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inverse elligator works, but at what cost?!?!!?

master
Michael Hamburg 8 years ago
parent
17347b04a7
commit
164342ebfd
8 changed files with 153 additions and 72 deletions
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  1. +40
    -27
      aux/ristretto/ristretto.sage
  2. +15
    -14
      src/GENERATED/c/curve25519/decaf.c
  3. +21
    -1
      src/GENERATED/c/curve25519/elligator.c
  4. +15
    -14
      src/GENERATED/c/ed448goldilocks/decaf.c
  5. +21
    -1
      src/GENERATED/c/ed448goldilocks/elligator.c
  6. +5
    -0
      src/include/field.h
  7. +15
    -14
      src/per_curve/decaf.tmpl.c
  8. +21
    -1
      src/per_curve/elligator.tmpl.c

+ 40
- 27
aux/ristretto/ristretto.sage View File

@@ -53,6 +53,8 @@ def isqrt(x,exn=InvalidEncodingException("Not on curve")):
if negative(s): s=-s
return 1/s

def inv0(x): return 1/x if x != 0 else 0

def isqrt_i(x):
"""Return 1/sqrt(x) or 1/sqrt(zeta * x)"""
if x==0: return True,0
@@ -325,8 +327,8 @@ class Decaf_1_1_Point(QuotientEdwardsPoint):
den = x*y
isr = isqrt(num*(a-d)*den^2)
iden = isr * den * self.isoMagic
inum = isr * num
iden = isr * den * self.isoMagic # 1/sqrt((z+y)(z-y)) = 1/sqrt(1-Y^2) / z
inum = isr * num # sqrt(1-Y^2) * z / xysqrt(a-d) ~ 1/sqrt(1-ax^2)/z
if negative(iden*inum*self.i*t^2*(d-a)) != toggle_rotation:
iden,inum = inum,iden
@@ -386,18 +388,29 @@ class Decaf_1_1_Point(QuotientEdwardsPoint):
for toggle_r in [False,True]:
s,m1,m12,swap = self.toJacobiQuartic(toggle_rotation,toggle_altx,toggle_s)

print
print toggle_rotation,toggle_altx,toggle_s
print m1
print m12
#print
#print toggle_rotation,toggle_altx,toggle_s
#print m1
#print m12
if self == self.__class__() and self.cofactor == 4:
# Hacks for identity!
if toggle_altx: m12 = 1
elif toggle_s: m1 = 1
elif toggle_r: continue
## BOTH???
if self == self.__class__():
if self.cofactor == 4:
# Hacks for identity!
if toggle_altx: m12 = 1
elif toggle_s: m1 = 1
elif toggle_r: continue
## BOTH???
else:
m12 = 1
imi = self.isoMagic * self.i
if toggle_rotation:
if toggle_altx: m1 = -imi
else: m1 = +imi
else:
if toggle_altx: m1 = 0
else: m1 = a-d
rnum = (d*a*m12-m1)
rden = ((d*a-1)*m12+m1)
@@ -406,7 +419,7 @@ class Decaf_1_1_Point(QuotientEdwardsPoint):
ok,sr = isqrt_i(rnum*rden*self.qnr)
if not ok: continue
sr *= rnum
print "Works! %d %x" % (swap,sr)
#print "Works! %d %x" % (swap,sr)
if negative(sr) != toggle_r: sr = -sr
ret = self.gfToBytes(sr)
@@ -681,12 +694,12 @@ def test(cls,n):
if Q1 + Q0 != Q2: raise TestFailedException("Scalarmul doesn't work")
Q = Q1

test(Ed25519Point,100)
test(NegEd25519Point,100)
test(IsoEd25519Point,100)
test(IsoEd448Point,100)
test(TwistedEd448GoldilocksPoint,100)
test(Ed448GoldilocksPoint,100)
#test(Ed25519Point,100)
#test(NegEd25519Point,100)
#test(IsoEd25519Point,100)
#test(IsoEd448Point,100)
#test(TwistedEd448GoldilocksPoint,100)
#test(Ed448GoldilocksPoint,100)
def testElligator(cls,n):
@@ -710,12 +723,12 @@ def testElligator(cls,n):
pass # TODO

