(no commit message provided)

crypto/ot/extension/kos/kos.go

@@ -0,0 +1,400 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+// Package kos in an implementation of maliciously secure OT extension protocol defined in "Protocol 9" of
+// [DKLs18](https://eprint.iacr.org/2018/499.pdf). The original protocol was presented in
+// [KOS15](https://eprint.iacr.org/2015/546.pdf).
+package kos
+
+import (
+	"crypto/rand"
+	"crypto/subtle"
+	"encoding/binary"
+	"fmt"
+
+	"golang.org/x/crypto/sha3"
+
+	"github.com/onsonr/hway/crypto/core/curves"
+	"github.com/onsonr/hway/crypto/ot/base/simplest"
+	"github.com/pkg/errors"
+)
+
+const (
+	// below are the "cryptographic parameters", including computational and statistical,
+	// as well as the cOT block size parameters, which depend on these in a pre-defined way.
+
+	// Kappa is the computational security parameter.
+	Kappa = 256
+
+	// KappaBytes is same as Kappa // 8, but avoids cpu division.
+	KappaBytes = Kappa >> 3
+
+	// L is the batch size used in the cOT functionality.
+	L = 2*Kappa + 2*s
+
+	// COtBlockSizeBytes is same as L // 8, but avoids cpu division.
+	COtBlockSizeBytes = L >> 3
+
+	// OtWidth is the number of scalars processed per "slot" of the cOT. by definition of this parameter,
+	// for each of the receiver's choice bits, the sender will provide `OTWidth` scalars.
+	// in turn, both the sender and receiver will obtain `OTWidth` shares _per_ slot / bit of the cOT.
+	// by definition of the cOT, these "vectors of" scalars will add (componentwise) to the sender's original scalars.
+	OtWidth = 2
+
+	s                         = 80 // statistical security parameter.
+	kappaOT                   = Kappa + s
+	lPrime                    = L + kappaOT // length of pseudorandom seed expansion, used within cOT protocol
+	cOtExtendedBlockSizeBytes = lPrime >> 3
+)
+
+type Receiver struct {
+	// OutputAdditiveShares are the ultimate output received. basically just the "pads".
+	OutputAdditiveShares [L][OtWidth]curves.Scalar
+
+	// seedOtResults are the results that this party has received by playing the sender role in a base OT protocol.
+	seedOtResults *simplest.SenderOutput
+
+	// extendedPackedChoices is storage for "choice vector || gamma^{ext}" in a packed format.
+	extendedPackedChoices [cOtExtendedBlockSizeBytes]byte
+	psi                   [lPrime][KappaBytes]byte // transpose of v^0. gets retained between messages
+
+	curve           *curves.Curve
+	uniqueSessionId [simplest.DigestSize]byte // store this between rounds
+}
+
+type Sender struct {
+	// OutputAdditiveShares are the ultimate output received. basically just the "pads".
+	OutputAdditiveShares [L][OtWidth]curves.Scalar
+
+	// seedOtResults are the results that this party has received by playing the receiver role in a base OT protocol.
+	seedOtResults *simplest.ReceiverOutput
+
+	curve *curves.Curve
+}
+
+func binaryFieldMul(A []byte, B []byte) []byte {
+	// multiplies `A` and `B` in the finite field of order 2^256.
+	// The reference is Hankerson, Vanstone and Menezes, Guide to Elliptic Curve Cryptography. https://link.springer.com/book/10.1007/b97644
+	// `A` and `B` are both assumed to be 32-bytes slices. here we view them as little-endian coordinate representations of degree-255 polynomials.
+	// the multiplication takes place modulo the irreducible (over F_2) polynomial f(X) = X^256 + X^10 + X^5 + X^2 + 1. see Table A.1.
+	// the techniques we use are given in section 2.3, Binary field arithmetic.
+	// for the multiplication part, we use Algorithm 2.34, "Right-to-left comb method for polynomial multiplication".
+	// for the reduction part, we use a variant of the idea of Figure 2.9, customized to our setting.
+	const W = 64             // the machine word width, in bits.
+	const t = 4              // the number of words needed to represent a polynomial.
