Add Montgomery_Int type

7 files changed, 456 insertions, 87 deletions

diff --git a/src/lib/math/numbertheory/def_powm.h b/src/lib/math/numbertheory/def_powm.h
index fe705bf96..6b1f33835 100644
--- a/src/lib/math/numbertheory/def_powm.h
+++ b/src/lib/math/numbertheory/def_powm.h
@@ -36,6 +36,7 @@ class Fixed_Window_Exponentiator final : public Modular_Exponentiator
       Power_Mod::Usage_Hints m_hints;
    };
 
+class Montgomery_Params;
 class Montgomery_Exponentation_State;
 
 /**
@@ -53,9 +54,11 @@ class Montgomery_Exponentiator final : public Modular_Exponentiator
 
       Montgomery_Exponentiator(const BigInt&, Power_Mod::Usage_Hints);
    private:
-      std::shared_ptr<const Montgomery_Exponentation_State> m_monty;
       BigInt m_p;
       Modular_Reducer m_mod_p;
+      std::shared_ptr<const Montgomery_Params> m_monty_params;
+      std::shared_ptr<const Montgomery_Exponentation_State> m_monty;
+
       BigInt m_e;
       Power_Mod::Usage_Hints m_hints;
    };
diff --git a/src/lib/math/numbertheory/info.txt b/src/lib/math/numbertheory/info.txt
index 01adb7345..eb348b7ef 100644
--- a/src/lib/math/numbertheory/info.txt
+++ b/src/lib/math/numbertheory/info.txt
@@ -8,6 +8,7 @@ load_on auto
 numthry.h
 pow_mod.h
 reducer.h
+monty.h
 </header:public>
 