testElligator(Ed25519Point,100)
testElligator(NegEd25519Point,100)
testElligator(IsoEd25519Point,100)
testElligator(IsoEd448Point,100)
testElligator(Ed448GoldilocksPoint,100)
testElligator(TwistedEd448GoldilocksPoint,100)
#testElligator(Ed25519Point,100)
#testElligator(NegEd25519Point,100)
#testElligator(IsoEd25519Point,100)
#testElligator(IsoEd448Point,100)
#testElligator(Ed448GoldilocksPoint,100)
#testElligator(TwistedEd448GoldilocksPoint,100)

def gangtest(classes,n):
print "Gang test",[cls.__name__ for cls in classes]
@@ -743,5 +756,5 @@ def gangtest(classes,n):
for c,ret in zip(classes,rets):
print c,binascii.hexlify(ret)
print
gangtest([IsoEd448Point,TwistedEd448GoldilocksPoint,Ed448GoldilocksPoint],100)
gangtest([Ed25519Point,IsoEd25519Point],100)
#gangtest([IsoEd448Point,TwistedEd448GoldilocksPoint,Ed448GoldilocksPoint],100)
#gangtest([Ed25519Point,IsoEd25519Point],100)

+ 15
- 14
src/GENERATED/c/curve25519/decaf.c View File

@@ -48,7 +48,8 @@ static const scalar_t point_scalarmul_adjustment = {{{

const uint8_t decaf_x25519_base_point[DECAF_X25519_PUBLIC_BYTES] = { 0x09 };

static const gf RISTRETTO_ISOMAGIC = {{{
#define RISTRETTO_FACTOR DECAF_255_RISTRETTO_FACTOR
const gf RISTRETTO_FACTOR = {{{
0x0fdaa805d40ea, 0x2eb482e57d339, 0x007610274bc58, 0x6510b613dc8ff, 0x786c8905cfaff
}}};

@@ -157,7 +158,7 @@ void API_NS(deisogenize) (
gf_mulw(t2,t1,-1-TWISTED_D); /* -x^2 * (a-d) * num */
gf_isr(t1,t2); /* t1 = isr */
gf_mul(t2,t1,t3); /* t2 = ratio */
gf_mul(t4,t2,RISTRETTO_ISOMAGIC);
gf_mul(t4,t2,RISTRETTO_FACTOR);
mask_t negx = gf_lobit(t4) ^ toggle_altx;
gf_cond_neg(t2, negx);
gf_mul(t3,t2,p->z);
@@ -183,12 +184,12 @@ void API_NS(deisogenize) (
gf_mulw(t1,t4,-1-TWISTED_D);
gf_isr(t4,t1); /* isqrt(num*(a-d)*den^2) */
gf_mul(t1,t2,t4);
gf_mul(t2,t1,RISTRETTO_ISOMAGIC); /* t2 = "iden" in ristretto.sage */
gf_mul(t2,t1,RISTRETTO_FACTOR); /* t2 = "iden" in ristretto.sage */
gf_mul(t1,t3,t4); /* t1 = "inum" in ristretto.sage */

/* Calculate altxy = iden*inum*i*t^2*(d-a) */
gf_mul(t3,t1,t2);
gf_mul_qnr(t4,t3);
gf_mul_i(t4,t3);
gf_mul(t3,t4,p->t);
gf_mul(t4,t3,p->t);
gf_mulw(t3,t4,TWISTED_D+1); /* iden*inum*i*t^2*(d-1) */
@@ -196,10 +197,10 @@ void API_NS(deisogenize) (
/* Rotate if altxy is negative */
gf_cond_swap(t1,t2,rotate);
gf_mul_qnr(t4,p->x);
gf_mul_i(t4,p->x);
gf_cond_sel(t4,p->y,t4,rotate); /* t4 = "fac" = ix if rotate, else y */
gf_mul_qnr(t5,RISTRETTO_ISOMAGIC); /* t5 = imi */
gf_mul_i(t5,RISTRETTO_FACTOR); /* t5 = imi */
gf_mul(t3,t5,t2); /* iden * imi */
gf_mul(t2,t5,t1);
gf_mul(t5,t2,p->t); /* "altx" = iden*imi*t */
@@ -258,20 +259,20 @@ decaf_error_t API_NS(point_decode) (
gf_add(tmp2,tmp2,tmp2); /* 2*s*isr*den */
gf_mul(tmp,tmp2,isr); /* 2*s*isr^2*den */
gf_mul(p->x,tmp,num); /* 2*s*isr^2*den*num */
gf_mul(tmp,tmp2,RISTRETTO_ISOMAGIC); /* 2*s*isr*den*magic */
gf_mul(tmp,tmp2,RISTRETTO_FACTOR); /* 2*s*isr*den*magic */
gf_cond_neg(p->x,gf_lobit(tmp)); /* flip x */
#if COFACTOR==8
/* Additionally check y != 0 and x*y*isomagic nonegative */
succ &= ~gf_eq(p->y,ZERO);
gf_mul(tmp,p->x,p->y);
gf_mul(tmp2,tmp,RISTRETTO_ISOMAGIC);
gf_mul(tmp2,tmp,RISTRETTO_FACTOR);
succ &= ~gf_lobit(tmp2);
#endif