+	c := make([]uint64, 2*t) // result
+	a := make([]uint64, t)
+	b := make([]uint64, t+1)  // will hold a copy of b, shifted by some amount
+	for i := 0; i < 32; i++ { // "condense" `A` and `B` into word-vectors, instead of byte-vectors
+		a[i>>3] |= uint64(A[i]) << (i & 0x07 << 3)
+		b[i>>3] |= uint64(B[i]) << (i & 0x07 << 3)
+	}
+	for k := 0; k < W; k++ {
+		for j := 0; j < t; j++ {
+			// conditionally add a copy of (the appropriately shifted) B to C, depending on the appropriate bit of A
+			// do this in constant-time; i.e., independent of A.
+			// technically, in each time we call this, the right-hand argument is a public datum,
+			// so we could arrange things so that it's _not_ constant-time, but the variable-time stuff always depends on something public.
+			// better to just be safe here though and make it constant-time anyway.
+			mask := -(a[j] >> k & 0x01) // if A[j] >> k & 0x01 == 1 then 0xFFFFFFFFFFFFFFFF else 0x0000000000000000
+			for i := 0; i < t+1; i++ {
+				c[j+i] ^= b[i] & mask // conditionally add B to C{j}
+			}
+		}
+		for i := t; i > 0; i-- {
+			b[i] = b[i]<<1 | b[i-1]>>63
+		}
+		b[0] <<= 1
+	}
+	// multiplication complete; begin reduction.
+	// things become actually somewhat simpler in our case, because the degree of the polynomial is a multiple of the word size
+	// the technique to come up with the numbers below comes essentially from going through the exact same process as on page 54,
+	// but with the polynomial f(X) = X^256 + X^10 + X^5 + X^2 + 1 above instead, and with parameters m = 256, W = 64, t = 4.
+	// the idea is exactly as described informally on that page, even though this particular polynomial isn't explicitly treated.
+	for i := 2*t - 1; i >= t; i-- {
+		c[i-4] ^= c[i] << 10
+		c[i-3] ^= c[i] >> 54
+		c[i-4] ^= c[i] << 5
+		c[i-3] ^= c[i] >> 59
+		c[i-4] ^= c[i] << 2
+		c[i-3] ^= c[i] >> 62
+		c[i-4] ^= c[i]
+	}
+	C := make([]byte, 32)
+	for i := 0; i < 32; i++ {
+		C[i] = byte(c[i>>3] >> (i & 0x07 << 3)) // truncate word to byte
+	}
+	return C
+}
+
+// NewCOtReceiver creates a `Receiver` instance, ready for use as the receiver in the KOS cOT protocol
+// you must supply the output gotten by running an instance of seed OT as the _sender_ (note the reversal of roles)
+func NewCOtReceiver(seedOTResults *simplest.SenderOutput, curve *curves.Curve) *Receiver {
+	return &Receiver{
+		seedOtResults: seedOTResults,
+		curve:         curve,
+	}
+}
+
+// NewCOtSender creates a `Sender` instance, ready for use as the sender in the KOS cOT protocol.
+// you must supply the output gotten by running an instance of seed OT as the _receiver_ (note the reversal of roles)
+func NewCOtSender(seedOTResults *simplest.ReceiverOutput, curve *curves.Curve) *Sender {
+	return &Sender{
+		seedOtResults: seedOTResults,
+		curve:         curve,
+	}
+}
+
+// Round1Output is Bob's first message to Alice during cOT extension;
+// these outputs are described in step 4) of Protocol 9) https://eprint.iacr.org/2018/499.pdf
+type Round1Output struct {
+	U      [Kappa][cOtExtendedBlockSizeBytes]byte
+	WPrime [simplest.DigestSize]byte
+	VPrime [simplest.DigestSize]byte
+}
+
+// Round2Output this is Alice's response to Bob in cOT extension;
+// the values `tau` are specified in Alice's step 6) of Protocol 9) https://eprint.iacr.org/2018/499.pdf
+type Round2Output struct {
+	Tau [L][OtWidth]curves.Scalar
+}
+
+// convertBitToBitmask converts a "bit"---i.e., a `byte` which is _assumed to be_ either 0 or 1---into a bitmask,
+// namely, it outputs 0x00 if `bit == 0` and 0xFF if `bit == 1`.
