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v/vlib/crypto/ed25519/internal/edwards25519/scalarmult.v

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module edwards25519
import sync
struct BasepointTablePrecomp {
mut:
table []AffineLookupTable
initonce sync.Once
}
// basepoint_table is a set of 32 affineLookupTables, where table i is generated
// from 256i * basepoint. It is precomputed the first time it's used.
fn basepoint_table() []AffineLookupTable {
mut bpt := &BasepointTablePrecomp{
table: []AffineLookupTable{len: 32}
initonce: sync.new_once()
}
// replaced to use do_with_param on newest sync lib
/*
bpt.initonce.do(fn [mut bpt] () {
mut p := new_generator_point()
for i := 0; i < 32; i++ {
bpt.table[i].from_p3(p)
for j := 0; j < 8; j++ {
p.add(p, p)
}
}
})*/
bpt.initonce.do_with_param(fn (mut o BasepointTablePrecomp) {
mut p := new_generator_point()
for i := 0; i < 32; i++ {
o.table[i].from_p3(p)
for j := 0; j < 8; j++ {
p.add(p, p)
}
}
}, bpt)
return bpt.table
}
// scalar_base_mult sets v = x * B, where B is the canonical generator, and
// returns v.
//
// The scalar multiplication is done in constant time.
pub fn (mut v Point) scalar_base_mult(mut x Scalar) Point {
mut bpt_table := basepoint_table()
// Write x = sum(x_i * 16^i) so x*B = sum( B*x_i*16^i )
// as described in the Ed25519 paper
//
// Group even and odd coefficients
// x*B = x_0*16^0*B + x_2*16^2*B + ... + x_62*16^62*B
// + x_1*16^1*B + x_3*16^3*B + ... + x_63*16^63*B
// x*B = x_0*16^0*B + x_2*16^2*B + ... + x_62*16^62*B
// + 16*( x_1*16^0*B + x_3*16^2*B + ... + x_63*16^62*B)
//
// We use a lookup table for each i to get x_i*16^(2*i)*B
// and do four doublings to multiply by 16.
digits := x.signed_radix16()
mut multiple := AffineCached{}
mut tmp1 := ProjectiveP1{}
mut tmp2 := ProjectiveP2{}
// Accumulate the odd components first
v.set(new_identity_point())
for i := 1; i < 64; i += 2 {
bpt_table[i / 2].select_into(mut multiple, digits[i])
tmp1.add_affine(v, multiple)
v.from_p1(tmp1)
}
// Multiply by 16
tmp2.from_p3(v) // tmp2 = v in P2 coords
tmp1.double(tmp2) // tmp1 = 2*v in P1xP1 coords
tmp2.from_p1(tmp1) // tmp2 = 2*v in P2 coords
tmp1.double(tmp2) // tmp1 = 4*v in P1xP1 coords
tmp2.from_p1(tmp1) // tmp2 = 4*v in P2 coords
tmp1.double(tmp2) // tmp1 = 8*v in P1xP1 coords
tmp2.from_p1(tmp1) // tmp2 = 8*v in P2 coords
tmp1.double(tmp2) // tmp1 = 16*v in P1xP1 coords
v.from_p1(tmp1) // now v = 16*(odd components)
// Accumulate the even components
for j := 0; j < 64; j += 2 {
bpt_table[j / 2].select_into(mut multiple, digits[j])
tmp1.add_affine(v, multiple)
v.from_p1(tmp1)
}
return v
}
// scalar_mult sets v = x * q, and returns v.
//
// The scalar multiplication is done in constant time.