#if IMAGINE_TWIST
gf_copy(tmp,p->x);
gf_mul_qnr(p->x,tmp);
gf_mul_i(p->x,tmp);
#endif

/* Fill in z and t */
@@ -1077,9 +1078,9 @@ void API_NS(point_mul_by_cofactor_and_encode_like_eddsa) (
gf_mul ( y, u, t ); // (x^2+y^2)(2z^2-y^2+x^2)
gf_mul ( u, z, t );
gf_copy( z, u );
gf_mul ( u, x, RISTRETTO_ISOMAGIC );
gf_mul ( u, x, RISTRETTO_FACTOR );
#if IMAGINE_TWIST
gf_mul_qnr( x, u );
gf_mul_i( x, u );
#else
#error "... probably wrong"
gf_copy( x, u );
@@ -1090,7 +1091,7 @@ void API_NS(point_mul_by_cofactor_and_encode_like_eddsa) (
{
API_NS(point_double)(q,q);
API_NS(point_double)(q,q);
gf_mul_qnr(x, q->x);
gf_mul_i(x, q->x);
gf_copy(y, q->y);
gf_copy(z, q->z);
}
@@ -1188,8 +1189,8 @@ decaf_error_t API_NS(point_decode_like_eddsa_and_ignore_cofactor) (
gf_sqr ( p->x, p->z );
gf_add ( p->z, p->x, p->x );
gf_sub ( c, p->z, p->t ); // 2z^2 - y^2 + x^2
gf_div_qnr ( a, c );
gf_mul ( c, a, RISTRETTO_ISOMAGIC );
gf_div_i ( a, c );
gf_mul ( c, a, RISTRETTO_FACTOR );
gf_mul ( p->x, b, p->t); // (2xy)(y^2-x^2)
gf_mul ( p->z, p->t, c ); // (y^2-x^2)sd(2z^2 - y^2 + x^2)
gf_mul ( p->y, d, c ); // (y^2+x^2)sd(2z^2 - y^2 + x^2)


+ 21
- 1
src/GENERATED/c/curve25519/elligator.c View File

@@ -21,6 +21,10 @@
#define IMAGINE_TWIST 1
#define COFACTOR 8
static const int EDWARDS_D = -121665;

#define RISTRETTO_FACTOR DECAF_255_RISTRETTO_FACTOR
extern const gf RISTRETTO_FACTOR;

/* End of template stuff */

extern mask_t API_NS(deisogenize) (
@@ -145,8 +149,23 @@ API_NS(invert_elligator_nonuniform) (
API_NS(deisogenize)(a,b,c,p,sgn_s,sgn_altx,sgn_ed_T);
mask_t is_identity = gf_eq(p->t,ZERO);
#if COFACTOR==4
gf_cond_sel(b,b,ONE,is_identity & sgn_altx);
gf_cond_sel(c,c,ONE,is_identity & sgn_s &~ sgn_altx);
#elif IMAGINE_TWIST
/* Terrible, terrible special casing due to lots of 0/0 is deisogenize
* Basically we need to generate -D and +- i*RISTRETTO_FACTOR
*/
gf_mul_i(a,RISTRETTO_FACTOR);
gf_cond_sel(b,b,ONE,is_identity);
gf_cond_neg(a,sgn_altx);
gf_cond_sel(c,c,a,is_identity & sgn_ed_T);
gf_cond_sel(c,c,ZERO,is_identity & ~sgn_ed_T);
gf_mulw(a,ONE,-EDWARDS_D);
gf_cond_sel(c,c,a,is_identity & ~sgn_ed_T &~ sgn_altx);
#else
#error "Different special-casing goes here!"
#endif
#if IMAGINE_TWIST
gf_mulw(a,b,-EDWARDS_D);
@@ -169,7 +188,8 @@ API_NS(invert_elligator_nonuniform) (
#endif
gf_cond_neg(b, sgn_r0^gf_lobit(b));
succ &= ~(gf_eq(b,ZERO) & sgn_r0);
/* Eliminate duplicate values for identity ... */
succ &= ~(gf_eq(b,ZERO) & (sgn_r0 | sgn_s));
// #if COFACTOR == 8
// succ &= ~(is_identity & sgn_ed_T); /* NB: there are no preimages of rotated identity. */
// #endif


