implement circulant multiplication by FFT +tooling
The thing in now used in mce_qcmdpc where possible. Also, some parameter tuning.
This commit is contained in:
parent
23cd287372
commit
3f625e3690
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@ -5,7 +5,7 @@
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NAME="ccr"
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COMMON_CPPFLAGS="-I/usr/local/include"
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COMMON_CFLAGS="-Wall"
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COMMON_CXXFLAGS="${COMMON_CFLAGS}"
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COMMON_CXXFLAGS="${COMMON_CFLAGS} -std=c++11"
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COMMON_LDFLAGS="-L/usr/local/lib"
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COMMON_LDADD=""
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@ -28,7 +28,7 @@ echo "${NAME}_CPPFLAGS = -I\$(srcdir)/$i/ ${COMMON_CPPFLAGS}" >>$OUT
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echo "${NAME}_CFLAGS = ${COMMON_CFLAGS}" >>$OUT
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echo "${NAME}_CXXFLAGS = ${COMMON_CXXFLAGS}" >>$OUT
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echo "${NAME}_LDFLAGS = ${COMMON_LDFLAGS}" >>$OUT
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echo "${NAME}_LDADD = -lgmp @CRYPTOPP_LIBS@ ${COMMON_LDADD} " >>$OUT
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echo "${NAME}_LDADD = -lgmp -lfftw3 -lm @CRYPTOPP_LIBS@ ${COMMON_LDADD} " >>$OUT
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libtoolize --force && aclocal && autoconf && automake --add-missing
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@ -18,6 +18,10 @@ AC_PROG_INSTALL
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AC_CHECK_HEADERS([gmp.h], , AC_MSG_ERROR([Codecrypt requires gmp.h]))
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AC_CHECK_LIB(gmp, __gmpz_init, , AC_MSG_ERROR([Codecrypt requires libgmp]))
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#check for FFTW library presnece
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AC_CHECK_HEADERS([fftw3.h], , AC_MSG_ERROR([Codecrytp requires fftw3.h]))
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AC_CHECK_LIB(fftw3, fftw_plan_dft_1d, , AC_MSG_ERROR([Codecrypt requires libfftw3]))
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#check whether to build with crypto++
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AC_ARG_WITH([cryptopp],
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AC_HELP_STRING([--with-cryptopp],[Build algorithms that need Crypto++ support]),
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@ -108,16 +108,15 @@ algspectable_t& algspectable()
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static bool init = false;
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if (!init) {
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table["enc"] = "MCEQD128FO-CUBE256-CHACHA20";
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table["enc-strong"] = "MCEQD192FO-CUBE384-CHACHA20";
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table["enc-strongest"] = "MCEQD256FO-CUBE512-CHACHA20";
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table["enc"] = "MCEQCMDPC128FO-CUBE256-CHACHA20";
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table["enc-256"] = "MCEQCMDPC256FO-CUBE512-CHACHA20";
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table["sig"] = "FMTSEQ128C-CUBE256-CUBE128";
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table["sig-strong"] = "FMTSEQ192C-CUBE384-CUBE192";
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table["sig-strongest"] = "FMTSEQ256C-CUBE512-CUBE256";
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table["sig-192"] = "FMTSEQ192C-CUBE384-CUBE192";
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table["sig-256"] = "FMTSEQ256C-CUBE512-CUBE256";
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table["sym"] = "chacha20,sha256";
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table["sym-strong"] = "chacha20,xsynd,arcfour,cube512,sha512";
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table["sym-combined"] = "chacha20,xsynd,arcfour,cube512,sha512";
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init = true;
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}
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@ -419,21 +419,21 @@ int algo_mceqcmdpc##name::create_keypair (sencode**pub, sencode**priv, prng&rng)
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#if HAVE_CRYPTOPP==1
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mceqcmdpc_create_keypair_func (128, 9857, 2, 71, 134, 60, 7)
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mceqcmdpc_create_keypair_func (256, 32771, 2, 137, 264, 60, 7)
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mceqcmdpc_create_keypair_func (128cha, 9857, 2, 71, 134, 60, 7)
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mceqcmdpc_create_keypair_func (256cha, 32771, 2, 137, 264, 60, 7)
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mceqcmdpc_create_keypair_func (128xs, 9857, 2, 71, 134, 60, 7)
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mceqcmdpc_create_keypair_func (256xs, 32771, 2, 137, 264, 60, 7)
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mceqcmdpc_create_keypair_func (128, 9857, 2, 71, 134, 60, 5)
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mceqcmdpc_create_keypair_func (256, 32771, 2, 137, 264, 60, 8)
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mceqcmdpc_create_keypair_func (128cha, 9857, 2, 71, 134, 60, 5)
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mceqcmdpc_create_keypair_func (256cha, 32771, 2, 137, 264, 60, 8)
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mceqcmdpc_create_keypair_func (128xs, 9857, 2, 71, 134, 60, 5)
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mceqcmdpc_create_keypair_func (256xs, 32771, 2, 137, 264, 60, 8)
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#endif //HAVE_CRYPTOPP==1
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mceqcmdpc_create_keypair_func (128cube, 9857, 2, 71, 134, 60, 7)
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mceqcmdpc_create_keypair_func (256cube, 32771, 2, 137, 264, 60, 7)
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mceqcmdpc_create_keypair_func (128cubecha, 9857, 2, 71, 134, 60, 7)
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mceqcmdpc_create_keypair_func (256cubecha, 32771, 2, 137, 264, 60, 7)
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mceqcmdpc_create_keypair_func (128cubexs, 9857, 2, 71, 134, 60, 7)
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mceqcmdpc_create_keypair_func (256cubexs, 32771, 2, 137, 264, 60, 7)
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mceqcmdpc_create_keypair_func (128cube, 9857, 2, 71, 134, 60, 5)
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mceqcmdpc_create_keypair_func (256cube, 32771, 2, 137, 264, 60, 8)
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mceqcmdpc_create_keypair_func (128cubecha, 9857, 2, 71, 134, 60, 5)
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mceqcmdpc_create_keypair_func (256cubecha, 32771, 2, 137, 264, 60, 8)
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mceqcmdpc_create_keypair_func (128cubexs, 9857, 2, 71, 134, 60, 5)
