // 2^16 - 2^8
+	p256Mul(&ftmp, &ftmp, &e8) // 2^16 - 2^0
+	p256Assign(&e16, &ftmp)
+	for i := 0; i < 16; i++ {
+		p256Square(&ftmp, &ftmp)
+	} // 2^32 - 2^16
+	p256Mul(&ftmp, &ftmp, &e16) // 2^32 - 2^0
+	p256Assign(&e32, &ftmp)
+	for i := 0; i < 32; i++ {
+		p256Square(&ftmp, &ftmp)
+	} // 2^64 - 2^32
+	p256Assign(&e64, &ftmp)
+	p256Mul(&ftmp, &ftmp, in) // 2^64 - 2^32 + 2^0
+	for i := 0; i < 192; i++ {
+		p256Square(&ftmp, &ftmp)
+	} // 2^256 - 2^224 + 2^192
+
+	p256Mul(&ftmp2, &e64, &e32) // 2^64 - 2^0
+	for i := 0; i < 16; i++ {
+		p256Square(&ftmp2, &ftmp2)
+	} // 2^80 - 2^16
+	p256Mul(&ftmp2, &ftmp2, &e16) // 2^80 - 2^0
+	for i := 0; i < 8; i++ {
+		p256Square(&ftmp2, &ftmp2)
+	} // 2^88 - 2^8
+	p256Mul(&ftmp2, &ftmp2, &e8) // 2^88 - 2^0
+	for i := 0; i < 4; i++ {
+		p256Square(&ftmp2, &ftmp2)
+	} // 2^92 - 2^4
+	p256Mul(&ftmp2, &ftmp2, &e4) // 2^92 - 2^0
+	p256Square(&ftmp2, &ftmp2)   // 2^93 - 2^1
+	p256Square(&ftmp2, &ftmp2)   // 2^94 - 2^2
+	p256Mul(&ftmp2, &ftmp2, &e2) // 2^94 - 2^0
+	p256Square(&ftmp2, &ftmp2)   // 2^95 - 2^1
+	p256Square(&ftmp2, &ftmp2)   // 2^96 - 2^2
+	p256Mul(&ftmp2, &ftmp2, in)  // 2^96 - 3
+
+	p256Mul(out, &ftmp2, &ftmp) // 2^256 - 2^224 + 2^192 + 2^96 - 3
+}
+
+// p256Scalar3 sets out=3*out.
+//
+// On entry: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
+// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
+func p256Scalar3(out *[p256Limbs]uint32) {
+	var carry uint32
+
+	for i := 0; ; i++ {
+		out[i] *= 3
+		out[i] += carry
+		carry = out[i] >> 29
+		out[i] &= bottom29Bits
+
+		i++
+		if i == p256Limbs {
+			break
+		}
+
+		out[i] *= 3
+		out[i] += carry
+		carry = out[i] >> 28
+		out[i] &= bottom28Bits
+	}
+
+	p256ReduceCarry(out, carry)
+}
+
+// p256Scalar4 sets out=4*out.
+//
+// On entry: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
+// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
+func p256Scalar4(out *[p256Limbs]uint32) {
+	var carry, nextCarry uint32
+
+	for i := 0; ; i++ {
+		nextCarry = out[i] >> 27
+		out[i] <<= 2
+		out[i] &= bottom29Bits
+		out[i] += carry
+		carry = nextCarry + (out[i] >> 29)
+		out[i] &= bottom29Bits
+
+		i++
+		if i == p256Limbs {
+			break
+		}
+		nextCarry = out[i] >> 26
+		out[i] <<= 2
+		out[i] &= bottom28Bits
+		out[i] += carry
+		carry = nextCarry + (out[i] >> 28)
+		out[i] &= bottom28Bits
+	}
+
+	p256ReduceCarry(out, carry)
+}
+
+// p256Scalar8 sets out=8*out.
+//
+// On entry: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
+// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29.
+func p256Scalar8(out *[p256Limbs]uint32) {
+	var carry, nextCarry uint32
+
+	for i := 0; ; i++ {
+		nextCarry = out[i] >> 26
+		out[i] <<= 3
+		out[i] &= bottom29Bits
+		out[i] += carry
+		carry = nextCarry + (out[i] >> 29)
+		out[i] &= bottom29Bits
+
+		i++
+		if i == p256Limbs {
+			break
+		}
+		nextCarry = out[i] >> 25
+		out[i] <<= 3
+		out[i] &= bottom28Bits
+		out[i] += carry
+		carry = nextCarry + (out[i] >> 28)
+		out[i] &= bottom28Bits
+	}
+
+	p256ReduceCarry(out, carry)
+}
+
+// p256CopyConditional sets out=in if mask = 0xffffffff in constant time.
+//
+// On entry: mask is either 0 or 0xffffffff.
+func p256CopyConditional(out, in *[p256Limbs]uint32, mask uint32) {
+	for i := 0; i < p256Limbs; i++ {
+		tmp := mask & (in[i] ^ out[i])
+		out[i] ^= tmp
+	}
+}
+
+// p256FromBig sets out = R*in.
+func p256FromBig(out *[p256Limbs]uint32, in *big.Int) {
+	tmp := new(big.Int).Lsh(in, 257)
+	tmp.Mod(tmp, p256Params.P)
+
+	for i := 0; i < p256Limbs; i++ {
+		if bits := tmp.Bits(); len(bits) > 0 {
+			out[i] = uint32(bits[0]) & bottom29Bits
+		} else {
+			out[i] = 0
+		}
+		tmp.Rsh(tmp, 29)
+
+		i++
+		if i == p256Limbs {
+			break
+		}
+
+		if bits := tmp.Bits(); len(bits) > 0 {
+			out[i] = uint32(bits[0]) & bottom28Bits
+		} else {
+			out[i] = 0
+		}
+		tmp.Rsh(tmp, 28)
+	}
+}
+
+// p256ToBig returns a *big.Int containing the value of in.
+func p256ToBig(in *[p256Limbs]uint32) *big.Int {
+	result, tmp := new(big.Int), new(big.Int)
+
+	result.SetInt64(int64(in[p256Limbs-1]))
+	for i := p256Limbs - 2; i >= 0; i-- {
+		if (i & 1) == 0 {
+			result.Lsh(result, 29)
+		} else {
+			result.Lsh(result, 28)
+		}
+		tmp.SetInt64(int64(in[i]))
+		result.Add(result, tmp)
+	}
+
+	result.Mul(result, p256RInverse)
+	result.Mod(result, p256Params.P)
+	return result
+}