peridot/vendor/github.com/cloudflare/circl/math/mlsbset/mlsbset.go

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// Package mlsbset provides a constant-time exponentiation method with precomputation.
//
// References: "Efficient and secure algorithms for GLV-based scalar
// multiplication and their implementation on GLVGLS 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())
}