+func convertBitToBitmask(bit byte) byte {
+	return ^(bit - 0x01)
+}
+
+// the below code takes as input a `kappa` by `lPrime` _boolean_ matrix, whose rows are actually "compacted" as bytes.
+// so in actuality, it's a `kappa` by `lPrime >> 3 == cOtExtendedBlockSizeBytes` matrix of _bytes_.
+// its output is the same boolean matrix, but transposed, so it has dimensions `lPrime` by `kappa`.
+// but likewise we want to compact the output matrix as bytes, again _row-wise_.
+// so the output matrix's dimensions are lPrime by `kappa >> 3 == KappaBytes`, as a _byte_ matrix.
+// the technique is fairly straightforward, but involves some bitwise operations.
+func transposeBooleanMatrix(input [Kappa][cOtExtendedBlockSizeBytes]byte) [lPrime][KappaBytes]byte {
+	output := [lPrime][KappaBytes]byte{}
+	for rowByte := 0; rowByte < KappaBytes; rowByte++ {
+		for rowBitWithinByte := 0; rowBitWithinByte < 8; rowBitWithinByte++ {
+			for columnByte := 0; columnByte < cOtExtendedBlockSizeBytes; columnByte++ {
+				for columnBitWithinByte := 0; columnBitWithinByte < 8; columnBitWithinByte++ {
+					rowBit := rowByte<<3 + rowBitWithinByte
+					columnBit := columnByte<<3 + columnBitWithinByte
+					// the below code grabs the _bit_ at input[rowBit][columnBit], if input were a viewed as a boolean matrix.
+					// in reality, it's packed into bytes, so instead we have to grab the `columnBitWithinByte`th bit within the appropriate byte.
+					bitAtInputRowBitColumnBit := input[rowBit][columnByte] >> columnBitWithinByte & 0x01
+					// now that we've grabbed the bit we care about, we need to write it into the appropriate place in the output matrix
+					// the output matrix is also packed---but in the "opposite" way (the short dimension is packed, instead of the long one)
+					// what we're going to do is take the _bit_ we got, and shift it by rowBitWithinByte.
+					// this has the effect of preparing for us to write it into the appropriate place into the output matrix.
+					shiftedBit := bitAtInputRowBitColumnBit << rowBitWithinByte
+					output[columnBit][rowByte] |= shiftedBit
+				}
+			}
+		}
+	}
+	return output
+}
+
+// Round1Initialize initializes the OT Extension. see page 17, steps 1), 2), 3) and 4) of Protocol 9 of the paper.
+// The input `choice` vector is "packed" (i.e., the underlying abstract vector of `L` bits is represented as a `cOTBlockSizeBytes` bytes).
+func (receiver *Receiver) Round1Initialize(uniqueSessionId [simplest.DigestSize]byte, choice [COtBlockSizeBytes]byte) (*Round1Output, error) {
+	// salt the transcript with the OT-extension session ID
+	receiver.uniqueSessionId = uniqueSessionId
+
+	// write the input choice vector into our local data. Since `otBatchSize` is the number of bits, we are working with
+	// bytes, we first need to calculate how many bytes are needed to store that many bits.
+	copy(receiver.extendedPackedChoices[0:COtBlockSizeBytes], choice[:])
+
+	// Fill the rest of the extended choice vector with random values. These random values correspond to `gamma^{ext}`.
+	if _, err := rand.Read(receiver.extendedPackedChoices[COtBlockSizeBytes:]); err != nil {
+		return nil, errors.Wrap(err, "sampling random coins for gamma^{ext}")
+	}
+
+	v := [2][Kappa][cOtExtendedBlockSizeBytes]byte{} // kappa * L array of _bits_, in "dense" form. contains _both_ v_0 and v_1.
+	result := &Round1Output{}
+
+	hash := sha3.New256() // basically this will contain a hash of the matrix U.
