summaryrefslogtreecommitdiffstats
path: root/botan/src/math/gfpmath/gfp_element.cpp
diff options
context:
space:
mode:
Diffstat (limited to 'botan/src/math/gfpmath/gfp_element.cpp')
-rw-r--r--botan/src/math/gfpmath/gfp_element.cpp699
1 files changed, 0 insertions, 699 deletions
diff --git a/botan/src/math/gfpmath/gfp_element.cpp b/botan/src/math/gfpmath/gfp_element.cpp
deleted file mode 100644
index b718093..0000000
--- a/botan/src/math/gfpmath/gfp_element.cpp
+++ /dev/null
@@ -1,699 +0,0 @@
-/******
- * Arithmetic for prime fields GF(p) (source file)
- *
- * (C) 2007 Martin Doering
- * doering@cdc.informatik.tu-darmstadt.de
- * Christoph Ludwig
- * ludwig@fh-worms.de
- * Falko Strenzke
- * strenzke@flexsecure.de
- ******/
-
-#include <botan/gfp_element.h>
-#include <botan/numthry.h>
-#include <botan/def_powm.h>
-#include <botan/mp_types.h>
-#include <botan/mp_asm.h>
-#include <botan/mp_asmi.h>
-#include <assert.h>
-#include <ostream>
-
-namespace Botan {
-
-namespace {
-
-void inner_montg_mult_sos(word result[], const word* a_bar, const word* b_bar, const word* n, const word* n_dash, u32bit s)
- {
- SecureVector<word> t;
- t.grow_to(2*s+1);
-
- // t = a_bar * b_bar
- for (u32bit i=0; i<s; i++)
- {
- word C = 0;
- word S = 0;
- for (u32bit j=0; j<s; j++)
- {
- // we use:
- // word word_madd3(word a, word b, word c, word d, word* carry)
- // returns a * b + c + d and resets the carry (not using it as input)
-
- S = word_madd3(a_bar[j], b_bar[i], t[i+j], &C);
- t[i+j] = S;
- }
- t[i+s] = C;
- }
-
- // ???
- for (u32bit i=0; i<s; i++)
- {
- // word word_madd2(word a, word b, word c, word* carry)
- // returns a * b + c, resets the carry
-
- word C = 0;
- word zero = 0;
- word m = word_madd2(t[i], n_dash[0], &zero);
-
- for (u32bit j=0; j<s; j++)
- {
- word S = word_madd3(m, n[j], t[i+j], &C);
- t[i+j] = S;
- }
-
- //// mp_mulop.cpp:
- ////word bigint_mul_add_words(word z[], const word x[], u32bit x_size, word y)
- u32bit cnt = 0;
- while (C > 0)
- {
- // we need not worry here about C > 1, because the other operand is zero
- word tmp = word_add(t[i+s+cnt], 0, &C);
- t[i+s+cnt] = tmp;
- cnt++;
- }
- }
-
- // u = t
- SecureVector<word> u;
- u.grow_to(s+1);
- for (u32bit j=0; j<s+1; j++)
- {
- u[j] = t[j+s];
- }
-
- // t = u - n
- word B = 0;
- word D = 0;
- for (u32bit i=0; i<s; i++)
- {
- D = word_sub(u[i], n[i], &B);
- t[i] = D;
- }
- D = word_sub(u[s], 0, &B);
- t[s] = D;
-
- // if t >= 0 (B == 0 -> no borrow), return t
- if(B == 0)
- {
- for (u32bit i=0; i<s; i++)
- {
- result[i] = t[i];
- }
- }
- else // else return u
- {
- for (u32bit i=0; i<s; i++)
- {
- result[i] = u[i];
- }
- }
- }
-
-void montg_mult(BigInt& result, BigInt& a_bar, BigInt& b_bar, const BigInt& m, const BigInt& m_dash, const BigInt)
- {
- if(m.is_zero() || m_dash.is_zero())
- throw Invalid_Argument("montg_mult(): neither modulus nor m_dash may be zero (and one of them was)");
-
- if(a_bar.is_zero() || b_bar.is_zero())
- result = 0;
-
- u32bit s = m.sig_words();
- a_bar.grow_to(s);
- b_bar.grow_to(s);
- result.grow_to(s);
-
- inner_montg_mult_sos(result.get_reg(), a_bar.data(), b_bar.data(),
- m.data(), m_dash.data(), s);
- }
-
-/**
-*calculates R=b^n (here b=2) with R>m (and R beeing as small as possible) for an odd modulus m.
