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123 lines
3.6 KiB
Go
123 lines
3.6 KiB
Go
// Package mlsbset provides a constant-time exponentiation method with precomputation.
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//
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// References: "Efficient and secure algorithms for GLV-based scalar
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// multiplication and their implementation on GLV–GLS curves" by (Faz-Hernandez et al.)
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// - https://doi.org/10.1007/s13389-014-0085-7
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// - https://eprint.iacr.org/2013/158
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package mlsbset
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import (
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"errors"
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"fmt"
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"math/big"
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"github.com/cloudflare/circl/internal/conv"
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)
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// EltG is a group element.
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type EltG interface{}
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// EltP is a precomputed group element.
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type EltP interface{}
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// Group defines the operations required by MLSBSet exponentiation method.
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type Group interface {
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Identity() EltG // Returns the identity of the group.
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Sqr(x EltG) // Calculates x = x^2.
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Mul(x EltG, y EltP) // Calculates x = x*y.
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NewEltP() EltP // Returns an arbitrary precomputed element.
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ExtendedEltP() EltP // Returns the precomputed element x^(2^(w*d)).
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Lookup(a EltP, v uint, s, u int32) // Sets a = s*T[v][u].
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}
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// Params contains the parameters of the encoding.
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type Params struct {
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T uint // T is the maximum size (in bits) of exponents.
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V uint // V is the number of tables.
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W uint // W is the window size.
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E uint // E is the number of digits per table.
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D uint // D is the number of digits in total.
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L uint // L is the length of the code.
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}
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// Encoder allows to convert integers into valid powers.
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type Encoder struct{ p Params }
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// New produces an encoder of the MLSBSet algorithm.
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func New(t, v, w uint) (Encoder, error) {
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if !(t > 1 && v >= 1 && w >= 2) {
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return Encoder{}, errors.New("t>1, v>=1, w>=2")
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}
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e := (t + w*v - 1) / (w * v)
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d := e * v
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l := d * w
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return Encoder{Params{t, v, w, e, d, l}}, nil
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}
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// Encode converts an odd integer k into a valid power for exponentiation.
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func (m Encoder) Encode(k []byte) (*Power, error) {
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if len(k) == 0 {
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return nil, errors.New("empty slice")
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}
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if !(len(k) <= int(m.p.L+7)>>3) {
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return nil, errors.New("k too big")
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}
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if k[0]%2 == 0 {
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return nil, errors.New("k must be odd")
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}
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ap := int((m.p.L+7)/8) - len(k)
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k = append(k, make([]byte, ap)...)
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s := m.signs(k)
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b := make([]int32, m.p.L-m.p.D)
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c := conv.BytesLe2BigInt(k)
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c.Rsh(c, m.p.D)
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var bi big.Int
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for i := m.p.D; i < m.p.L; i++ {
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c0 := int32(c.Bit(0))
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b[i-m.p.D] = s[i%m.p.D] * c0
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bi.SetInt64(int64(b[i-m.p.D] >> 1))
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c.Rsh(c, 1)
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c.Sub(c, &bi)
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}
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carry := int(c.Int64())
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return &Power{m, s, b, carry}, nil
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}
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// signs calculates the set of signs.
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func (m Encoder) signs(k []byte) []int32 {
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s := make([]int32, m.p.D)
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s[m.p.D-1] = 1
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for i := uint(1); i < m.p.D; i++ {
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ki := int32((k[i>>3] >> (i & 0x7)) & 0x1)
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s[i-1] = 2*ki - 1
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}
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return s
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}
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// GetParams returns the complementary parameters of the encoding.
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func (m Encoder) GetParams() Params { return m.p }
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// tableSize returns the size of each table.
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func (m Encoder) tableSize() uint { return 1 << (m.p.W - 1) }
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// Elts returns the total number of elements that must be precomputed.
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func (m Encoder) Elts() uint { return m.p.V * m.tableSize() }
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// IsExtended returns true if the element x^(2^(wd)) must be calculated.
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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 }
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// Ops returns the number of squares and multiplications executed during an exponentiation.
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func (m Encoder) Ops() (S uint, M uint) {
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S = m.p.E
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M = m.p.E * m.p.V
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if m.IsExtended() {
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M++
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}
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return
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}
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func (m Encoder) String() string {
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return fmt.Sprintf("T: %v W: %v V: %v e: %v d: %v l: %v wv|t: %v",
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m.p.T, m.p.W, m.p.V, m.p.E, m.p.D, m.p.L, m.IsExtended())
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}
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