+	for i := 0; i < Kappa; i++ {
+		for j := 0; j < 2; j++ {
+			shake := sha3.NewCShake256(uniqueSessionId[:], []byte("Coinbase_DKLs_cOT"))
+			if _, err := shake.Write(receiver.seedOtResults.OneTimePadEncryptionKeys[i][j][:]); err != nil {
+				return nil, errors.Wrap(err, "writing seed OT into shake in cOT receiver round 1")
+			}
+			// this is the core pseudorandom expansion of the secret OT input seeds s_i^0 and s_i^1
+			// see Extension, 2), in Protocol 9, page 17 of DKLs https://eprint.iacr.org/2018/499.pdf
+			// use the uniqueSessionId as the "domain separator", and the _secret_ seed rho as the input!
+			if _, err := shake.Read(v[j][i][:]); err != nil {
+				return nil, errors.Wrap(err, "reading from shake to compute v^j in cOT receiver round 1")
+			}
+		}
+		for j := 0; j < cOtExtendedBlockSizeBytes; j++ {
+			result.U[i][j] = v[0][i][j] ^ v[1][i][j] ^ receiver.extendedPackedChoices[j]
+			// U := v_i^0 ^ v_i^1 ^ w. note: in step 4) of Prot. 9, i think `w` should be bolded?
+		}
+		if _, err := hash.Write(result.U[i][:]); err != nil {
+			return nil, err
+		}
+	}
+	receiver.psi = transposeBooleanMatrix(v[0])
+	digest := hash.Sum(nil) // go ahead and record this, so that we only have to hash the big matrix U once.
+	for j := 0; j < lPrime; j++ {
+		hash = sha3.New256()
+		jBytes := [2]byte{}
+		binary.BigEndian.PutUint16(jBytes[:], uint16(j))
+		if _, err := hash.Write(jBytes[:]); err != nil { // write j into shake
+			return nil, errors.Wrap(err, "writing nonce into hash while computing chiJ in cOT receiver round 1")
+		}
+		if _, err := hash.Write(digest); err != nil {
+			return nil, errors.Wrap(err, "writing input digest into hash while computing chiJ in cOT receiver round 1")
+		}
+		chiJ := hash.Sum(nil)
+		wJ := convertBitToBitmask(simplest.ExtractBitFromByteVector(receiver.extendedPackedChoices[:], j)) // extract j^th bit from vector of bytes w.
+		psiJTimesChiJ := binaryFieldMul(receiver.psi[j][:], chiJ)
+		for k := 0; k < KappaBytes; k++ {
+			result.WPrime[k] ^= wJ & chiJ[k]
+			result.VPrime[k] ^= psiJTimesChiJ[k]
+		}
+	}
+	return result, nil
+}
+
+// Round2Transfer computes the OT sender ("Alice")'s part of cOT; this includes steps 2) 5) and 6) of Protocol 9
+// `input` is the sender's main vector of inputs alpha_j; these are the things tA_j and tB_j will add to if w_j == 1.
+// `message` contains the message the receiver ("Bob") sent us. this itself contains Bob's values WPrime, VPrime, and U
+// the output is just the values `Tau` we send back to Bob.
+// as a side effect of this function, our (i.e., the sender's) outputs tA_j from the cOT will be populated.
+func (sender *Sender) Round2Transfer(uniqueSessionId [simplest.DigestSize]byte, input [L][OtWidth]curves.Scalar, round1Output *Round1Output) (*Round2Output, error) {
+	z := [Kappa][cOtExtendedBlockSizeBytes]byte{}
+	hash := sha3.New256() // basically this will contain a hash of the matrix U.
+
+	for i := 0; i < Kappa; i++ {
+		v := make([]byte, cOtExtendedBlockSizeBytes) // will contain alice's expanded PRG output for the row i, namely v_i^{\Nabla_i}.
+		shake := sha3.NewCShake256(uniqueSessionId[:], []byte("Coinbase_DKLs_cOT"))
+		if _, err := shake.Write(sender.seedOtResults.OneTimePadDecryptionKey[i][:]); err != nil {
+			return nil, errors.Wrap(err, "sender writing seed OT decryption key into shake in sender round 2 transfer")
+		}
+		if _, err := shake.Read(v); err != nil {
+			return nil, errors.Wrap(err, "reading from shake into row `v` in sender round 2 transfer")
+		}
+		// use the idExt as the domain separator, and the _secret_ seed rho as the input!