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mceqcmdpc_create_keypair_func (256cubexs, 32771, 2, 137, 264, 60, 8)
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#define mceqcmdpc_create_encdec_func(name,bs,bc,errcount,hash_type,pad_hash_type,scipher,ranksize) \
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int algo_mceqcmdpc##name::encrypt (const bvector&plain, bvector&cipher, \
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@ -214,6 +214,91 @@ bool bvector::zero() const
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return true;
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}
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bool bvector::one() const
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{
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//zero padding again
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for (size_t i = 0; i < _data.size(); ++i) if (i == 0) {
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if (_data[i] != 1) return false;
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} else if (_data[i] != 0) return false;
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return true;
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}
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int bvector::degree()
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{
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//find the position of the last non-zero item
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int r;
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for (r = _data.size() - 1; r >= 0; --r) if (_data[r]) break;
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if (r < 0) return -1; //only zeroes.
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uint64_t tmp = _data[r];
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int res = 64 * r;
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while (tmp > 1) {
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++res;
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tmp >>= 1;
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}
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return res;
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}
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void bvector::poly_strip()
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{
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resize (degree() + 1);
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}
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bvector bvector::ext_gcd (const bvector&b, bvector&s0, bvector&t0)
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{
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//result gcd(this,b) = s*this + t*b
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bvector s1, t1;
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s0.clear();
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s1.clear();
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t0.clear();
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t1.clear();
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s0.resize (1, 1);
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t1.resize (1, 1);
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bvector r1 = b;
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bvector r0 = *this;
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for (;;) {
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int d0 = r0.degree();
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int d1 = r1.degree();
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//out ("r0" << r0 << "r1" << r1 << "s0" << s0 << "s1" << s1 << "t0" << t0 << "t1" << t1 << "d0=" << d0 << " d1=" << d1);
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if (d0 < 0) {
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s0.swap (s1);
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t0.swap (t1);
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return r1;
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}
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if (d1 < 0) {
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//this would result in reorganization and failure in
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//next step, return it the other way
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return r0;
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}
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if (d0 > d1) {
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//quotient is zero, reverse the thing manually
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s0.swap (s1);
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t0.swap (t1);
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r0.swap (r1);
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continue;
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}
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//we only consider quotient in form q=x^(log q)
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//("only subtraction, not divmod, still slow")
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int logq = d1 - d0;
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//r(i+1)=r(i-1)-q*r(i)
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//s(i+1)=s(i-1)-q*s(i)
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//t(i+1)=t(i-1)-q*t(i)
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r1.add_offset (r0, logq);
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s1.add_offset (s0, logq);
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t1.add_offset (t0, logq);
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r1.poly_strip();
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s1.poly_strip();
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t1.poly_strip();
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//"rotate" the thing to new positions
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r1.swap (r0);
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s1.swap (s0);
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t1.swap (t0);
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}
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}
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void bvector::from_poly_cotrace (const polynomial&r, gf2m&fld)
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{
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clear();
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@ -100,11 +100,11 @@ private:
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return s >> 6;
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}
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void fix_padding();
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protected:
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_ccr_declare_vector_item
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public:
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void fix_padding();
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bvector() {
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_size = 0;
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}
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@ -176,13 +176,15 @@ public:
