diff --git a/pkg/bits/bits.mpcl b/pkg/bits/bits.mpcl new file mode 100644 index 00000000..32401bdb --- /dev/null +++ b/pkg/bits/bits.mpcl @@ -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 +} \ No newline at end of file diff --git a/pkg/encoding/binary/getput.mpcl b/pkg/encoding/binary/getput.mpcl index b8791fd8..4e82236c 100644 --- a/pkg/encoding/binary/getput.mpcl +++ b/pkg/encoding/binary/getput.mpcl @@ -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 +} diff --git a/pkg/math/uint256.mpcl b/pkg/math/uint256.mpcl new file mode 100644 index 00000000..6f497b4c --- /dev/null +++ b/pkg/math/uint256.mpcl @@ -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) + } + 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 +}