+ 15
- 14
src/GENERATED/c/ed448goldilocks/decaf.c View File

@@ -48,7 +48,8 @@ static const scalar_t point_scalarmul_adjustment = {{{

const uint8_t decaf_x448_base_point[DECAF_X448_PUBLIC_BYTES] = { 0x05 };

static const gf RISTRETTO_ISOMAGIC = {{{
#define RISTRETTO_FACTOR DECAF_448_RISTRETTO_FACTOR
const gf RISTRETTO_FACTOR = {{{
0x42ef0f45572736, 0x7bf6aa20ce5296, 0xf4fd6eded26033, 0x968c14ba839a66, 0xb8d54b64a2d780, 0x6aa0a1f1a7b8a5, 0x683bf68d722fa2, 0x22d962fbeb24f7
}}};

@@ -157,7 +158,7 @@ void API_NS(deisogenize) (
gf_mulw(t2,t1,-1-TWISTED_D); /* -x^2 * (a-d) * num */
gf_isr(t1,t2); /* t1 = isr */
gf_mul(t2,t1,t3); /* t2 = ratio */
gf_mul(t4,t2,RISTRETTO_ISOMAGIC);
gf_mul(t4,t2,RISTRETTO_FACTOR);
mask_t negx = gf_lobit(t4) ^ toggle_altx;
gf_cond_neg(t2, negx);
gf_mul(t3,t2,p->z);
@@ -183,12 +184,12 @@ void API_NS(deisogenize) (
gf_mulw(t1,t4,-1-TWISTED_D);
gf_isr(t4,t1); /* isqrt(num*(a-d)*den^2) */
gf_mul(t1,t2,t4);
gf_mul(t2,t1,RISTRETTO_ISOMAGIC); /* t2 = "iden" in ristretto.sage */
gf_mul(t2,t1,RISTRETTO_FACTOR); /* t2 = "iden" in ristretto.sage */
gf_mul(t1,t3,t4); /* t1 = "inum" in ristretto.sage */

/* Calculate altxy = iden*inum*i*t^2*(d-a) */
gf_mul(t3,t1,t2);
gf_mul_qnr(t4,t3);
gf_mul_i(t4,t3);
gf_mul(t3,t4,p->t);
gf_mul(t4,t3,p->t);
gf_mulw(t3,t4,TWISTED_D+1); /* iden*inum*i*t^2*(d-1) */
@@ -196,10 +197,10 @@ void API_NS(deisogenize) (
/* Rotate if altxy is negative */
gf_cond_swap(t1,t2,rotate);
gf_mul_qnr(t4,p->x);
gf_mul_i(t4,p->x);
gf_cond_sel(t4,p->y,t4,rotate); /* t4 = "fac" = ix if rotate, else y */
gf_mul_qnr(t5,RISTRETTO_ISOMAGIC); /* t5 = imi */
gf_mul_i(t5,RISTRETTO_FACTOR); /* t5 = imi */
gf_mul(t3,t5,t2); /* iden * imi */
gf_mul(t2,t5,t1);
gf_mul(t5,t2,p->t); /* "altx" = iden*imi*t */
@@ -258,20 +259,20 @@ decaf_error_t API_NS(point_decode) (
gf_add(tmp2,tmp2,tmp2); /* 2*s*isr*den */
gf_mul(tmp,tmp2,isr); /* 2*s*isr^2*den */
gf_mul(p->x,tmp,num); /* 2*s*isr^2*den*num */
gf_mul(tmp,tmp2,RISTRETTO_ISOMAGIC); /* 2*s*isr*den*magic */
gf_mul(tmp,tmp2,RISTRETTO_FACTOR); /* 2*s*isr*den*magic */
gf_cond_neg(p->x,gf_lobit(tmp)); /* flip x */
#if COFACTOR==8
/* Additionally check y != 0 and x*y*isomagic nonegative */
succ &= ~gf_eq(p->y,ZERO);
gf_mul(tmp,p->x,p->y);
gf_mul(tmp2,tmp,RISTRETTO_ISOMAGIC);
gf_mul(tmp2,tmp,RISTRETTO_FACTOR);
succ &= ~gf_lobit(tmp2);
#endif

