Commit ece7af39 authored by Niels Möller's avatar Niels Möller

Merge branch 'curve25519'

parents 19ef5194 eec8e972
This diff is collapsed.
......@@ -164,18 +164,23 @@ hogweed_SOURCES = sexp.c sexp-format.c \
ecc-mod.c ecc-generic-modp.c ecc-generic-modq.c \
ecc-modp.c ecc-modq.c ecc-generic-redc.c \
ecc-192.c ecc-224.c ecc-256.c ecc-384.c ecc-521.c \
ecc-25519.c \
ecc-size.c ecc-j-to-a.c ecc-a-to-j.c \
ecc-dup-jj.c ecc-add-jja.c ecc-add-jjj.c \
ecc-a-to-eh.c ecc-eh-to-a.c \
ecc-dup-eh.c ecc-add-eh.c ecc-add-ehh.c \
ecc-mul-g-eh.c ecc-mul-a-eh.c \
ecc-mul-g.c ecc-mul-a.c ecc-hash.c ecc-random.c \
ecc-point.c ecc-scalar.c ecc-point-mul.c ecc-point-mul-g.c \
ecc-ecdsa-sign.c ecdsa-sign.c \
ecc-ecdsa-verify.c ecdsa-verify.c ecdsa-keygen.c \
curve25519-mul-g.c curve25519-mul.c \
$(OPT_HOGWEED_SOURCES)
HEADERS = aes.h arcfour.h arctwo.h asn1.h blowfish.h \
base16.h base64.h buffer.h camellia.h cast128.h \
cbc.h ccm.h chacha.h chacha-poly1305.h ctr.h \
des.h des-compat.h dsa.h dsa-compat.h eax.h \
curve25519.h des.h des-compat.h dsa.h dsa-compat.h eax.h \
ecc-curve.h ecc.h ecdsa.h \
gcm.h gosthash94.h hmac.h \
knuth-lfib.h \
......@@ -347,6 +352,9 @@ ecc-384.h: eccdata.stamp
ecc-521.h: eccdata.stamp
./eccdata$(EXEEXT_FOR_BUILD) 521 56 6 $(GMP_NUMB_BITS) > $@T && mv $@T $@
ecc-25519.h: eccdata.stamp
./eccdata$(EXEEXT_FOR_BUILD) 255 14 6 $(GMP_NUMB_BITS) > $@T && mv $@T $@
eccdata.stamp: eccdata.c
$(MAKE) eccdata$(EXEEXT_FOR_BUILD)
echo stamp > eccdata.stamp
......@@ -356,12 +364,14 @@ ecc-224.$(OBJEXT): ecc-224.h
ecc-256.$(OBJEXT): ecc-256.h
ecc-384.$(OBJEXT): ecc-384.h
ecc-521.$(OBJEXT): ecc-521.h
ecc-25519.$(OBJEXT): ecc-25519.h
ecc-192.p$(OBJEXT): ecc-192.h
ecc-224.p$(OBJEXT): ecc-224.h
ecc-256.p$(OBJEXT): ecc-256.h
ecc-384.p$(OBJEXT): ecc-384.h
ecc-521.p$(OBJEXT): ecc-521.h
ecc-25519.p$(OBJEXT): ecc-25519.h
.asm.s: $(srcdir)/asm.m4 machine.m4 config.m4
$(M4) $(srcdir)/asm.m4 machine.m4 config.m4 $< >$@T \
......@@ -619,7 +629,7 @@ distcheck: dist
clean-here:
-rm -f $(TARGETS) $(IMPLICIT_TARGETS) *.$(OBJEXT) *.p$(OBJEXT) *.s \
ecc-192.h ecc-224.h ecc-256.h ecc-384.h ecc-521.h \
ecc-192.h ecc-224.h ecc-256.h ecc-384.h ecc-521.h ecc-25519.h \
eccdata$(EXEEXT_FOR_BUILD) eccdata.stamp
-rm -rf .lib libnettle.stamp libhogweed.stamp
......