 <header:internal>
diff --git a/src/lib/math/numbertheory/monty.cpp b/src/lib/math/numbertheory/monty.cpp
new file mode 100644
index 000000000..64646a61a
--- /dev/null
+++ b/src/lib/math/numbertheory/monty.cpp
@@ -0,0 +1,254 @@
+/*
+* (C) 2018 Jack Lloyd
+*
+* Botan is released under the Simplified BSD License (see license.txt)
+*/
+
+#include <botan/monty.h>
+#include <botan/reducer.h>
+#include <botan/internal/mp_core.h>
+
+namespace Botan {
+
+Montgomery_Params::Montgomery_Params(const BigInt& p,
+                                     const Modular_Reducer& mod_p)
+   {
+   if(p.is_negative() || p.is_even())
+      throw Invalid_Argument("Montgomery_Params invalid modulus");
+
+   m_p = p;
+   m_p_words = m_p.sig_words();
+   m_p_dash = monty_inverse(m_p.word_at(0));
+
+   const BigInt r = BigInt::power_of_2(m_p_words * BOTAN_MP_WORD_BITS);
+
+   m_r1 = mod_p.reduce(r);
+   m_r2 = mod_p.square(m_r1);
+   m_r3 = mod_p.multiply(m_r1, m_r2);
+   }
+
+BigInt Montgomery_Params::inv_mod_p(const BigInt& x) const
+   {
+   return ct_inverse_mod_odd_modulus(x, p());
+   }
+
+BigInt Montgomery_Params::redc(const BigInt& x) const
+   {
+   const size_t output_size = 2*m_p_words + 2;
+   std::vector<word> ws(output_size);
+   BigInt z = x;
+   z.grow_to(output_size);
+
+   bigint_monty_redc(z.mutable_data(),
+                     m_p.data(), m_p_words, m_p_dash,
+                     ws.data(), ws.size());
+
+   secure_scrub_memory(ws.data(), ws.size() * sizeof(word));
+   return z;
+   }
+
+BigInt Montgomery_Params::mul(const BigInt& x, const BigInt& y) const
+   {
+   const size_t output_size = 2*m_p_words + 2;
+   std::vector<word> ws(output_size);
+   BigInt z(BigInt::Positive, output_size);
+   bigint_monty_mul(z, x, y,
+                    m_p.data(), m_p_words, m_p_dash,
+                    ws.data(), ws.size());
+   secure_scrub_memory(ws.data(), ws.size() * sizeof(word));
+   return z;
+   }
+
+BigInt Montgomery_Params::mul(const BigInt& x, const secure_vector<word>& y) const
+   {
+   const size_t output_size = 2*m_p_words + 2;
+   std::vector<word> ws(output_size);
+   BigInt z(BigInt::Positive, output_size);
+
+   bigint_mul(z.mutable_data(), z.size(),
+              x.data(), x.size(), x.sig_words(),
+              y.data(), y.size(), y.size(),
+              ws.data(), ws.size());
+
+   bigint_monty_redc(z.mutable_data(),
+                     m_p.data(), m_p_words, m_p_dash,
+                     ws.data(), ws.size());
+
+   secure_scrub_memory(ws.data(), ws.size() * sizeof(word));
+   return z;
+   }
+
+BigInt Montgomery_Params::sqr(const BigInt& x) const
+   {
+   const size_t output_size = 2*m_p_words + 2;
+   std::vector<word> ws(output_size);
+   BigInt z(BigInt::Positive, output_size);
+
+   bigint_sqr(z.mutable_data(), z.size(),
+              x.data(), x.size(), x.sig_words(),
+              ws.data(), ws.size());
+
+   bigint_monty_redc(z.mutable_data(),
+                     m_p.data(), m_p_words, m_p_dash,
+                     ws.data(), ws.size());
+
+   secure_scrub_memory(ws.data(), ws.size() * sizeof(word));
+   return z;
+   }
+
+Montgomery_Int::Montgomery_Int(const std::shared_ptr<const Montgomery_Params> params,
+                               const BigInt& v,
+                               bool redc_needed) :
+   m_params(params),
+   m_v(redc_needed ? m_params->mul(v % m_params->p(), m_params->R2()) : v)
+   {}
+
+void Montgomery_Int::fix_size()
+   {
+   const size_t p_words = m_params->p_words();
+
+   if(m_v.sig_words() > p_words)
+      throw Internal_Error("Montgomery_Int::fix_size v too large");
+
+   secure_vector<word>& w = m_v.get_word_vector();
+
+   if(w.size() != p_words)
+      {
+      w.resize(p_words);
+      w.shrink_to_fit();
+      }
+   }
+
+bool Montgomery_Int::operator==(const Montgomery_Int& other) const
+   {
+   return m_v == other.m_v && m_params->p() == other.m_params->p();
+   }
+
+std::vector<uint8_t> Montgomery_Int::serialize() const
+   {
+   std::vector<uint8_t> v(size());
+   BigInt::encode_1363(v.data(), v.size(), value());
+   return v;
+   }
+
+size_t Montgomery_Int::size() const
+   {
+   return m_params->p().bytes();
+   }
+
+bool Montgomery_Int::is_one() const
+   {
+   return m_v == m_params->R1();
+   }
+
+bool Montgomery_Int::is_zero() const
+   {
+   return m_v.is_zero();
+   }
+
+BigInt Montgomery_Int::value() const
+   {
+   return m_params->redc(m_v);
+   }
+
+Montgomery_Int Montgomery_Int::operator+(const Montgomery_Int& other) const
+   {
+   BigInt z = m_v + other.m_v;
+   secure_vector<word> ws;
+   z.reduce_below(m_params->p(), ws);
+   return Montgomery_Int(m_params, z, false);
+   }
+
+Montgomery_Int Montgomery_Int::operator-(const Montgomery_Int& other) const
+   {
+   BigInt z = m_v - other.m_v;
+   if(z.is_negative())
+      z += m_params->p();
+   return Montgomery_Int(m_params, z, false);
+   }
+
+Montgomery_Int& Montgomery_Int::operator+=(const Montgomery_Int& other)
+   {
+   m_v += other.m_v;
+   secure_vector<word> ws;
+   m_v.reduce_below(m_params->p(), ws);
+   return (*this);
+   }
+
+Montgomery_Int& Montgomery_Int::operator-=(const Montgomery_Int& other)
+   {
+   m_v -= other.m_v;
+   if(m_v.is_negative())
+      m_v += m_params->p();
+   return (*this);
+   }
+
+Montgomery_Int Montgomery_Int::operator*(const Montgomery_Int& other) const
+   {
+   return Montgomery_Int(m_params, m_params->mul(m_v, other.m_v), false);