-* no check for oddity is performed!
-*
-* Distributed under the terms of the Botan license
-*/
-BigInt montgm_calc_r_oddmod(const BigInt& prime)
- {
- u32bit n = prime.sig_words();
- BigInt result(1);
- result <<= n*BOTAN_MP_WORD_BITS;
- return result;
- }
-
-/**
-*calculates m' with r*r^-1 - m*m' = 1
-* where r^-1 is the multiplicative inverse of r to the modulus m
-*/
-BigInt montgm_calc_m_dash(const BigInt& r, const BigInt& m, const BigInt& r_inv)
- {
- BigInt result = ((r * r_inv) - BigInt(1))/m;
- return result;
- }
-
-BigInt montg_trf_to_mres(const BigInt& ord_res, const BigInt& r, const BigInt& m)
- {
- BigInt result(ord_res);
- result *= r;
- result %= m;
- return result;
- }
-
-BigInt montg_trf_to_ordres(const BigInt& m_res, const BigInt& m, const BigInt& r_inv)
- {
- BigInt result(m_res);
- result *= r_inv;
- result %= m;
- return result;
- }
-
-}
-
-GFpElement::GFpElement(const BigInt& p, const BigInt& value, bool use_montgm)
- : mp_mod(),
- m_value(value %p),
- m_use_montgm(use_montgm),
- m_is_trf(false)
- {
- assert(mp_mod.get() == 0);
- mp_mod = std::tr1::shared_ptr<GFpModulus>(new GFpModulus(p));
- assert(mp_mod->m_p_dash == 0);
- if(m_use_montgm)
- ensure_montgm_precomp();
- }
-
-GFpElement::GFpElement(std::tr1::shared_ptr<GFpModulus> const mod, const BigInt& value, bool use_montgm)
- : mp_mod(),
- m_value(value % mod->m_p),
- m_use_montgm(use_montgm),
- m_is_trf(false)
- {
- assert(mp_mod.get() == 0);
- mp_mod = mod;
- }
-
-GFpElement::GFpElement(const GFpElement& other)
- : m_value(other.m_value),
- m_use_montgm(other.m_use_montgm),
- m_is_trf(other.m_is_trf)
-
- {
- //creates an independent copy
- assert((other.m_is_trf && other.m_use_montgm) || !other.m_is_trf);
- mp_mod.reset(new GFpModulus(*other.mp_mod)); // copy-ctor of GFpModulus
- }
-
-void GFpElement::turn_on_sp_red_mul() const
- {
- ensure_montgm_precomp();
- m_use_montgm = true;
- }
-
-void GFpElement::turn_off_sp_red_mul() const
- {
- if(m_is_trf)
- {
- trf_to_ordres();
- // will happen soon anyway, so we can do it here already
- // (this is not lazy but way more secure concerning our internal logic here)
- }
- m_use_montgm = false;
- }
-
-void GFpElement::ensure_montgm_precomp() const
- {
- if((!mp_mod->m_r.is_zero()) && (!mp_mod->m_r_inv.is_zero()) && (!mp_mod->m_p_dash.is_zero()))
- {
- // values are already set, nothing more to do
- }
- else
- {
- BigInt tmp_r(montgm_calc_r_oddmod(mp_mod->m_p));
-
- BigInt tmp_r_inv(inverse_mod(tmp_r, mp_mod->m_p));
-
- BigInt tmp_p_dash(montgm_calc_m_dash(tmp_r, mp_mod->m_p, tmp_r_inv));
-
- mp_mod->m_r.grow_reg(tmp_r.size());
- mp_mod->m_r_inv.grow_reg(tmp_r_inv.size());
- mp_mod->m_p_dash.grow_reg(tmp_p_dash.size());
-
- mp_mod->m_r = tmp_r;
- mp_mod->m_r_inv = tmp_r_inv;
- mp_mod->m_p_dash = tmp_p_dash;
-
- assert(!mp_mod->m_r.is_zero());
- assert(!mp_mod->m_r_inv.is_zero());
- assert(!mp_mod->m_p_dash.is_zero());
- }
-
- }
-
-void GFpElement::set_shrd_mod(std::tr1::shared_ptr<GFpModulus> const p_mod)
- {
- mp_mod = p_mod;
- }
-
-void GFpElement::trf_to_mres() const
- {
- if(!m_use_montgm)
- {
- throw Illegal_Transformation("GFpElement is not allowed to be transformed to m-residue");
- }
- assert(m_is_trf == false);
- assert(!mp_mod->m_r_inv.is_zero());
- assert(!mp_mod->m_p_dash.is_zero());
- m_value = montg_trf_to_mres(m_value, mp_mod->m_r, mp_mod->m_p);
- m_is_trf = true;
- }
-
-void GFpElement::trf_to_ordres() const
- {
- assert(m_is_trf == true);
- m_value = montg_trf_to_ordres(m_value, mp_mod->m_p, mp_mod->m_r_inv);
- m_is_trf = false;
- }
-