+		mask := convertBitToBitmask(byte(sender.seedOtResults.RandomChoiceBits[i]))
+		for j := 0; j < cOtExtendedBlockSizeBytes; j++ {
+			z[i][j] = v[j] ^ mask&round1Output.U[i][j]
+		}
+		if _, err := hash.Write(round1Output.U[i][:]); err != nil {
+			return nil, errors.Wrap(err, "writing matrix U to hash in cOT sender round 2 transfer")
+		}
+	}
+	zeta := transposeBooleanMatrix(z)
+	digest := hash.Sum(nil) // go ahead and record this, so that we only have to hash the big matrix U once.
+	zPrime := [simplest.DigestSize]byte{}
+	for j := 0; j < lPrime; j++ {
+		hash = sha3.New256()
+		jBytes := [2]byte{}
+		binary.BigEndian.PutUint16(jBytes[:], uint16(j))
+		if _, err := hash.Write(jBytes[:]); err != nil { // write j into hash
+			return nil, errors.Wrap(err, "writing nonce into hash while computing chiJ in cOT sender round 2 transfer")
+		}
+		if _, err := hash.Write(digest); err != nil {
+			return nil, errors.Wrap(err, "writing input digest into hash while computing chiJ in cOT sender round 2 transfer")
+		}
+		chiJ := hash.Sum(nil)
+		zetaJTimesChiJ := binaryFieldMul(zeta[j][:], chiJ)
+		for k := 0; k < KappaBytes; k++ {
+			zPrime[k] ^= zetaJTimesChiJ[k]
+		}
+	}
+	rhs := [simplest.DigestSize]byte{}
+	nablaTimesWPrime := binaryFieldMul(sender.seedOtResults.PackedRandomChoiceBits, round1Output.WPrime[:])
+	for i := 0; i < KappaBytes; i++ {
+		rhs[i] = round1Output.VPrime[i] ^ nablaTimesWPrime[i]
+	}
+	if subtle.ConstantTimeCompare(zPrime[:], rhs[:]) != 1 {
+		return nil, fmt.Errorf("cOT receiver's consistency check failed; this may be an attempted attack; do NOT re-run the protocol")
+	}
+	result := &Round2Output{}
+	for j := 0; j < L; j++ {
+		column := make([]byte, OtWidth*simplest.DigestSize)
+		shake := sha3.NewCShake256(uniqueSessionId[:], []byte("Coinbase_DKLs_cOT"))
+		jBytes := [2]byte{}
+		binary.BigEndian.PutUint16(jBytes[:], uint16(j))
+		if _, err := shake.Write(jBytes[:]); err != nil { // write j into hash
+			return nil, errors.Wrap(err, "writing nonce into shake while computing OutputAdditiveShares in cOT sender round 2 transfer")
+		}
+		if _, err := shake.Write(zeta[j][:]); err != nil {
+			return nil, errors.Wrap(err, "writing input zeta_j into shake while computing OutputAdditiveShares in cOT sender round 2 transfer")
+		}
+		if _, err := shake.Read(column[:]); err != nil {
+			return nil, errors.Wrap(err, "reading shake into column while computing OutputAdditiveShares in cOT sender round 2 transfer")
+		}
+		var err error
+		for k := 0; k < OtWidth; k++ {
+			sender.OutputAdditiveShares[j][k], err = sender.curve.Scalar.SetBytes(column[k*simplest.DigestSize : (k+1)*simplest.DigestSize])
+			if err != nil {
+				return nil, errors.Wrap(err, "OutputAdditiveShares scalar from bytes")
+			}
+		}
+		for i := 0; i < KappaBytes; i++ {
+			zeta[j][i] ^= sender.seedOtResults.PackedRandomChoiceBits[i] // note: overwrites zeta_j. just using it as a place to store
+		}
+		column = make([]byte, OtWidth*simplest.DigestSize)
+		shake = sha3.NewCShake256(uniqueSessionId[:], []byte("Coinbase_DKLs_cOT"))
+		binary.BigEndian.PutUint16(jBytes[:], uint16(j))
+		if _, err := shake.Write(jBytes[:]); err != nil { // write j into hash
+			return nil, errors.Wrap(err, "writing nonce into shake while computing tau in cOT sender round 2 transfer")
+		}
+		if _, err := shake.Write(zeta[j][:]); err != nil {
+			return nil, errors.Wrap(err, "writing input zeta_j into shake while computing tau in cOT sender round 2 transfer")
+		}
+		if _, err := shake.Read(column[:]); err != nil {
+			return nil, errors.Wrap(err, "reading shake into column while computing tau in cOT sender round 2 transfer")
+		}
+		for k := 0; k < OtWidth; k++ {
+			result.Tau[j][k], err = sender.curve.Scalar.SetBytes(column[k*simplest.DigestSize : (k+1)*simplest.DigestSize])
+			if err != nil {
+				return nil, errors.Wrap(err, "scalar Tau from bytes")
+			}
+			result.Tau[j][k] = result.Tau[j][k].Sub(sender.OutputAdditiveShares[j][k])
+			result.Tau[j][k] = result.Tau[j][k].Add(input[j][k])
+		}
+	}
+	return result, nil
+}
+
+// Round3Transfer does the receiver (Bob)'s step 7) of Protocol 9, namely the computation of the outputs tB.