+   }
+
+Montgomery_Int& Montgomery_Int::operator*=(const Montgomery_Int& other)
+   {
+   m_v = m_params->mul(m_v, other.m_v);
+   return (*this);
+   }
+
+Montgomery_Int& Montgomery_Int::operator*=(const secure_vector<word>& other)
+   {
+   m_v = m_params->mul(m_v, other);
+   return (*this);
+   }
+
+Montgomery_Int& Montgomery_Int::square_this()
+   {
+   m_v = m_params->sqr(m_v);
+   return (*this);
+   }
+
+Montgomery_Int Montgomery_Int::square() const
+   {
+   const BigInt v = m_params->sqr(m_v);
+   return Montgomery_Int(m_params, v, false);
+   }
+
+Montgomery_Int Montgomery_Int::multiplicative_inverse() const
+   {
+   const BigInt iv = m_params->mul(m_params->inv_mod_p(m_v), m_params->R3());
+   return Montgomery_Int(m_params, iv, false);
+   }
+
+Montgomery_Int Montgomery_Int::additive_inverse() const
+   {
+   return Montgomery_Int(m_params, m_params->p()) - (*this);
+   }
+
+Montgomery_Int& Montgomery_Int::mul_by_2(secure_vector<word>& ws)
+   {
+   m_v <<= 1;
+   m_v.reduce_below(m_params->p(), ws);
+   return (*this);
+   }
+
+Montgomery_Int& Montgomery_Int::mul_by_3(secure_vector<word>& ws)
+   {
+   m_v *= 3;
+   m_v.reduce_below(m_params->p(), ws);
+   return (*this);
+   }
+
+Montgomery_Int& Montgomery_Int::mul_by_4(secure_vector<word>& ws)
+   {
+   m_v <<= 2;
+   m_v.reduce_below(m_params->p(), ws);
+   return (*this);
+   }
+
+Montgomery_Int& Montgomery_Int::mul_by_8(secure_vector<word>& ws)
+   {
+   m_v <<= 3;
+   m_v.reduce_below(m_params->p(), ws);
+   return (*this);
+   }
+
+}
diff --git a/src/lib/math/numbertheory/monty.h b/src/lib/math/numbertheory/monty.h
new file mode 100644
index 000000000..ea08789e1
--- /dev/null
+++ b/src/lib/math/numbertheory/monty.h
@@ -0,0 +1,134 @@
+/*
+* (C) 2018 Jack Lloyd
+*
+* Botan is released under the Simplified BSD License (see license.txt)
+*/
+
+#ifndef BOTAN_MONTY_INT_H_
+#define BOTAN_MONTY_INT_H_
+
+#include <botan/bigint.h>
+
+namespace Botan {
+
+class Modular_Reducer;
+
+class Montgomery_Params;
+
+/**
+* The Montgomery representation of an integer
+*/
+class Montgomery_Int final
+   {
+   public:
+      /**
+      * Create a zero-initialized Montgomery_Int
+      */
+      Montgomery_Int(std::shared_ptr<const Montgomery_Params> params) : m_params(params) {}
+
+      /**
+      * Create a Montgomery_Int
+      */
+      Montgomery_Int(std::shared_ptr<const Montgomery_Params> params,
+                     const BigInt& v,
+                     bool redc_needed = true);
+
+      bool operator==(const Montgomery_Int& other) const;
+      bool operator!=(const Montgomery_Int& other) const { return (m_v != other.m_v); }
+
+      std::vector<uint8_t> serialize() const;
+
+      size_t size() const;
+      bool is_one() const;
+      bool is_zero() const;
+
+      void fix_size();
+
+      /**
+      * Return the value to normal mod-p space
+      */
+      BigInt value() const;
+
+      /**
+      * Return the Montgomery representation
+      */
+      const BigInt& repr() const { return m_v; }
+
+      Montgomery_Int operator+(const Montgomery_Int& other) const;
+
+      Montgomery_Int operator-(const Montgomery_Int& other) const;
+
+      Montgomery_Int& operator+=(const Montgomery_Int& other);
+
+      Montgomery_Int& operator-=(const Montgomery_Int& other);
+
+      Montgomery_Int operator*(const Montgomery_Int& other) const;
+
+      Montgomery_Int& operator*=(const Montgomery_Int& other);
+
+      Montgomery_Int& operator*=(const secure_vector<word>& other);
+
+      Montgomery_Int square() const;
+
+      Montgomery_Int& square_this();
+
+      Montgomery_Int multiplicative_inverse() const;
+
+      Montgomery_Int additive_inverse() const;
+
+      Montgomery_Int& mul_by_2(secure_vector<word>& ws);
+
+      Montgomery_Int& mul_by_3(secure_vector<word>& ws);
+
+      Montgomery_Int& mul_by_4(secure_vector<word>& ws);
+
+      Montgomery_Int& mul_by_8(secure_vector<word>& ws);
+
+   private:
+      std::shared_ptr<const Montgomery_Params> m_params;
+      BigInt m_v;
+   };
+
+/**
+* Parameters for Montgomery Reduction
+*/
+class Montgomery_Params final
+   {
+   public:
+      /**
+      * Initialize a set of Montgomery reduction parameters. These values
+      * can be shared by all values in a specific Montgomery domain.
+      */
+      Montgomery_Params(const BigInt& p, const Modular_Reducer& mod_p);
+
+      const BigInt& p() const { return m_p; }
+      const BigInt& R1() const { return m_r1; }
+      const BigInt& R2() const { return m_r2; }
+      const BigInt& R3() const { return m_r3; }
+
+      word p_dash() const { return m_p_dash; }
+
+      size_t p_words() const { return m_p_words; }
+
+      BigInt redc(const BigInt& x) const;
+
+      BigInt mul(const BigInt& x, const BigInt& y) const;
+
+      BigInt mul(const BigInt& x, const secure_vector<word>& y) const;
+
+      BigInt sqr(const BigInt& x) const;
+
+      BigInt inv_mod_p(const BigInt& x) const;
+
+   private:
+      BigInt m_p;
+      BigInt m_r1;
+      BigInt m_r2;
+      BigInt m_r3;
+      word m_p_dash;
+      size_t m_p_words;
+   };
+
+}
+
+#endif
diff --git a/src/lib/math/numbertheory/monty_exp.cpp b/src/lib/math/numbertheory/monty_exp.cpp
index bfb17a87c..6b7af3b09 100644
--- a/src/lib/math/numbertheory/monty_exp.cpp
+++ b/src/lib/math/numbertheory/monty_exp.cpp
@@ -7,140 +7,115 @@
 */
 