-bool GFpElement::align_operands_res(const GFpElement& lhs, const GFpElement& rhs) //static
- {
- assert(lhs.mp_mod->m_p == rhs.mp_mod->m_p);
- if(lhs.m_use_montgm && rhs.m_use_montgm)
- {
- assert(rhs.mp_mod->m_p_dash == lhs.mp_mod->m_p_dash);
- assert(rhs.mp_mod->m_r == lhs.mp_mod->m_r);
- assert(rhs.mp_mod->m_r_inv == lhs.mp_mod->m_r_inv);
- if(!lhs.m_is_trf && !rhs.m_is_trf)
- {
- return false;
- }
- else if(lhs.m_is_trf && rhs.m_is_trf)
- {
- return true;
- }
- else // one is transf., the other not
- {
- if(!lhs.m_is_trf)
- {
- lhs.trf_to_mres();
- assert(rhs.m_is_trf==true);
- return true;
- }
- assert(rhs.m_is_trf==false);
- assert(lhs.m_is_trf==true);
- rhs.trf_to_mres(); // the only possibility left...
- return true;
- }
- }
- else // at least one of them does not use mm
- // (so it is impossible that both use it)
- {
- if(lhs.m_is_trf)
- {
- lhs.trf_to_ordres();
- assert(rhs.m_is_trf == false);
- return false;
- }
- if(rhs.m_is_trf)
- {
- rhs.trf_to_ordres();
- assert(lhs.m_is_trf == false);
- return false;
- }
- return false;
- }
- assert(false);
- }
-
-bool GFpElement::is_trf_to_mres() const
- {
- return m_is_trf;
- }
-
-const BigInt& GFpElement::get_p() const
- {
- return (mp_mod->m_p);
- }
-
-const BigInt& GFpElement::get_value() const
- {
- if(m_is_trf)
- {
- assert(m_use_montgm);
- trf_to_ordres();
- }
- return m_value;
- }
-
-const BigInt& GFpElement::get_mres() const
- {
- if(!m_use_montgm)
- {
- // does the following exception really make sense?
- // wouldn´t it be better to simply turn on montg.mult. when
- // this explicit request is made?
- throw Illegal_Transformation("GFpElement is not allowed to be transformed to m-residue");
- }
- if(!m_is_trf)
- {
- trf_to_mres();
- }
-
- return m_value;
- }
-
-const GFpElement& GFpElement::operator=(const GFpElement& other)
- {
- m_value.grow_reg(other.m_value.size()); // grow first for exception safety
-
- //m_value = other.m_value;
-
- // m_use_montgm = other.m_use_montgm;
- // m_is_trf = other.m_is_trf;
- // we want to keep the member pointers, which might be part of a "sharing group"
- // but we may not simply overwrite the BigInt values with those of the argument!!
- // if ours already contains precomputations, it would be hazardous to
- // set them back to zero.
- // thus we first check for equality of the moduli,
- // then whether either of the two objects already contains
- // precomputed values.
-
- // we also deal with the case were the pointers themsevles are equal:
- if(mp_mod.get() == other.mp_mod.get())
- {
- // everything ok, we are in the same sharing group anyway, nothing to do
- m_value = other.m_value; // cannot throw
- m_use_montgm = other.m_use_montgm;
- m_is_trf = other.m_is_trf;
- return *this;
- }
- if(mp_mod->m_p != other.mp_mod->m_p)
- {
- // the moduli are different, this is a special case
- // which will not occur in usual applications,
- // so we don´t hesitate to simply create new objects
- // (we do want to create an independent copy)
- mp_mod.reset(new GFpModulus(*other.mp_mod)); // this could throw,
- // and because of this
- // we haven't modified
- // anything so far
- m_value = other.m_value; // can't throw
- m_use_montgm = other.m_use_montgm;
- m_is_trf = other.m_is_trf;
- return *this;
- }
- // exception safety note: from now on we are on the safe
- // side with respect to the modulus,
- // so we can assign the value now:
- m_value = other.m_value;
- m_use_montgm = other.m_use_montgm;
- m_is_trf = other.m_is_trf;
- // the moduli are equal, but we deal with different sharing groups.