......@@ -285,7 +285,7 @@ asm_nettle_optional_list="gcm-hash8.asm"
asm_hogweed_optional_list=""
if test "x$enable_public_key" = "xyes" ; then
asm_hogweed_optional_list="ecc-192-modp.asm ecc-224-modp.asm \
ecc-256-redc.asm ecc-384-modp.asm ecc-521-modp.asm"
ecc-25519-modp.asm ecc-256-redc.asm ecc-384-modp.asm ecc-521-modp.asm"
fi
OPT_ASM_NETTLE_SOURCES=""
......@@ -365,6 +365,7 @@ AH_VERBATIM([HAVE_NATIVE],
#undef HAVE_NATIVE_ecc_192_redc
#undef HAVE_NATIVE_ecc_224_modp
#undef HAVE_NATIVE_ecc_224_redc
#undef HAVE_NATIVE_ecc_25519_modp
#undef HAVE_NATIVE_ecc_256_modp
#undef HAVE_NATIVE_ecc_256_redc
#undef HAVE_NATIVE_ecc_384_modp
......
/* curve25519-mul-g.c
Copyright (C) 2014 Niels Möller
This file is part of GNU Nettle.
GNU Nettle is free software: you can redistribute it and/or
modify it under the terms of either:
* the GNU Lesser General Public License as published by the Free
Software Foundation; either version 3 of the License, or (at your
option) any later version.
or
* the GNU General Public License as published by the Free
Software Foundation; either version 2 of the License, or (at your
option) any later version.
or both in parallel, as here.
GNU Nettle is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License for more details.
You should have received copies of the GNU General Public License and
the GNU Lesser General Public License along with this program. If
not, see http://www.gnu.org/licenses/.
*/
#if HAVE_CONFIG_H
# include "config.h"
#endif
#include <string.h>
#include "curve25519.h"
#include "ecc.h"
#include "ecc-internal.h"
/* Intended to be compatible with NaCl's crypto_scalarmult_base. */
void
curve25519_mul_g (uint8_t *r, const uint8_t *n)
{
uint8_t t[CURVE25519_SIZE];
mp_limb_t *scratch;
mp_size_t ecc_size;
mp_size_t itch;
#define p scratch
#define x (scratch + 3*ecc_size)
#define scratch_out (scratch + 4*ecc_size)
memcpy (t, n, sizeof(t));
t[0] &= ~7;
t[CURVE25519_SIZE-1] = (t[CURVE25519_SIZE-1] & 0x3f) | 0x40;
ecc_size = nettle_curve25519.size;
itch = 4*ecc_size + ECC_MUL_G_EH_ITCH(ecc_size);
scratch = gmp_alloc_limbs (itch);
mpn_set_base256_le (x, ecc_size, t, CURVE25519_SIZE);
ecc_mul_g_eh (&nettle_curve25519, p, x, scratch_out);
ecc_eh_to_a (&nettle_curve25519, 2, x, p, scratch_out);
mpn_get_base256_le (r, CURVE25519_SIZE, x, ecc_size);
gmp_free_limbs (scratch, itch);
}
/* curve25519-mul.c
Copyright (C) 2014 Niels Möller
This file is part of GNU Nettle.
GNU Nettle is free software: you can redistribute it and/or
modify it under the terms of either:
* the GNU Lesser General Public License as published by the Free
Software Foundation; either version 3 of the License, or (at your
option) any later version.
or
* the GNU General Public License as published by the Free
Software Foundation; either version 2 of the License, or (at your
option) any later version.
or both in parallel, as here.
GNU Nettle is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License for more details.
You should have received copies of the GNU General Public License and
the GNU Lesser General Public License along with this program. If
not, see http://www.gnu.org/licenses/.