+func (receiver *Receiver) Round3Transfer(round2Output *Round2Output) error {
+	for j := 0; j < L; j++ {
+		column := make([]byte, OtWidth*simplest.DigestSize)
+		shake := sha3.NewCShake256(receiver.uniqueSessionId[:], []byte("Coinbase_DKLs_cOT"))
+		jBytes := [2]byte{}
+		binary.BigEndian.PutUint16(jBytes[:], uint16(j))
+		if _, err := shake.Write(jBytes[:]); err != nil { // write j into hash
+			return errors.Wrap(err, "writing nonce into shake while computing tB in cOT receiver round 3 transfer")
+		}
+		if _, err := shake.Write(receiver.psi[j][:]); err != nil {
+			return errors.Wrap(err, "writing input zeta_j into shake while computing tB in cOT receiver round 3 transfer")
+		}
+		if _, err := shake.Read(column[:]); err != nil {
+			return errors.Wrap(err, "reading shake into column while computing tB in cOT receiver round 3 transfer")
+		}
+		bit := int(simplest.ExtractBitFromByteVector(receiver.extendedPackedChoices[:], j))
+		var err error
+		for k := 0; k < OtWidth; k++ {
+			receiver.OutputAdditiveShares[j][k], err = receiver.curve.Scalar.SetBytes(column[k*simplest.DigestSize : (k+1)*simplest.DigestSize])
+			if err != nil {
+				return errors.Wrap(err, "scalar output additive shares from bytes")
+			}
+			receiver.OutputAdditiveShares[j][k] = receiver.OutputAdditiveShares[j][k].Neg()
+			wj0 := receiver.OutputAdditiveShares[j][k].Bytes()
+			wj1 := receiver.OutputAdditiveShares[j][k].Add(round2Output.Tau[j][k]).Bytes()
+			subtle.ConstantTimeCopy(bit, wj0, wj1)
+			if receiver.OutputAdditiveShares[j][k], err = receiver.curve.Scalar.SetBytes(wj0); err != nil {
+				return errors.Wrap(err, "scalar output additive shares from bytes")
+			}
+		}
+	}
+	return nil
+}

crypto/ot/extension/kos/kos_test.go

@@ -0,0 +1,141 @@
+package kos
+
+import (
+	"crypto/rand"
+	"testing"
+
+	"github.com/stretchr/testify/require"
+
+	"github.com/onsonr/hway/crypto/core/curves"
+	"github.com/onsonr/hway/crypto/ot/base/simplest"
+	"github.com/onsonr/hway/crypto/ot/ottest"
+)
+
+func TestBinaryMult(t *testing.T) {
+	for i := 0; i < 100; i++ {
+		temp := make([]byte, 32)
+		_, err := rand.Read(temp)
+		require.NoError(t, err)
+		expected := make([]byte, 32)
+		copy(expected, temp)
+		// this test is based on Fermat's little theorem.
+		// the multiplicative group of units of a finite field has order |F| - 1
+		// (in fact, it's necessarily cyclic; see e.g. https://math.stackexchange.com/a/59911, but this test doesn't rely on that fact)
+		// thus raising any element to the |F|th power should yield that element itself.