- // we will NOT fuse the sharing goups
- // and we will NOT reset already precomputed values
- if(mp_mod->has_precomputations())
- {
- // our own sharing group already has precomputed values,
- // so nothing to do.
- return *this;
- }
- else
- {
- // let´s see whether the argument has something for us...
- if(other.mp_mod->has_precomputations())
- {
- // fetch them for our sharing group
- // exc. safety note: grow first
- mp_mod->m_p_dash.grow_reg(other.mp_mod->m_p_dash.size());
- mp_mod->m_r.grow_reg(other.mp_mod->m_r.size());
- mp_mod->m_r_inv.grow_reg(other.mp_mod->m_r_inv.size());
-
- mp_mod->m_p_dash = other.mp_mod->m_p_dash;
- mp_mod->m_r = other.mp_mod->m_r;
- mp_mod->m_r_inv = other.mp_mod->m_r_inv;
- return *this;
- }
- }
- // our precomputations aren´t set, the arguments neither,
- // so we let them alone
- return *this;
- }
-
-void GFpElement::share_assign(const GFpElement& other)
- {
- assert((other.m_is_trf && other.m_use_montgm) || !other.m_is_trf);
-
- // use grow_to to make it exc safe
- m_value.grow_reg(other.m_value.size());
- m_value = other.m_value;
-
- m_use_montgm = other.m_use_montgm;
- m_is_trf = other.m_is_trf;
- mp_mod = other.mp_mod; // cannot throw
- }
-
-GFpElement& GFpElement::operator+=(const GFpElement& rhs)
- {
- GFpElement::align_operands_res(*this, rhs);
-
- workspace = m_value;
- workspace += rhs.m_value;
- if(workspace >= mp_mod->m_p)
- workspace -= mp_mod->m_p;
-
- m_value = workspace;
- assert(m_value < mp_mod->m_p);
- assert(m_value >= 0);
-
- return *this;
- }
-
-GFpElement& GFpElement::operator-=(const GFpElement& rhs)
- {
- GFpElement::align_operands_res(*this, rhs);
-
- workspace = m_value;
-
- workspace -= rhs.m_value;
-
- if(workspace.is_negative())
- workspace += mp_mod->m_p;
-
- m_value = workspace;
- assert(m_value < mp_mod->m_p);
- assert(m_value >= 0);
- return *this;
- }
-
-GFpElement& GFpElement::operator*= (u32bit rhs)
- {
- workspace = m_value;
- workspace *= rhs;
- workspace %= mp_mod->m_p;
- m_value = workspace;
- return *this;
- }
-
-GFpElement& GFpElement::operator*=(const GFpElement& rhs)
- {
- assert(rhs.mp_mod->m_p == mp_mod->m_p);
- // here, we do not use align_operands_res() for one simple reason:
- // we want to enforce the transformation to an m-residue, otherwise it would
- // never happen
- if(m_use_montgm && rhs.m_use_montgm)
- {
- assert(rhs.mp_mod->m_p == mp_mod->m_p); // is montgm. mult is on, then precomps must be there
- assert(rhs.mp_mod->m_p_dash == mp_mod->m_p_dash);
- assert(rhs.mp_mod->m_r == mp_mod->m_r);
- if(!m_is_trf)
- {
- trf_to_mres();
- }
- if(!rhs.m_is_trf)
- {
- rhs.trf_to_mres();
- }
- workspace = m_value;
- montg_mult(m_value, workspace, rhs.m_value, mp_mod->m_p, mp_mod->m_p_dash, mp_mod->m_r);
- }
- else // ordinary multiplication
- {
- if(m_is_trf)
- {
- assert(m_use_montgm);
- trf_to_ordres();
- }
- if(rhs.m_is_trf)
- {
- assert(rhs.m_use_montgm);
- rhs.trf_to_ordres();
- }
-
- workspace = m_value;
- workspace *= rhs.m_value;
- workspace %= mp_mod->m_p;
- m_value = workspace;
- }
- return *this;
- }
-
-GFpElement& GFpElement::operator/=(const GFpElement& rhs)
- {
- bool use_mres = GFpElement::align_operands_res(*this, rhs);
- assert((this->m_is_trf && rhs.m_is_trf) || !(this->m_is_trf && rhs.m_is_trf));
- // (internal note: see C86)
- if(use_mres)
- {
- assert(m_use_montgm && rhs.m_use_montgm);
- GFpElement rhs_ordres(rhs);
- rhs_ordres.trf_to_ordres();
- rhs_ordres.inverse_in_place();
