github.com/cloudflare/circl@v1.5.0/math/mlsbset/mlsbset.go

// Package mlsbset provides a constant-time exponentiation method with precomputation.
//
// References: "Efficient and secure algorithms for GLV-based scalar
// multiplication and their implementation on GLV–GLS curves" by (Faz-Hernandez et al.)
//   - https://doi.org/10.1007/s13389-014-0085-7
//   - https://eprint.iacr.org/2013/158
package mlsbset

import (
	"errors"
	"fmt"
	"math/big"

	"github.com/cloudflare/circl/internal/conv"
)

// EltG is a group element.
type EltG interface{}

// EltP is a precomputed group element.
type EltP interface{}

// Group defines the operations required by MLSBSet exponentiation method.
type Group interface {
	Identity() EltG                    // Returns the identity of the group.
	Sqr(x EltG)                        // Calculates x = x^2.
	Mul(x EltG, y EltP)                // Calculates x = x*y.
	NewEltP() EltP                     // Returns an arbitrary precomputed element.
	ExtendedEltP() EltP                // Returns the precomputed element x^(2^(w*d)).
	Lookup(a EltP, v uint, s, u int32) // Sets a = s*T[v][u].
}

// Params contains the parameters of the encoding.
type Params struct {
	T uint // T is the maximum size (in bits) of exponents.
	V uint // V is the number of tables.
	W uint // W is the window size.
	E uint // E is the number of digits per table.
	D uint // D is the number of digits in total.
	L uint // L is the length of the code.
}

// Encoder allows to convert integers into valid powers.
type Encoder struct{ p Params }

// New produces an encoder of the MLSBSet algorithm.
func New(t, v, w uint) (Encoder, error) {
	if !(t > 1 && v >= 1 && w >= 2) {
		return Encoder{}, errors.New("t>1, v>=1, w>=2")
	}
	e := (t + w*v - 1) / (w * v)
	d := e * v
	l := d * w
	return Encoder{Params{t, v, w, e, d, l}}, nil
}

// Encode converts an odd integer k into a valid power for exponentiation.
func (m Encoder) Encode(k []byte) (*Power, error) {
	if len(k) == 0 {
		return nil, errors.New("empty slice")
	}
	if !(len(k) <= int(m.p.L+7)>>3) {
		return nil, errors.New("k too big")
	}
	if k[0]%2 == 0 {
		return nil, errors.New("k must be odd")
	}
	ap := int((m.p.L+7)/8) - len(k)
	k = append(k, make([]byte, ap)...)
	s := m.signs(k)
	b := make([]int32, m.p.L-m.p.D)
	c := conv.BytesLe2BigInt(k)
	c.Rsh(c, m.p.D)
	var bi big.Int
	for i := m.p.D; i < m.p.L; i++ {
		c0 := int32(c.Bit(0))
		b[i-m.p.D] = s[i%m.p.D] * c0
		bi.SetInt64(int64(b[i-m.p.D] >> 1))
		c.Rsh(c, 1)
		c.Sub(c, &bi)
	}
	carry := int(c.Int64())
	return &Power{m, s, b, carry}, nil
}

// signs calculates the set of signs.
func (m Encoder) signs(k []byte) []int32 {
	s := make([]int32, m.p.D)
	s[m.p.D-1] = 1
	for i := uint(1); i < m.p.D; i++ {
		ki := int32((k[i>>3] >> (i & 0x7)) & 0x1)
		s[i-1] = 2*ki - 1
	}
	return s
}

// GetParams returns the complementary parameters of the encoding.
func (m Encoder) GetParams() Params { return m.p }

// tableSize returns the size of each table.
func (m Encoder) tableSize() uint { return 1 << (m.p.W - 1) }

// Elts returns the total number of elements that must be precomputed.
func (m Encoder) Elts() uint { return m.p.V * m.tableSize() }

// IsExtended returns true if the element x^(2^(wd)) must be calculated.
func (m Encoder) IsExtended() bool { q := m.p.T / (m.p.V * m.p.W); return m.p.T == q*m.p.V*m.p.W }

// Ops returns the number of squares and multiplications executed during an exponentiation.
func (m Encoder) Ops() (S uint, M uint) {
	S = m.p.E
	M = m.p.E * m.p.V
	if m.IsExtended() {
		M++
	}
	return
}

func (m Encoder) String() string {
	return fmt.Sprintf("T: %v W: %v V: %v e: %v d: %v l: %v wv|t: %v",
		m.p.T, m.p.W, m.p.V, m.p.E, m.p.D, m.p.L, m.IsExtended())
}