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uint hamming_weight();
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void append (const bvector&);
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void add (const bvector&);
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void add_offset (const bvector&, size_t offset_from, size_t offset_to, size_t cnt = 0);
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void add_offset (const bvector&,
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size_t offset_from, size_t offset_to,
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size_t cnt = 0);
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void add_offset (const bvector&, size_t offset_to);
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void add_range (const bvector&, size_t, size_t);
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void rot_add (const bvector&, size_t);
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void set_block (const bvector&, size_t);
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void get_block (size_t, size_t, bvector&) const;
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void get_block (size_t start, size_t cnt, bvector&) const;
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uint and_hamming_weight (const bvector&) const;
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inline bool operator* (const bvector&a) const {
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@ -191,6 +193,11 @@ public:
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}
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bool zero() const;
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bool one() const;
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int degree();
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void poly_strip();
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bvector ext_gcd (const bvector&b, bvector&s, bvector&t);
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void from_poly_cotrace (const polynomial&, gf2m&);
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71
src/fft.cpp
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71
src/fft.cpp
Normal file
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@ -0,0 +1,71 @@
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/*
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* This file is part of Codecrypt.
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*
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* Codecrypt is free software: you can redistribute it and/or modify it
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* under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or (at
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* your option) any later version.
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*
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* Codecrypt is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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* License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with Codecrypt. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "fft.h"
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#include <complex.h>
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#include <fftw3.h>
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#include <math.h>
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/*
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* FFTW wraparound for performing fast multiplication of cyclic matrices.
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*
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* It would probably be cool to save wisdom manually or generate better plans,
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* but since we're usually doing less than 10 FFTs for each run of codecrypt,
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* the thing doesn't pay off. Feel free to implement it.
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*/
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#include "iohelpers.h"
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void fft (bool forward, std::vector<dcx>&in, std::vector<dcx>&out)
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{
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fftw_plan p;
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out.resize (in.size(), dcx (0, 0));
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p = fftw_plan_dft_1d (in.size(),
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//Cin, Cout,
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reinterpret_cast<fftw_complex*> (in.data()),
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reinterpret_cast<fftw_complex*> (out.data()),
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forward ? FFTW_FORWARD : FFTW_BACKWARD,
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FFTW_ESTIMATE);
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if (!forward)
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for (size_t i = 0; i < out.size(); ++i)
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out[i] /= (double) out.size();
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fftw_execute (p);
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fftw_destroy_plan (p);
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}
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void fft (bvector&inb, std::vector<dcx>&out)
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{
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std::vector<dcx> in;
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in.resize (inb.size(), dcx (0, 0));
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for (size_t i = 0; i < inb.size(); ++i) if (inb[i]) in[i] = dcx (1, 0);
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fft (true, in, out);
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}
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void fft (std::vector<dcx>&in, bvector&outb)
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{
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std::vector<dcx> out;
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fft (false, in, out);
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outb.resize (out.size());
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outb.fill_zeros();
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for (size_t i = 0; i < out.size(); ++i)
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if (1 & (int) round (out[i].real())) outb[i] = 1;
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}
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32
src/fft.h
Normal file
32
src/fft.h
Normal file
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@ -0,0 +1,32 @@
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/*
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* This file is part of Codecrypt.
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*
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* Codecrypt is free software: you can redistribute it and/or modify it
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* under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or (at
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* your option) any later version.