- workspace = m_value;
- workspace *= rhs_ordres.get_value();
- workspace %= mp_mod->m_p;
- m_value = workspace;
-
- }
- else
- {
- GFpElement inv_rhs(rhs);
- inv_rhs.inverse_in_place();
- *this *= inv_rhs;
- }
- return *this;
- }
-
-bool GFpElement::is_zero()
- {
- return (m_value.is_zero());
- // this is correct because x_bar = x * r = x = 0 for x = 0
- }
-
-GFpElement& GFpElement::inverse_in_place()
- {
- m_value = inverse_mod(m_value, mp_mod->m_p);
- if(m_is_trf)
- {
- assert(m_use_montgm);
-
- m_value *= mp_mod->m_r;
- m_value *= mp_mod->m_r;
- m_value %= mp_mod->m_p;
- }
- assert(m_value <= mp_mod->m_p);
- return *this;
- }
-
-GFpElement& GFpElement::negate()
- {
- m_value = mp_mod->m_p - m_value;
- assert(m_value <= mp_mod->m_p);
- return *this;
- }
-
-void GFpElement::swap(GFpElement& other)
- {
- m_value.swap(other.m_value);
- mp_mod.swap(other.mp_mod);
- std::swap<bool>(m_use_montgm,other.m_use_montgm);
- std::swap<bool>(m_is_trf,other.m_is_trf);
- }
-
-std::ostream& operator<<(std::ostream& output, const GFpElement& elem)
- {
- return output << '(' << elem.get_value() << "," << elem.get_p() << ')';
- }
-
-bool operator==(const GFpElement& lhs, const GFpElement& rhs)
- {
- // for effeciency reasons we firstly check whether
- //the modulus pointers are different in the first place:
- if(lhs.get_ptr_mod() != rhs.get_ptr_mod())
- {
- if(lhs.get_p() != rhs.get_p())
- {
- return false;
- }
- }
- // so the modulus is equal, now check the values
- bool use_mres = GFpElement::align_operands_res(lhs, rhs);
-
- if(use_mres)
- {
- return (lhs.get_mres() == rhs.get_mres());
- }
- else
- {
- return(lhs.get_value() == rhs.get_value());
- }
- }
-
-GFpElement operator+(const GFpElement& lhs, const GFpElement& rhs)
- {
- // consider the case that lhs and rhs both use montgm:
- // then += returns an element which uses montgm.
- // thus the return value of op+ here will be an element
- // using montgm in this case
- // NOTE: the rhs might be transformed when using op+, the lhs never
- GFpElement result(lhs);
- result += rhs;
- return result;
- }
-
-GFpElement operator-(const GFpElement& lhs, const GFpElement& rhs)
- {
- GFpElement result(lhs);
- result -= rhs;
- return result;
- // NOTE: the rhs might be transformed when using op-, the lhs never
- }
-
-GFpElement operator-(const GFpElement& lhs)
- {
- return(GFpElement(lhs)).negate();
- }
-
-GFpElement operator*(const GFpElement& lhs, const GFpElement& rhs)
- {
- // consider the case that lhs and rhs both use montgm:
- // then *= returns an element which uses montgm.
- // thus the return value of op* here will be an element
- // using montgm in this case
- GFpElement result(lhs);
- result *= rhs;
- return result;
- }
-
-GFpElement operator*(const GFpElement& lhs, u32bit rhs)
- {
- GFpElement result(lhs);
- result *= rhs;
- return result;
- }
-
-GFpElement operator*(u32bit lhs, const GFpElement& rhs)
- {
- return rhs*lhs;
- }
-
-GFpElement operator/(const GFpElement& lhs, const GFpElement& rhs)
- {
- GFpElement result (lhs);
- result /= rhs;
- return result;
- }
-
-SecureVector<byte> FE2OSP(const GFpElement& elem)
- {
- return BigInt::encode_1363(elem.get_value(), elem.get_p().bytes());
- }
-
-GFpElement OS2FEP(MemoryRegion<byte> const& os, BigInt p)
- {
- return GFpElement(p, BigInt::decode(os.begin(), os.size()));
- }
-
-GFpElement inverse(const GFpElement& elem)
- {
- return GFpElement(elem).inverse_in_place();
- }
-
-}
-