*/
#if HAVE_CONFIG_H
# include "config.h"
#endif
#include <string.h>
#include "curve25519.h"
#include "ecc.h"
#include "ecc-internal.h"
/* Intended to be compatible with NaCl's crypto_scalarmult. NOTE: Not
side-channel silent, due to the sqrt. */
int
curve25519_mul (uint8_t *q, const uint8_t *n, const uint8_t *p)
{
uint8_t t[CURVE25519_SIZE];
mp_size_t itch;
mp_limb_t *scratch;
const struct ecc_curve *ecc = &nettle_curve25519;
#define x scratch
#define y (scratch + ecc->size)
#define s (scratch + 3*ecc->size)
#define scratch_out (scratch + 4*ecc->size)
itch = 5*ecc->size + ECC_MUL_A_EH_ITCH (ecc->size);
scratch = gmp_alloc_limbs (itch);
mpn_set_base256_le (x, ecc->size, p, CURVE25519_SIZE);
/* First compute y coordinate, from
y^2 = x^3 + b x^2 + x = (x^2 + bx + 1) x
*/
ecc_modp_sqr (&nettle_curve25519, y, x);
ecc_modp_addmul_1 (&nettle_curve25519, y, x, 0x76d06ULL);
ecc_modp_add (ecc, s, y, ecc->unit);
ecc_modp_mul (ecc, y, s, x);
/* FIXME: Pass s as scratch space to ecc_25519_sqrt */
if (!ecc_25519_sqrt (y, y))
/* y-coordinate doesn't belong to base field F_p. FIXME: Implement
case of y in F_{p^2}? */
return 0;
memcpy (t, n, sizeof(t));
t[0] &= ~7;
t[CURVE25519_SIZE-1] = (t[CURVE25519_SIZE-1] & 0x3f) | 0x40;
mpn_set_base256_le (s, ecc->size, t, CURVE25519_SIZE);
ecc_mul_a_eh (ecc, x, s, x, scratch_out);
ecc_eh_to_a (ecc, 2, s, x, scratch_out);
mpn_get_base256_le (q, CURVE25519_SIZE, s, ecc->size);
gmp_free_limbs (scratch, itch);
return 1;
}
/* curve25519.h
Copyright (C) 2014 Niels Möller
This file is part of GNU Nettle.
GNU Nettle is free software: you can redistribute it and/or
modify it under the terms of either:
* the GNU Lesser General Public License as published by the Free
Software Foundation; either version 3 of the License, or (at your
option) any later version.
or
* the GNU General Public License as published by the Free
Software Foundation; either version 2 of the License, or (at your
option) any later version.
or both in parallel, as here.
GNU Nettle is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License for more details.
You should have received copies of the GNU General Public License and
the GNU Lesser General Public License along with this program. If
not, see http://www.gnu.org/licenses/.
*/
#ifndef NETTLE_CURVE25519_H
#define NETTLE_CURVE25519_H
#include "nettle-types.h"
#ifdef __cplusplus
extern "C" {
#endif
/* Name mangling */
#define curve25519_mul_g nettle_curve25519_mul_g
#define curve25519_mul nettle_curve25519_mul
#define CURVE25519_SIZE 32
void
curve25519_mul_g (uint8_t *q, const uint8_t *n);
int
curve25519_mul (uint8_t *q, const uint8_t *n, const uint8_t *p);
#endif /* NETTLE_CURVE25519_H */
......@@ -39,6 +39,9 @@
#include <assert.h>
/* FIXME: Remove ecc.h include, once prototypes of more internal
functions are moved to ecc-internal.h */
#include "ecc.h"
#include "ecc-internal.h"
#define USE_REDC 0
......@@ -117,15 +120,26 @@ const struct ecc_curve nettle_secp_192r1 =
ECC_REDC_SIZE,
ECC_PIPPENGER_K,
ECC_PIPPENGER_C,
ECC_MUL_A_ITCH (ECC_LIMB_SIZE),
ECC_MUL_G_ITCH (ECC_LIMB_SIZE),
ECC_J_TO_A_ITCH (ECC_LIMB_SIZE),
ecc_192_modp,
ecc_generic_redc,
ecc_192_modp,
ecc_generic_modq,
ecc_mul_a,
ecc_mul_g,
ecc_j_to_a,
ecc_p,
ecc_b,
ecc_q,
ecc_g,
ecc_redc_g,
ecc_192_modp,
ecc_generic_redc,
ecc_192_modp,
ecc_generic_modq,
NULL,
ecc_Bmodp,
ecc_Bmodp_shifted,
ecc_pp1h,
......
