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implement Uint256 and modular add #23

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implement Uint256 and modular add #23

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33 changes: 33 additions & 0 deletions pkg/bits/bits.mpcl
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Original file line number Diff line number Diff line change
@@ -0,0 +1,33 @@
// -*- go -*-

package bits

// Add64 returns the sum with carry of x, y and carry: sum = x + y + carry.
// The carry input must be 0 or 1; otherwise the behavior is undefined.
// The carryOut output is guaranteed to be 0 or 1.
//
// This function's execution time does not depend on the inputs.
func Add64(x, y, carry uint64) (sum, carryOut uint64) {
sum = x + y + carry
// The sum will overflow if both top bits are set (x & y) or if one of them
// is (x | y), and a carry from the lower place happened. If such a carry
// happens, the top bit will be 1 + 0 + 1 = 0 (&^ sum).
carryOut = ((x & y) | ((x | y) &^ sum)) >> 63
return
}


// Sub64 returns the difference of x, y and borrow: diff = x - y - borrow.
// The borrow input must be 0 or 1; otherwise the behavior is undefined.
// The borrowOut output is guaranteed to be 0 or 1.
//
// This function's execution time does not depend on the inputs.
func Sub64(x, y, borrow uint64) (diff, borrowOut uint64) {
diff = x - y - borrow
// borrowOut = ((^x & y) | (^(x ^ y) & diff)) >> 63

temp1 := 0xffffffffffffffff ^ x
temp2 := 0xffffffffffffffff ^ (x ^ y)
borrowOut = ((temp1 & y) | (temp2 & diff)) >> 63
return
}
27 changes: 27 additions & 0 deletions pkg/encoding/binary/getput.mpcl
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Expand Up @@ -53,3 +53,30 @@ func PutUint32(d []byte, offset int, v uint32) []byte {
func GetUint32LSB(d []byte) uint32 {
return uint32(d[0]) | uint32(d[1])<<8 | uint32(d[2])<<16 | uint32(d[3])<<24
}


// GetUint64 gets a MSB-encoded uint64 value from the argument buffer.
func GetUint64(d []byte) uint64 {
return uint64(d[0])<<56 | uint64(d[1])<<48 | uint64(d[2])<<40 | uint64(d[3])<<32 |
uint64(d[4])<<24 | uint64(d[5])<<16 | uint64(d[6])<<8 | uint64(d[7])
}

// PutUint64 puts the uint64 value v to the buffer d starting from the
// offset offset in MSB-order.
func PutUint64(d []byte, offset int, v uint64) []byte {
d[offset+0] = byte(v >> 56)
d[offset+1] = byte(v >> 48)
d[offset+2] = byte(v >> 40)
d[offset+3] = byte(v >> 32)
d[offset+4] = byte(v >> 24)
d[offset+5] = byte(v >> 16)
d[offset+6] = byte(v >> 8)
d[offset+7] = byte(v)
return d
}

// GetUint64LSB gets a LSB-encoded uint64 value from the argument buffer.
func GetUint64LSB(d []byte) uint64 {
return uint64(d[0]) | uint64(d[1])<<8 | uint64(d[2])<<16 | uint64(d[3])<<24 |
uint64(d[4])<<32 | uint64(d[5])<<40 | uint64(d[6])<<48 | uint64(d[7])<<56
}
160 changes: 160 additions & 0 deletions pkg/math/uint256.mpcl
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@@ -0,0 +1,160 @@
// -*- go -*-

package math

import (
"bits"
"encoding/binary"
)

// Uint256 is represented as an array of 4 uint64, in little-endian order,
// so that Int[3] is the most significant, and Int[0] is the least significant
type Uint256 [4]uint64

func NewUint256(in [32]byte) Uint256 {
var z Uint256
z[3] = binary.GetUint64(in[0:8])
z[2] = binary.GetUint64(in[8:16])
z[1] = binary.GetUint64(in[16:24])
z[0] = binary.GetUint64(in[24:32])

return z
}

// Clear sets z to 0
func NewZero() Uint256 {
var z Uint256
z[3] = 0
z[2] = 0
z[1] = 0
z[0] = 0

return z
}

// Clone creates a new Int identical to z
func Clone(z Uint256) Uint256 {
var c Uint256
c[0] = z[0]
c[1] = z[1]
c[2] = z[2]
c[3] = z[3]

return c
}

// IsZero returns true if z == 0
func IsZero(z Uint256) bool {
return (z[0] | z[1] | z[2] | z[3]) == 0
}

// IsEqual returns true if z == y
func IsEqual(x, y Uint256) bool {
return (x[0] == y[0] &&
x[1] == y[1] &&
x[2] == y[2] &&
x[3] == y[3])
}

// AddOverflow returns the sum x+y, and returns z and whether overflow occurred
func AddOverflow(x Uint256, y Uint256) (Uint256, bool) {
var z Uint256
var carry uint64
z[0], carry = bits.Add64(x[0], y[0], 0)
z[1], carry = bits.Add64(x[1], y[1], carry)
z[2], carry = bits.Add64(x[2], y[2], carry)
z[3], carry = bits.Add64(x[3], y[3], carry)
return z, carry != 0
}