pub fn (mut v Point) scalar_mult(mut x Scalar, q Point) Point {
check_initialized(q)
mut table := ProjLookupTable{}
table.from_p3(q)
// Write x = sum(x_i * 16^i)
// so x*Q = sum( Q*x_i*16^i )
// = Q*x_0 + 16*(Q*x_1 + 16*( ... + Q*x_63) ... )
// <------compute inside out---------
//
// We use the lookup table to get the x_i*Q values
// and do four doublings to compute 16*Q
digits := x.signed_radix16()
// Unwrap first loop iteration to save computing 16*identity
mut multiple := ProjectiveCached{}
mut tmp1 := ProjectiveP1{}
mut tmp2 := ProjectiveP2{}
table.select_into(mut multiple, digits[63])
v.set(new_identity_point())
tmp1.add(v, multiple) // tmp1 = x_63*Q in P1xP1 coords
for i := 62; i >= 0; i-- {
tmp2.from_p1(tmp1) // tmp2 = (prev) in P2 coords
tmp1.double(tmp2) // tmp1 = 2*(prev) in P1xP1 coords
tmp2.from_p1(tmp1) // tmp2 = 2*(prev) in P2 coords
tmp1.double(tmp2) // tmp1 = 4*(prev) in P1xP1 coords
tmp2.from_p1(tmp1) // tmp2 = 4*(prev) in P2 coords
tmp1.double(tmp2) // tmp1 = 8*(prev) in P1xP1 coords
tmp2.from_p1(tmp1) // tmp2 = 8*(prev) in P2 coords
tmp1.double(tmp2) // tmp1 = 16*(prev) in P1xP1 coords
v.from_p1(tmp1) // v = 16*(prev) in P3 coords
table.select_into(mut multiple, digits[i])
tmp1.add(v, multiple) // tmp1 = x_i*Q + 16*(prev) in P1xP1 coords
}
v.from_p1(tmp1)
return v
}
struct BasepointNaftablePrecomp {
mut:
table NafLookupTable8
initonce sync.Once
}
fn basepoint_naf_table() NafLookupTable8 {
mut bnft := &BasepointNaftablePrecomp{}
bnft.initonce.do_with_param(fn (mut o BasepointNaftablePrecomp) {
o.table.from_p3(new_generator_point())
}, bnft)
return bnft.table
}
// vartime_double_scalar_base_mult sets v = a * A + b * B, where B is the canonical
// generator, and returns v.
//
// Execution time depends on the inputs.
pub fn (mut v Point) vartime_double_scalar_base_mult(xa Scalar, aa Point, xb Scalar) Point {
check_initialized(aa)
// Similarly to the single variable-base approach, we compute
// digits and use them with a lookup table. However, because
// we are allowed to do variable-time operations, we don't
// need constant-time lookups or constant-time digit
// computations.
//
// So we use a non-adjacent form of some width w instead of
// radix 16. This is like a binary representation (one digit
// for each binary place) but we allow the digits to grow in
// magnitude up to 2^{w-1} so that the nonzero digits are as
// sparse as possible. Intuitively, this "condenses" the
// "mass" of the scalar onto sparse coefficients (meaning
// fewer additions).
mut bp_naftable := basepoint_naf_table()
mut atable := NafLookupTable5{}
atable.from_p3(aa)
// Because the basepoint is fixed, we can use a wider NAF
// corresponding to a bigger table.
mut a := xa
mut b := xb
anaf := a.non_adjacent_form(5)
bnaf := b.non_adjacent_form(8)
// Find the first nonzero coefficient.
mut i := 255
for j := i; j >= 0; j-- {
if anaf[j] != 0 || bnaf[j] != 0 {
break
}
}
mut multa := ProjectiveCached{}
mut multb := AffineCached{}
mut tmp1 := ProjectiveP1{}
mut tmp2 := ProjectiveP2{}
tmp2.zero()
// Move from high to low bits, doubling the accumulator
// at each iteration and checking whether there is a nonzero
// coefficient to look up a multiple of.
for ; i >= 0; i-- {
tmp1.double(tmp2)
// Only update v if we have a nonzero coeff to add in.
if anaf[i] > 0 {
v.from_p1(tmp1)
atable.select_into(mut multa, anaf[i])
tmp1.add(v, multa)
} else if anaf[i] < 0 {
v.from_p1(tmp1)
atable.select_into(mut multa, -anaf[i])
tmp1.sub(v, multa)
}
if bnaf[i] > 0 {
v.from_p1(tmp1)
bp_naftable.select_into(mut multb, bnaf[i])
tmp1.add_affine(v, multb)
} else if bnaf[i] < 0 {
v.from_p1(tmp1)
bp_naftable.select_into(mut multb, -bnaf[i])
tmp1.sub_affine(v, multb)
}
tmp2.from_p1(tmp1)
}
v.from_p2(tmp2)
return v
}