#if IMAGINE_TWIST
gf_copy(tmp,p->x);
gf_mul_qnr(p->x,tmp);
gf_mul_i(p->x,tmp);
#endif

/* Fill in z and t */
@@ -1077,9 +1078,9 @@ void API_NS(point_mul_by_cofactor_and_encode_like_eddsa) (
gf_mul ( y, u, t ); // (x^2+y^2)(2z^2-y^2+x^2)
gf_mul ( u, z, t );
gf_copy( z, u );
gf_mul ( u, x, RISTRETTO_ISOMAGIC );
gf_mul ( u, x, RISTRETTO_FACTOR );
#if IMAGINE_TWIST
gf_mul_qnr( x, u );
gf_mul_i( x, u );
#else
#error "... probably wrong"
gf_copy( x, u );
@@ -1090,7 +1091,7 @@ void API_NS(point_mul_by_cofactor_and_encode_like_eddsa) (
{
API_NS(point_double)(q,q);
API_NS(point_double)(q,q);
gf_mul_qnr(x, q->x);
gf_mul_i(x, q->x);
gf_copy(y, q->y);
gf_copy(z, q->z);
}
@@ -1188,8 +1189,8 @@ decaf_error_t API_NS(point_decode_like_eddsa_and_ignore_cofactor) (
gf_sqr ( p->x, p->z );
gf_add ( p->z, p->x, p->x );
gf_sub ( c, p->z, p->t ); // 2z^2 - y^2 + x^2
gf_div_qnr ( a, c );
gf_mul ( c, a, RISTRETTO_ISOMAGIC );
gf_div_i ( a, c );
gf_mul ( c, a, RISTRETTO_FACTOR );
gf_mul ( p->x, b, p->t); // (2xy)(y^2-x^2)
gf_mul ( p->z, p->t, c ); // (y^2-x^2)sd(2z^2 - y^2 + x^2)
gf_mul ( p->y, d, c ); // (y^2+x^2)sd(2z^2 - y^2 + x^2)


+ 21
- 1
src/GENERATED/c/ed448goldilocks/elligator.c View File

@@ -21,6 +21,10 @@
#define IMAGINE_TWIST 0
#define COFACTOR 4
static const int EDWARDS_D = -39081;

#define RISTRETTO_FACTOR DECAF_448_RISTRETTO_FACTOR
extern const gf RISTRETTO_FACTOR;

/* End of template stuff */

extern mask_t API_NS(deisogenize) (
@@ -145,8 +149,23 @@ API_NS(invert_elligator_nonuniform) (
API_NS(deisogenize)(a,b,c,p,sgn_s,sgn_altx,sgn_ed_T);
mask_t is_identity = gf_eq(p->t,ZERO);
#if COFACTOR==4
gf_cond_sel(b,b,ONE,is_identity & sgn_altx);
gf_cond_sel(c,c,ONE,is_identity & sgn_s &~ sgn_altx);
#elif IMAGINE_TWIST
/* Terrible, terrible special casing due to lots of 0/0 is deisogenize
* Basically we need to generate -D and +- i*RISTRETTO_FACTOR
*/
gf_mul_i(a,RISTRETTO_FACTOR);
gf_cond_sel(b,b,ONE,is_identity);
gf_cond_neg(a,sgn_altx);
gf_cond_sel(c,c,a,is_identity & sgn_ed_T);
gf_cond_sel(c,c,ZERO,is_identity & ~sgn_ed_T);
gf_mulw(a,ONE,-EDWARDS_D);
gf_cond_sel(c,c,a,is_identity & ~sgn_ed_T &~ sgn_altx);
#else
#error "Different special-casing goes here!"
#endif
#if IMAGINE_TWIST
gf_mulw(a,b,-EDWARDS_D);
@@ -169,7 +188,8 @@ API_NS(invert_elligator_nonuniform) (
#endif
gf_cond_neg(b, sgn_r0^gf_lobit(b));
succ &= ~(gf_eq(b,ZERO) & sgn_r0);
/* Eliminate duplicate values for identity ... */
succ &= ~(gf_eq(b,ZERO) & (sgn_r0 | sgn_s));
// #if COFACTOR == 8
// succ &= ~(is_identity & sgn_ed_T); /* NB: there are no preimages of rotated identity. */
// #endif