+		// this is a good test because it relies on subtle facts about the field structure, and will fail if anything goes wrong.
+		for j := 0; j < 256; j++ {
+			expected = binaryFieldMul(expected, expected)
+		}
+		require.Equal(t, temp, expected)
+	}
+}
+
+func TestCOTExtension(t *testing.T) {
+	curveInstances := []*curves.Curve{
+		curves.K256(),
+		curves.P256(),
+	}
+	for _, curve := range curveInstances {
+		uniqueSessionId := [simplest.DigestSize]byte{}
+		_, err := rand.Read(uniqueSessionId[:])
+		require.NoError(t, err)
+		baseOtSenderOutput, baseOtReceiverOutput, err := ottest.RunSimplestOT(curve, Kappa, uniqueSessionId)
+		require.NoError(t, err)
+		for i := 0; i < Kappa; i++ {
+			require.Equal(t, baseOtReceiverOutput.OneTimePadDecryptionKey[i], baseOtSenderOutput.OneTimePadEncryptionKeys[i][baseOtReceiverOutput.RandomChoiceBits[i]])
+		}
+
+		sender := NewCOtSender(baseOtReceiverOutput, curve)
+		receiver := NewCOtReceiver(baseOtSenderOutput, curve)
+		choice := [COtBlockSizeBytes]byte{} // receiver's input, namely choice vector. just random
+		_, err = rand.Read(choice[:])
+		require.NoError(t, err)
+		input := [L][OtWidth]curves.Scalar{} // sender's input, namely integer "sums" in case w_j == 1.
+		for i := 0; i < L; i++ {
+			for j := 0; j < OtWidth; j++ {
+				input[i][j] = curve.Scalar.Random(rand.Reader)
+				require.NoError(t, err)
+			}
+		}
+		firstMessage, err := receiver.Round1Initialize(uniqueSessionId, choice)
+		require.NoError(t, err)
+		responseTau, err := sender.Round2Transfer(uniqueSessionId, input, firstMessage)
+		require.NoError(t, err)
+		err = receiver.Round3Transfer(responseTau)
+		require.NoError(t, err)
+		for j := 0; j < L; j++ {
+			bit := simplest.ExtractBitFromByteVector(choice[:], j) == 1
+			for k := 0; k < OtWidth; k++ {
+				temp := sender.OutputAdditiveShares[j][k].Add(receiver.OutputAdditiveShares[j][k])
+				if bit {
+					require.Equal(t, temp, input[j][k])
+				} else {
+					require.Equal(t, temp, curve.Scalar.Zero())
+				}
+			}
+		}
+	}
+}
+
+func TestCOTExtensionStreaming(t *testing.T) {
+	curve := curves.K256()
+	hashKeySeed := [simplest.DigestSize]byte{}
+	_, err := rand.Read(hashKeySeed[:])
+	require.NoError(t, err)
+	baseOtReceiver, err := simplest.NewReceiver(curve, Kappa, hashKeySeed)
+	require.NoError(t, err)
+	sender := NewCOtSender(baseOtReceiver.Output, curve)
+	baseOtSender, err := simplest.NewSender(curve, Kappa, hashKeySeed)
+	require.NoError(t, err)
+	receiver := NewCOtReceiver(baseOtSender.Output, curve)
+
+	// first run the seed OT
+	senderPipe, receiverPipe := simplest.NewPipeWrappers()
+	errorsChannel := make(chan error, 2)
+	go func() {
+		errorsChannel <- simplest.SenderStreamOTRun(baseOtSender, senderPipe)
+	}()
+	go func() {
+		errorsChannel <- simplest.ReceiverStreamOTRun(baseOtReceiver, receiverPipe)
+	}()
+	for i := 0; i < 2; i++ {
+		require.Nil(t, <-errorsChannel)
+	}
+	for i := 0; i < Kappa; i++ {
+		require.Equal(t, baseOtReceiver.Output.OneTimePadDecryptionKey[i], baseOtSender.Output.OneTimePadEncryptionKeys[i][baseOtReceiver.Output.RandomChoiceBits[i]])
+	}
+
+	// begin test of cOT extension. first populate both parties' inputs randomly
+	choice := [COtBlockSizeBytes]byte{} // receiver's input, namely choice vector. just random
+	_, err = rand.Read(choice[:])
+	require.NoError(t, err)