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*
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* Codecrypt is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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* License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with Codecrypt. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef _ccr_fft_h_
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#define _ccr_fft_h_
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#include "bvector.h"
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#include <complex>
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typedef std::complex<double> dcx;
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void fft (bool forward, std::vector<dcx>&in, std::vector<dcx>&out);
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//direct conversion from/to GF(2)
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void fft (bvector&in, std::vector<dcx>&out);
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void fft (std::vector<dcx>&in, bvector&out);
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#endif
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@ -18,78 +18,99 @@
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#include "mce_qcmdpc.h"
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#include "gf2m.h"
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#include "polynomial.h"
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#include "fft.h"
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#include <cmath>
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using namespace mce_qcmdpc;
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using namespace std;
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#include "iohelpers.h"
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#include "ios.h"
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int mce_qcmdpc::generate (pubkey&pub, privkey&priv, prng&rng,
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uint block_size, uint block_count, uint wi,
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uint t, uint rounds, uint delta)
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{
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uint i, j;
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priv.H.resize (block_count);
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if (wi > block_size / 2) return 1; //safety
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priv.H.resize (block_count);
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pub.G.resize (block_count - 1);
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/*
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* Trick. Cyclomatic matrix of size n is invertible if a
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* polynomial that's made up from its first row is coprime to
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* (x^n-1), the polynomial inversion and matrix inversion are
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* then isomorphic.
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* Cyclic matrices are diagonalizable by FFT so this stuff gets pretty
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* fast. Otherwise they behave like simple polynomials over GF(2) mod
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* (1+x^n).
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*/
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gf2m gf;
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gf.create (1); //binary
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polynomial xmm1; //x^m-1
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xmm1.resize (block_size + 1, 0);
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xmm1[0] = 1;
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xmm1[block_size] = 1;
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polynomial last_inv_H;
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vector<dcx> H_last_inv;
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for (;;) {
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//retry generating the rightmost block until it is invertible
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polynomial g;
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g.resize (block_size, 0);
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bvector Hb;
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Hb.resize (block_size, 0);
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for (i = 0; i < wi; ++i)
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for (uint pos = rng.random (block_size);
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g[pos] ? 1 : (g[pos] = 1, 0);
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Hb[pos] ? 1 : (Hb[pos] = 1, 0);
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pos = rng.random (block_size));
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//try if it is coprime to (x^n-1)
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polynomial gcd = g.gcd (xmm1, gf);
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if (!gcd.one()) continue; //it isn't.
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bvector xnm1, Hb_inv, tmp;
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xnm1.resize (block_size + 1, 0);
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xnm1[0] = 1;
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xnm1[block_size] = 1; //poly (x^n-1) in gf(2)
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//if it is, save it to matrix (in "reverse" order for columns)
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priv.H[block_count - 1].resize (block_size, 0);
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for (i = 0; i < block_size && i < g.size(); ++i)
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priv.H[block_count - 1][i] = g[ (-i) % block_size];
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/*
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* TODO This is quadratic, speed it up.
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*
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* No one actually cares about keygen speed yet, but this can
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* be done in O(n*log(n)) using Schönhage-Strassen algorithm.
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* If speed is required (e.g. for SPF in some ssl replacement,
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* *wink* *wink*), use libNTL's GF2X.
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*
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* NTL one uses simpler Karatsuba with ~O(n^1.58) which should
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* (according to wikipedia) be faster for sizes under 32k bits
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* because of constant factors involved.
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||||
*/
|
||||
bvector rem = Hb.ext_gcd (xnm1, Hb_inv, tmp);
|
||||
if (!rem.one()) continue; //not invertible, retry
|
||||
if (Hb_inv.size() > block_size) continue; //totally weird.
|
||||
Hb_inv.resize (block_size, 0); //pad polynomial with zeros
|
||||
|
||||
//invert it, save for later and succeed.
|
||||
g.inv (xmm1, gf);
|
||||
last_inv_H = g;
|
||||
break;
|
||||
//if it is, save it to matrix
|
||||
priv.H[block_count - 1] = Hb;
|
||||
|
||||
//precompute the fft of the inverted last block
|
||||
fft (Hb_inv, H_last_inv);
|
||||
|
||||
break; //success
|
||||
}
|
||||
|
||||
//generate the rests of matrix blocks, fill the G right away.
