forked from toolshed/abra
123 lines
3.6 KiB
Go
123 lines
3.6 KiB
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())
|
||
}
|