+	input := [L][OtWidth]curves.Scalar{} // sender's input, namely integer "sums" in case w_j == 1. random for the test
+	for i := 0; i < L; i++ {
+		for j := 0; j < OtWidth; j++ {
+			input[i][j] = curve.Scalar.Random(rand.Reader)
+			require.NoError(t, err)
+		}
+	}
+
+	// now actually run it, stream-wise
+	go func() {
+		errorsChannel <- SenderStreamCOtRun(sender, hashKeySeed, input, receiverPipe)
+	}()
+	go func() {
+		errorsChannel <- ReceiverStreamCOtRun(receiver, hashKeySeed, choice, senderPipe)
+	}()
+	for i := 0; i < 2; i++ {
+		require.Nil(t, <-errorsChannel)
+	}
+	for j := 0; j < L; j++ {
+		bit := simplest.ExtractBitFromByteVector(choice[:], j) == 1
+		for k := 0; k < OtWidth; k++ {
+			temp := sender.OutputAdditiveShares[j][k].Add(receiver.OutputAdditiveShares[j][k])
+			if bit {
+				require.Equal(t, temp, input[j][k])
+			} else {
+				require.Equal(t, temp, curve.Scalar.Zero())
+			}
+		}
+	}
+}

crypto/ot/extension/kos/stream.go

@@ -0,0 +1,57 @@
+package kos
+
+import (
+	"encoding/gob"
+	"io"
+
+	"github.com/pkg/errors"
+
+	"github.com/onsonr/hway/crypto/core/curves"
+	"github.com/onsonr/hway/crypto/ot/base/simplest"
+)
+
+// ReceiverStreamCOtRun exposes an end-to-end "streaming" version of the cOT process for the receiver.
+// this is similar to what we're also doing in the base OT side. the user only passes an arbitrary `ReadWriter` here,
+// together with the relevant inputs (namely a choice vector); this method handles all parts of the process,
+// including both encoding / decoding and writing to / reading from the stream.
+func ReceiverStreamCOtRun(receiver *Receiver, hashKeySeed [simplest.DigestSize]byte, choice [COtBlockSizeBytes]byte, rw io.ReadWriter) error {
+	enc := gob.NewEncoder(rw)
+	dec := gob.NewDecoder(rw)
+
+	firstMessage, err := receiver.Round1Initialize(hashKeySeed, choice)
+	if err != nil {
+		return errors.Wrap(err, "computing first message in receiver stream cOT")
+	}
+	if err = enc.Encode(firstMessage); err != nil {
+		return errors.Wrap(err, "encoding first message in receiver stream cOT")
+	}
+	responseTau := &Round2Output{}
+	if err = dec.Decode(responseTau); err != nil {
+		return errors.Wrap(err, "decoding responseTau in receiver stream OT")
+	}
+	if err = receiver.Round3Transfer(responseTau); err != nil {
+		return errors.Wrap(err, "error during round 3 in receiver stream OT")
+	}
+	return nil
+}
+
+// SenderStreamCOtRun exposes the end-to-end "streaming" version of cOT for the sender.
+// the sender should pass an arbitrary ReadWriter together with their input; this will handle the whole process,
+// including all component methods, plus reading to and writing from the network.
+func SenderStreamCOtRun(sender *Sender, hashKeySeed [simplest.DigestSize]byte, input [L][OtWidth]curves.Scalar, rw io.ReadWriter) error {
+	enc := gob.NewEncoder(rw)
+	dec := gob.NewDecoder(rw)
+
+	firstMessage := &Round1Output{}
+	if err := dec.Decode(firstMessage); err != nil {
+		return errors.Wrap(err, "decoding first message in sender stream cOT")
+	}
+	responseTau, err := sender.Round2Transfer(hashKeySeed, input, firstMessage)
+	if err != nil {
+		return errors.Wrap(err, "error in round 2 in sender stream cOT")
+	}
+	if err = enc.Encode(responseTau); err != nil {
+		return errors.Wrap(err, "encoding responseTau in sender stream cOT")
+	}
+	return nil
+}