......@@ -37,6 +37,7 @@
# include "config.h"
#endif
#include "ecc.h"
#include "ecc-internal.h"
#if HAVE_NATIVE_ecc_224_modp
......@@ -63,15 +64,26 @@ const struct ecc_curve nettle_secp_224r1 =
ECC_REDC_SIZE,
ECC_PIPPENGER_K,
ECC_PIPPENGER_C,
ECC_MUL_A_ITCH (ECC_LIMB_SIZE),
ECC_MUL_G_ITCH (ECC_LIMB_SIZE),
ECC_J_TO_A_ITCH (ECC_LIMB_SIZE),
ecc_224_modp,
ecc_generic_redc,
USE_REDC ? ecc_generic_redc : ecc_224_modp,
ecc_generic_modq,
ecc_mul_a,
ecc_mul_g,
ecc_j_to_a,
ecc_p,
ecc_b,
ecc_q,
ecc_g,
ecc_redc_g,
ecc_224_modp,
ecc_generic_redc,
USE_REDC ? ecc_generic_redc : ecc_224_modp,
ecc_generic_modq,
NULL,
ecc_Bmodp,
ecc_Bmodp_shifted,
ecc_pp1h,
......
/* ecc-25519.c
Arithmetic and tables for curve25519,
Copyright (C) 2014 Niels Möller
This file is part of GNU Nettle.
GNU Nettle is free software: you can redistribute it and/or
modify it under the terms of either:
* the GNU Lesser General Public License as published by the Free
Software Foundation; either version 3 of the License, or (at your
option) any later version.
or
* the GNU General Public License as published by the Free
Software Foundation; either version 2 of the License, or (at your
option) any later version.
or both in parallel, as here.
GNU Nettle is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License for more details.
You should have received copies of the GNU General Public License and
the GNU Lesser General Public License along with this program. If
not, see http://www.gnu.org/licenses/.
*/
#if HAVE_CONFIG_H
# include "config.h"
#endif
#include <assert.h>
#include "ecc.h"
#include "ecc-internal.h"
#define USE_REDC 0
#include "ecc-25519.h"
#if HAVE_NATIVE_ecc_25519_modp
#define ecc_25519_modp nettle_ecc_25519_modp
void
ecc_25519_modp (const struct ecc_curve *ecc, mp_limb_t *rp);
#else
#define PHIGH_BITS (GMP_NUMB_BITS * ECC_LIMB_SIZE - 255)
#if PHIGH_BITS == 0
#error Unsupported limb size */
#endif
static void
ecc_25519_modp(const struct ecc_curve *ecc UNUSED, mp_limb_t *rp)
{
mp_limb_t hi, cy;
cy = mpn_addmul_1 (rp, rp + ECC_LIMB_SIZE, ECC_LIMB_SIZE,
(mp_limb_t) 19 << PHIGH_BITS);
hi = rp[ECC_LIMB_SIZE-1];
cy = (cy << PHIGH_BITS) + (hi >> (GMP_NUMB_BITS - PHIGH_BITS));
rp[ECC_LIMB_SIZE-1] = (hi & (GMP_NUMB_MASK >> PHIGH_BITS))
+ sec_add_1 (rp, rp, ECC_LIMB_SIZE - 1, 19 * cy);
}
#endif /* HAVE_NATIVE_ecc_25519_modp */
#define QHIGH_BITS (GMP_NUMB_BITS * ECC_LIMB_SIZE - 252)
#if QHIGH_BITS == 0
#error Unsupported limb size */
#endif
static void
ecc_25519_modq (const struct ecc_curve *ecc, mp_limb_t *rp)
{
mp_size_t n;
mp_limb_t cy;