+ 5
- 0
src/include/field.h View File

@@ -103,5 +103,10 @@ static DECAF_INLINE void gf_div_qnr(gf_s *__restrict__ out, const gf x) {
#endif
}

#if P_MOD_8 == 5
#define gf_mul_i gf_mul_qnr
#define gf_div_i gf_div_qnr
#endif


#endif // __GF_H__

+ 15
- 14
src/per_curve/decaf.tmpl.c View File

@@ -37,7 +37,8 @@ static const scalar_t point_scalarmul_adjustment = {{{

const uint8_t decaf_x$(gf_shortname)_base_point[DECAF_X$(gf_shortname)_PUBLIC_BYTES] = { $(ser(mont_base,8)) };

static const gf RISTRETTO_ISOMAGIC = {{{
#define RISTRETTO_FACTOR $(C_NS)_RISTRETTO_FACTOR
const gf RISTRETTO_FACTOR = {{{
$(ser(msqrt(d-1 if imagine_twist else -d,modulus,lo_bit_clear=True),gf_lit_limb_bits))
}}};

@@ -146,7 +147,7 @@ void API_NS(deisogenize) (
gf_mulw(t2,t1,-1-TWISTED_D); /* -x^2 * (a-d) * num */
gf_isr(t1,t2); /* t1 = isr */
gf_mul(t2,t1,t3); /* t2 = ratio */
gf_mul(t4,t2,RISTRETTO_ISOMAGIC);
gf_mul(t4,t2,RISTRETTO_FACTOR);
mask_t negx = gf_lobit(t4) ^ toggle_altx;
gf_cond_neg(t2, negx);
gf_mul(t3,t2,p->z);
@@ -172,12 +173,12 @@ void API_NS(deisogenize) (
gf_mulw(t1,t4,-1-TWISTED_D);
gf_isr(t4,t1); /* isqrt(num*(a-d)*den^2) */
gf_mul(t1,t2,t4);
gf_mul(t2,t1,RISTRETTO_ISOMAGIC); /* t2 = "iden" in ristretto.sage */
gf_mul(t2,t1,RISTRETTO_FACTOR); /* t2 = "iden" in ristretto.sage */
gf_mul(t1,t3,t4); /* t1 = "inum" in ristretto.sage */

/* Calculate altxy = iden*inum*i*t^2*(d-a) */
gf_mul(t3,t1,t2);
gf_mul_qnr(t4,t3);
gf_mul_i(t4,t3);
gf_mul(t3,t4,p->t);
gf_mul(t4,t3,p->t);
gf_mulw(t3,t4,TWISTED_D+1); /* iden*inum*i*t^2*(d-1) */
@@ -185,10 +186,10 @@ void API_NS(deisogenize) (
/* Rotate if altxy is negative */
gf_cond_swap(t1,t2,rotate);
gf_mul_qnr(t4,p->x);
gf_mul_i(t4,p->x);
gf_cond_sel(t4,p->y,t4,rotate); /* t4 = "fac" = ix if rotate, else y */
gf_mul_qnr(t5,RISTRETTO_ISOMAGIC); /* t5 = imi */
gf_mul_i(t5,RISTRETTO_FACTOR); /* t5 = imi */
gf_mul(t3,t5,t2); /* iden * imi */
gf_mul(t2,t5,t1);
gf_mul(t5,t2,p->t); /* "altx" = iden*imi*t */
@@ -247,20 +248,20 @@ decaf_error_t API_NS(point_decode) (
gf_add(tmp2,tmp2,tmp2); /* 2*s*isr*den */
gf_mul(tmp,tmp2,isr); /* 2*s*isr^2*den */
gf_mul(p->x,tmp,num); /* 2*s*isr^2*den*num */
gf_mul(tmp,tmp2,RISTRETTO_ISOMAGIC); /* 2*s*isr*den*magic */
gf_mul(tmp,tmp2,RISTRETTO_FACTOR); /* 2*s*isr*den*magic */
gf_cond_neg(p->x,gf_lobit(tmp)); /* flip x */
#if COFACTOR==8
/* Additionally check y != 0 and x*y*isomagic nonegative */
succ &= ~gf_eq(p->y,ZERO);
gf_mul(tmp,p->x,p->y);
gf_mul(tmp2,tmp,RISTRETTO_ISOMAGIC);
gf_mul(tmp2,tmp,RISTRETTO_FACTOR);
succ &= ~gf_lobit(tmp2);
#endif