// SubBurrow returns the difference of x, y.
func SubBurrow(x Uint256, y Uint256, borrow bool) Uint256 {
var z Uint256
var carry uint64
if borrow {
// carry = 1
}
z[0], carry = bits.Sub64(x[0], y[0], carry)
z[1], carry = bits.Sub64(x[1], y[1], carry)
z[2], carry = bits.Sub64(x[2], y[2], carry)
z[3], carry = bits.Sub64(x[3], y[3], carry)

return z
}

// LessThan returns true if z < x
func LessThan(x Uint256, y Uint256) bool {
if x[3] < y[3] {
return true
} else if x[3] > y[3] {
return false
} else {
if x[2] < y[2] {
return true
} else if x[2] > y[2] {
return false
} else {
if x[1] < y[1] {
return true
} else if x[1] > y[1] {
return false
} else {
if x[0] < y[0] {
return true
} else if x[0] > y[0] {
return false
} else {
return false
}
}
}
}
}

// AddMod returns the sum ( x+y ) mod m.

// Case 1
// 0x29d9048e6f8e7d0b8ae00c99180aa1f973d068b7d186c3b9776353d442127322
// + 0x57675a30368f86be2cd6b21556fc2e482758b33c3e68a8c9021abf8fb00e487f
// = 0x81405ebea61e03c9b7b6beae6f06d0419b291bf40fef6c82797e1363f220bba1
//
// 0x81405ebea61e03c9b7b6beae6f06d0419b291bf40fef6c82797e1363f220bba1
// % 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 (q)
// = 0x81405ebea61e03c9b7b6beae6f06d0419b291bf40fef6c82797e1363f220bba1

// Case 2
// 0x538c7f96b164bf1b97bb9f4bb472e89f5b1484f25209c9d9343e92ba09dd9d52
// + 0xdfd79b4d76429b617a0c9f9f0d3ba55b0cc0d6144c888535841acbe0709b0758
// = 0x133641ae427a75a7d11c83eeac1ae8dfa67d55b069e924f0eb8595e9a7a78a4aa (overflow)
//
// 0x133641ae427a75a7d11c83eeac1ae8dfa67d55b069e924f0eb8595e9a7a78a4aa
// % 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 (q)
// = 0x33641ae427a75a7d11c83eeac1ae8dfbad267e1fef49aed2f887000daa426369

// Case 3
// 0x71e796a2dc2dc25a5b74b2e129705e273f05c92326828e2b056e3817658e1061
// + 0x498947fdf344410ed4c116023fa8e3576b6fed27ff8974bac0cafd9ad05692b1
// = 0xbb70dea0cf7203693035c8e36919417eaa75b64b260c02e5c63935b235e4a312
//
// 0xbb70dea0cf7203693035c8e36919417eaa75b64b260c02e5c63935b235e4a312
// % 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 (q)
// = 0xbb70dea0cf7203693035c8e36919417eaa75b64b260c02e5c63935b235e4a312

func AddMod(x Uint256, y Uint256, m Uint256) Uint256 {
z, overflow := AddOverflow(x, y)

if overflow || !LessThan(z, m) {
return SubBurrow(z, m, overflow)
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@markkurossi

Do you have any better ideas for calculating modular addition for MPC, especially for generating the Garble Circuit? You may not like this line of code, as it only works for large prime numbers (modulus). For small modulus, it may not return the correct value.

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The MPCL language does not have fixed integer sizes but you can specify any bit size from 1-n bits. So it is possible to define variables, for example, of type uint256 directly in the code:

package main

type Garbler struct {
	val uint256
	mod uint256
}

func main(g Garbler, e uint256) uint {
	sum := g.val + e
	if sum > g.mod {
		sum -= g.mod
	}
	return sum
}

The compiler uses half and full adders and subtractors to create circuits for the specified parameter size. The example above computes modular addition assuming that g.val and e are smaller than g.mod. This produces circuit of size:

circuit: #gates=4341 (XOR=2549 XNOR=768 AND=1023 OR=0 INV=1 xor=3317 !xor=1024 levels=771 width=256) #w=5109

The same example can be converted to support input sizes bigger than g.mod by using the % operator:

package main

type Garbler struct {
	val uint256
	mod uint256
}

func main(g Garbler, e uint256) uint {
	return (g.val + e) % g.mod
}

However, this produces significantly bigger circuit:

circuit: #gates=525823 (XOR=394238 XNOR=0 AND=131583 OR=1 INV=1 xor=394238 !xor=131585 levels=197888 width=259) #w=526591

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@hextrust-0 hextrust-0 May 1, 2024 •
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@markkurossi Thanks for the explanation. I try to write an example and compare both approaches.
Do we have any built-in operator to convert int1-n into bytes?

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The encoding/binary/PutUint(d []byte, offset int, v uint) []byte is parameterizable and can be instantiated to any integer size v (1-n bits). It encodes the value into buffer d in MSB-order. LSB-order encoding would be an easy addition if needed.

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@markkurossi Thanks for the explanation.

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@markkurossi
Both ways have potential issues: they can overflow.
That's why in native implementations, they check for overflow.
Technically, to sum two uint256 numbers, we need 257 bits. One bit accounts for overflow.

}
return z
}

func Bytes32(z Uint256) [32]byte {
var b [32]byte

binary.PutUint64(b[0:8], 0, z[3])
binary.PutUint64(b[8:16], 0, z[2])
binary.PutUint64(b[16:24], 0, z[1])
binary.PutUint64(b[24:32], 0, z[0])
return b
}