|
||||
pub.G.resize (block_count - 1);
|
||||
for (i = 0; i < block_count - 1; ++i) {
|
||||
polynomial hi;
|
||||
hi.resize (block_size, 0);
|
||||
bvector Hb;
|
||||
Hb.resize (block_size, 0);
|
||||
|
||||
//generate the polynomial corresponding to the first row
|
||||
for (j = 0; j < wi; ++j)
|
||||
for (uint pos = rng.random (block_size);
|
||||
hi[pos] ? 1 : (hi[pos] = 1, 0);
|
||||
Hb[pos] ? 1 : (Hb[pos] = 1, 0);
|
||||
pos = rng.random (block_size));
|
||||
|
||||
//save it to H
|
||||
priv.H[i].resize (block_size);
|
||||
for (j = 0; j < block_size; ++j) priv.H[i][j] = hi[ (-j) % block_size];
|
||||
priv.H[i] = Hb;
|
||||
|
||||
//compute inv(H[last])*H[i]
|
||||
hi.mult (last_inv_H, gf);
|
||||
hi.mod (xmm1, gf);
|
||||
vector<dcx> H;
|
||||
fft (Hb, H);
|
||||
for (j = 0; j < block_size; ++j)
|
||||
H[j] *= H_last_inv[j];
|
||||
fft (H, Hb);
|
||||
|
||||
//save it to G
|
||||
pub.G[i].resize (block_size);
|
||||
for (j = 0; j < block_size; ++j) pub.G[i][j] = hi[j % block_size];
|
||||
pub.G[i] = Hb;
|
||||
pub.G[i].resize (block_size, 0);
|
||||
//for (j = 0; j < block_size; ++j) pub.G[i][j] = Hb[j];
|
||||
}
|
||||
|
||||
//save the target params
|
||||
|
|
@ -128,18 +149,37 @@ int pubkey::encrypt (const bvector&in, bvector&out, const bvector&errors)
|
|||
uint ps = plain_size();
|
||||
if (in.size() != ps) return 1;
|
||||
uint bs = G[0].size();
|
||||
for (uint i = 1; i < G.size(); ++i) if (G[i].size() != bs) return 1; //prevent mangled keys
|
||||
uint blocks = G.size();
|
||||
for (uint i = 1; i < blocks; ++i)
|
||||
if (G[i].size() != bs) return 1; //prevent mangled keys
|
||||
|
||||
//first, the checksum part
|
||||
bvector bcheck;
|
||||
vector<dcx> bcheck, Pd, Gd;
|
||||
bcheck.resize (bs, dcx (0, 0)); //initially zero
|
||||
bvector block;
|
||||
|
||||
//G stores first row(s) of the circulant matrix blocks, proceed row-by-row and construct the checkum
|
||||
for (uint i = 0; i < ps; ++i)
|
||||
if (in[i]) bcheck.rot_add (G[ (i % ps) / bs], i % bs);
|
||||
/*
|
||||
* G stores first row(s) of the circulant matrix blocks. Proceed block
|
||||
* by block and construct the checksum.
|
||||
*
|
||||
* On a side note, it would be cool to store the G already pre-FFT'd,
|
||||
* but the performance gain wouldn't be interesting enough to
|
||||
* compensate for 128 times larger public key (each bit would get
|
||||
* expanded to two doubles). Do it if you want to encrypt bulk data.
|
||||
*/
|
||||
|
||||
for (size_t i = 0; i < blocks; ++i) {
|
||||
in.get_block (i * bs, bs, block);
|
||||
fft (block, Pd);
|
||||
fft (G[i], Gd);
|
||||
for (size_t j = 0; j < bs; ++j)
|
||||
bcheck[j] += Pd[j] * Gd[j];
|
||||
}
|
||||
|
||||
//compute the ciphertext
|
||||
out = in;
|
||||
out.append (bcheck);
|
||||
fft (bcheck, block); //get the checksum part
|
||||
out.append (block);
|
||||
out.add (errors);
|
||||
|
||||
return 0;
|
||||
|
|
@ -155,53 +195,73 @@ int privkey::decrypt (const bvector & in, bvector & out)
|
|||
|
||||
int privkey::decrypt (const bvector & in_orig, bvector & out, bvector & errors)
|
||||
{
|
||||
uint i;
|
||||
uint i, j;
|
||||
uint cs = cipher_size();
|
||||
|
||||
if (in_orig.size() != cs) return 1;
|
||||
uint bs;
|
||||
bs = H[0].size();
|
||||
uint bs = H[0].size();
|
||||
uint blocks = H.size();
|
||||
for (i = 1; i < blocks; ++i) if (H[i].size() != bs) return 2;
|
||||
|
||||
bvector in = in_orig; //we will modify this.