/* n is the offset where we add in the next term */
for (n = ECC_LIMB_SIZE; n-- > 0;)
{
mp_limb_t cy;
cy = mpn_submul_1 (rp + n,
ecc->Bmodq_shifted, ECC_LIMB_SIZE,
rp[n + ECC_LIMB_SIZE]);
/* Top limb of mBmodq_shifted is zero, so we get cy == 0 or 1 */
assert (cy < 2);
cnd_add_n (cy, rp+n, ecc_q, ECC_LIMB_SIZE);
}
cy = mpn_submul_1 (rp, ecc_q, ECC_LIMB_SIZE,
rp[ECC_LIMB_SIZE-1] >> (GMP_NUMB_BITS - QHIGH_BITS));
assert (cy < 2);
cnd_add_n (cy, rp, ecc_q, ECC_LIMB_SIZE);
}
/* Needs 2*ecc->size limbs at rp, and 2*ecc->size additional limbs of
scratch space. No overlap allowed. */
static void
ecc_modp_powm_2kp1 (const struct ecc_curve *ecc,
mp_limb_t *rp, const mp_limb_t *xp,
unsigned k, mp_limb_t *tp)
{
if (k & 1)
{
ecc_modp_sqr (ecc, tp, xp);
k--;
}
else
{
ecc_modp_sqr (ecc, rp, xp);
ecc_modp_sqr (ecc, tp, rp);
k -= 2;
}
while (k > 0)
{
ecc_modp_sqr (ecc, rp, tp);
ecc_modp_sqr (ecc, tp, rp);
k -= 2;
}
ecc_modp_mul (ecc, rp, tp, xp);
#undef t1
#undef t2
}
/* Compute x such that x^2 = a (mod p). Returns one on success, zero
on failure. using the e == 2 special case of the Shanks-Tonelli
algorithm (see http://www.math.vt.edu/people/brown/doc/sqrts.pdf,
or Henri Cohen, Computational Algebraic Number Theory, 1.5.1.
NOTE: Not side-channel silent. FIXME: Compute square root in the
extended field if a isn't a square (mod p)? FIXME: Accept scratch
space from caller (could allow scratch == rp). */
#if ECC_SQRT_E != 2
#error Broken curve25519 parameters
#endif
int
ecc_25519_sqrt(mp_limb_t *rp, const mp_limb_t *ap)
{
mp_size_t itch;
mp_limb_t *scratch;
int res;
const struct ecc_curve *ecc = &nettle_curve25519;
itch = 7*ECC_LIMB_SIZE;
scratch = gmp_alloc_limbs (itch);
#define t0 scratch
#define a7 (scratch + 2*ECC_LIMB_SIZE)
#define t1 (scratch + 3*ECC_LIMB_SIZE)
#define t2 (scratch + 5*ECC_LIMB_SIZE)
#define scratch_out (scratch + 3*ECC_LIMB_SIZE) /* overlap t1, t2 */
#define xp (scratch + ECC_LIMB_SIZE)
#define bp (scratch + 2*ECC_LIMB_SIZE)
/* a^{2^252 - 3} = a^{(p-5)/8}, using the addition chain
2^252 - 3
= 1 + (2^252-4)
= 1 + 4 (2^250-1)
= 1 + 4 (2^125+1)(2^125-1)
= 1 + 4 (2^125+1)(1+2(2^124-1))
= 1 + 4 (2^125+1)(1+2(2^62+1)(2^62-1))
= 1 + 4 (2^125+1)(1+2(2^62+1)(2^31+1)(2^31-1))
= 1 + 4 (2^125+1)(1+2(2^62+1)(2^31+1)(7+8(2^28-1)))
= 1 + 4 (2^125+1)(1+2(2^62+1)(2^31+1)(7+8(2^14+1)(2^14-1)))
= 1 + 4 (2^125+1)(1+2(2^62+1)(2^31+1)(7+8(2^14+1)(2^7+1)(2^7-1)))
= 1 + 4 (2^125+1)(1+2(2^62+1)(2^31+1)(7+8(2^14+1)(2^7+1)(1+2(2^6-1))))
= 1 + 4 (2^125+1)(1+2(2^62+1)(2^31+1)(7+8(2^14+1)(2^7+1)(1+2(2^3+1)*7)))