#if IMAGINE_TWIST
gf_copy(tmp,p->x);
gf_mul_qnr(p->x,tmp);
gf_mul_i(p->x,tmp);
#endif

/* Fill in z and t */
@@ -1066,9 +1067,9 @@ void API_NS(point_mul_by_cofactor_and_encode_like_eddsa) (
gf_mul ( y, u, t ); // (x^2+y^2)(2z^2-y^2+x^2)
gf_mul ( u, z, t );
gf_copy( z, u );
gf_mul ( u, x, RISTRETTO_ISOMAGIC );
gf_mul ( u, x, RISTRETTO_FACTOR );
#if IMAGINE_TWIST
gf_mul_qnr( x, u );
gf_mul_i( x, u );
#else
#error "... probably wrong"
gf_copy( x, u );
@@ -1079,7 +1080,7 @@ void API_NS(point_mul_by_cofactor_and_encode_like_eddsa) (
{
API_NS(point_double)(q,q);
API_NS(point_double)(q,q);
gf_mul_qnr(x, q->x);
gf_mul_i(x, q->x);
gf_copy(y, q->y);
gf_copy(z, q->z);
}
@@ -1177,8 +1178,8 @@ decaf_error_t API_NS(point_decode_like_eddsa_and_ignore_cofactor) (
gf_sqr ( p->x, p->z );
gf_add ( p->z, p->x, p->x );
gf_sub ( c, p->z, p->t ); // 2z^2 - y^2 + x^2
gf_div_qnr ( a, c );
gf_mul ( c, a, RISTRETTO_ISOMAGIC );
gf_div_i ( a, c );
gf_mul ( c, a, RISTRETTO_FACTOR );
gf_mul ( p->x, b, p->t); // (2xy)(y^2-x^2)
gf_mul ( p->z, p->t, c ); // (y^2-x^2)sd(2z^2 - y^2 + x^2)
gf_mul ( p->y, d, c ); // (y^2+x^2)sd(2z^2 - y^2 + x^2)


+ 21
- 1
src/per_curve/elligator.tmpl.c View File

@@ -10,6 +10,10 @@
#define IMAGINE_TWIST $(imagine_twist)
#define COFACTOR $(cofactor)
static const int EDWARDS_D = $(d);

#define RISTRETTO_FACTOR $(C_NS)_RISTRETTO_FACTOR
extern const gf RISTRETTO_FACTOR;

/* End of template stuff */

extern mask_t API_NS(deisogenize) (
@@ -134,8 +138,23 @@ API_NS(invert_elligator_nonuniform) (
API_NS(deisogenize)(a,b,c,p,sgn_s,sgn_altx,sgn_ed_T);
mask_t is_identity = gf_eq(p->t,ZERO);
#if COFACTOR==4
gf_cond_sel(b,b,ONE,is_identity & sgn_altx);
gf_cond_sel(c,c,ONE,is_identity & sgn_s &~ sgn_altx);
#elif IMAGINE_TWIST
/* Terrible, terrible special casing due to lots of 0/0 is deisogenize
* Basically we need to generate -D and +- i*RISTRETTO_FACTOR
*/
gf_mul_i(a,RISTRETTO_FACTOR);
gf_cond_sel(b,b,ONE,is_identity);
gf_cond_neg(a,sgn_altx);
gf_cond_sel(c,c,a,is_identity & sgn_ed_T);
gf_cond_sel(c,c,ZERO,is_identity & ~sgn_ed_T);
gf_mulw(a,ONE,-EDWARDS_D);
gf_cond_sel(c,c,a,is_identity & ~sgn_ed_T &~ sgn_altx);
#else
#error "Different special-casing goes here!"
#endif
#if IMAGINE_TWIST
gf_mulw(a,b,-EDWARDS_D);
@@ -158,7 +177,8 @@ API_NS(invert_elligator_nonuniform) (
#endif
gf_cond_neg(b, sgn_r0^gf_lobit(b));
succ &= ~(gf_eq(b,ZERO) & sgn_r0);
/* Eliminate duplicate values for identity ... */
succ &= ~(gf_eq(b,ZERO) & (sgn_r0 | sgn_s));
// #if COFACTOR == 8
// succ &= ~(is_identity & sgn_ed_T); /* NB: there are no preimages of rotated identity. */
// #endif


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