|
||||
|
||||
/*
|
||||
* probabilistic decoding!
|
||||
*/
|
||||
|
||||
//compute the syndrome first
|
||||
bvector syndrome;
|
||||
syndrome.resize (bs, 0);
|
||||
bvector in = in_orig; //we will modify it
|
||||
vector<dcx> synd_diag, tmp, Htmp;
|
||||
synd_diag.resize (bs, dcx (0, 0));
|
||||
|
||||
for (i = 0; i < cs; ++i) if (in[i])
|
||||
syndrome.rot_add (H[i / bs], (cs - i) % bs);
|
||||
|
||||
//minimize counts of unsatisfied equations by flipping
|
||||
std::vector<uint> unsatisfied;
|
||||
unsatisfied.resize (cs, 0);
|
||||
|
||||
for (i = 0; i < rounds; ++i) {
|
||||
uint bit, max_unsat;
|
||||
bvector tmp;
|
||||
max_unsat = 0;
|
||||
for (bit = 0; bit < cs; ++bit) {
|
||||
tmp.fill_zeros();
|
||||
tmp.rot_add (H[bit / bs], (cs - bit) % bs);
|
||||
unsatisfied[bit] = tmp.and_hamming_weight (syndrome);
|
||||
if (unsatisfied[bit] > max_unsat) max_unsat = unsatisfied[bit];
|
||||
//precompute the syndrome
|
||||
for (i = 0; i < blocks; ++i) {
|
||||
bvector b;
|
||||
b.resize (bs, 0);
|
||||
b.add_offset (in, bs * i, 0, bs);
|
||||
fft (b, tmp);
|
||||
fft (H[i], Htmp);
|
||||
for (j = 0; j < bs; ++j) synd_diag[j] += Htmp[j] * tmp[j];
|
||||
}
|
||||
|
||||
//TODO what about timing attacks?
|
||||
bvector (syndrome);
|
||||
fft (synd_diag, syndrome);
|
||||
|
||||
vector<unsigned> unsat;
|
||||
unsat.resize (cs, 0);
|
||||
|
||||
for (i = 0; i < rounds; ++i) {
|
||||
|
||||
/*
|
||||
* count the correlations, abuse the sparsity of matrices.
|
||||
*
|
||||
* TODO this is the slowest part of the whole thing. It's all
|
||||
* probabilistic, maybe there could be some potential to speed
|
||||
* it up by discarding some (already missing) precision.
|
||||
*/
|
||||
|
||||
for (j = 0; j < cs; ++j) unsat[j] = 0;
|
||||
for (uint Hi = 0; Hi < cs; ++Hi)
|
||||
if (H[Hi / bs][Hi % bs]) {
|
||||
uint blk = Hi / bs;
|
||||
for (j = 0; j < bs; ++j)
|
||||
if (syndrome[j])
|
||||
++unsat[blk * bs +
|
||||
(j + cs - Hi) % bs];
|
||||
}
|
||||
|
||||
uint max_unsat = 0;
|
||||
for (j = 0; j < cs; ++j)
|
||||
if (unsat[j] > max_unsat) max_unsat = unsat[j];
|
||||
if (!max_unsat) break;
|
||||
//TODO what about timing attacks? :]
|
||||
|
||||
uint threshold = 0;
|
||||
if (max_unsat > delta) threshold = max_unsat - delta;
|
||||
|
||||
//TODO also timing (but it gets pretty statistically hard here I guess)
|
||||
uint flipped = 0;
|
||||
for (bit = 0; bit < cs; ++bit)
|
||||
if (unsatisfied[bit] > threshold) {
|
||||
for (uint bit = 0; bit < cs; ++bit)
|
||||
if (unsat[bit] > threshold) {
|
||||
in[bit] = !in[bit];
|
||||
syndrome.rot_add (H[bit / bs], (cs - bit) % bs);
|
||||
++flipped;
|
||||
syndrome.rot_add (H[bit / bs], bit % bs);
|
||||
}
|
||||
}
|
||||
|
||||
|
|
|
|||
Loading…
Reference in a new issue