*/
ecc_modp_powm_2kp1 (ecc, t1, ap, 1, t2); /* a^3 */
ecc_modp_sqr (ecc, t0, t1); /* a^6 */
ecc_modp_mul (ecc, a7, t0, ap); /* a^7 */
ecc_modp_powm_2kp1 (ecc, t0, a7, 3, t1); /* a^63 = a^{2^6-1} */
ecc_modp_sqr (ecc, t1, t0); /* a^{2^7-2} */
ecc_modp_mul (ecc, t0, t1, ap); /* a^{2^7-1} */
ecc_modp_powm_2kp1 (ecc, t1, t0, 7, t2); /* a^{2^14-1}*/
ecc_modp_powm_2kp1 (ecc, t0, t1, 14, t2); /* a^{2^28-1} */
ecc_modp_sqr (ecc, t1, t0); /* a^{2^29-2} */
ecc_modp_sqr (ecc, t2, t1); /* a^{2^30-4} */
ecc_modp_sqr (ecc, t1, t2); /* a^{2^31-8} */
ecc_modp_mul (ecc, t0, t1, a7); /* a^{2^31-1} */
ecc_modp_powm_2kp1 (ecc, t1, t0, 31, t2); /* a^{2^62-1} */
ecc_modp_powm_2kp1 (ecc, t0, t1, 62, t2); /* a^{2^124-1}*/
ecc_modp_sqr (ecc, t1, t0); /* a^{2^125-2} */
ecc_modp_mul (ecc, t0, t1, ap); /* a^{2^125-1} */
ecc_modp_powm_2kp1 (ecc, t1, t0, 125, t2); /* a^{2^250-1} */
ecc_modp_sqr (ecc, t0, t1); /* a^{2^251-2} */
ecc_modp_sqr (ecc, t1, t0); /* a^{2^252-4} */
ecc_modp_mul (ecc, t0, t1, ap); /* a^{2^252-3} */
/* Compute candidate root x and fudgefactor b. */
ecc_modp_mul (ecc, xp, t0, ap); /* a^{(p+3)/8 */
ecc_modp_mul (ecc, bp, t0, xp); /* a^{(p-1)/4} */
/* Check if b == 1 (mod p) */
if (mpn_cmp (bp, ecc->p, ECC_LIMB_SIZE) >= 0)
mpn_sub_n (bp, bp, ecc->p, ECC_LIMB_SIZE);
if (mpn_cmp (bp, ecc->unit, ECC_LIMB_SIZE) == 0)
{
mpn_copyi (rp, xp, ECC_LIMB_SIZE);
res = 1;
}
else
{
mpn_add_1 (bp, bp, ECC_LIMB_SIZE, 1);
if (mpn_cmp (bp, ecc->p, ECC_LIMB_SIZE) == 0)
{
ecc_modp_mul (&nettle_curve25519, bp, xp, ecc_sqrt_z);
mpn_copyi (rp, bp, ECC_LIMB_SIZE);
res = 1;
}
else
res = 0;
}
gmp_free_limbs (scratch, itch);
return res;
#undef t0
#undef t1
#undef t2
#undef a7
#undef xp
#undef bp
#undef scratch_out
}
const struct ecc_curve nettle_curve25519 =
{
255,
ECC_LIMB_SIZE,
ECC_BMODP_SIZE,
ECC_BMODQ_SIZE,
0, /* No redc */
0,
ECC_PIPPENGER_K,
ECC_PIPPENGER_C,
ECC_MUL_A_EH_ITCH (ECC_LIMB_SIZE),
ECC_MUL_G_EH_ITCH (ECC_LIMB_SIZE),
ECC_EH_TO_A_ITCH (ECC_LIMB_SIZE),
ecc_25519_modp,
NULL,
ecc_25519_modp,
ecc_25519_modq,
ecc_mul_a_eh,
ecc_mul_g_eh,
ecc_eh_to_a,
ecc_p,
ecc_d, /* Use the Edwards curve constant. */
ecc_q,
ecc_g,
ecc_redc_g,
ecc_edwards,
ecc_Bmodp,
ecc_Bmodp_shifted,
ecc_pp1h,
ecc_redc_ppm1,
ecc_unit,
ecc_Bmodq,
ecc_mBmodq_shifted, /* Use q - 2^{252} instead. */
ecc_qp1h,
ecc_table
};
......@@ -39,6 +39,7 @@
#include <assert.h>
#include "ecc.h"
#include "ecc-internal.h"
#if HAVE_NATIVE_ecc_256_redc
......@@ -228,15 +229,26 @@ const struct ecc_curve nettle_secp_256r1 =
ECC_REDC_SIZE,
ECC_PIPPENGER_K,
ECC_PIPPENGER_C,