 #include <botan/internal/monty_exp.h>
+#include <botan/internal/ct_utils.h>
 #include <botan/numthry.h>
 #include <botan/reducer.h>
-#include <botan/internal/mp_core.h>
+#include <botan/monty.h>
 
 namespace Botan {
 
 class Montgomery_Exponentation_State
    {
    public:
-      Montgomery_Exponentation_State(const BigInt& g,
-                                     const BigInt& p,
-                                     const Modular_Reducer& mod_p,
+      Montgomery_Exponentation_State(std::shared_ptr<const Montgomery_Params> params,
+                                     const BigInt& g,
                                      size_t window_bits);
 
       BigInt exponentiation(const BigInt& k) const;
    private:
-      BigInt m_p;
-      BigInt m_R_mod;
-      BigInt m_R2_mod;
-      word m_mod_prime;
-      size_t m_p_words;
+      std::shared_ptr<const Montgomery_Params> m_params;
+      std::vector<Montgomery_Int> m_g;
       size_t m_window_bits;
-      std::vector<BigInt> m_g;
    };
 
-Montgomery_Exponentation_State::Montgomery_Exponentation_State(const BigInt& g,
-                                                               const BigInt& p,
-                                                               const Modular_Reducer& mod_p,
+Montgomery_Exponentation_State::Montgomery_Exponentation_State(std::shared_ptr<const Montgomery_Params> params,
+                                                               const BigInt& g,
                                                                size_t window_bits) :
-   m_p(p),
-   m_p_words(p.sig_words()),
-   m_window_bits(window_bits)
+   m_params(params),
+   m_window_bits(window_bits == 0 ? 4 : window_bits)
    {
-   if(p.is_positive() == false || p.is_even())
-      throw Invalid_Argument("Cannot use Montgomery reduction on even or negative integer");
+   if(m_window_bits < 1 || m_window_bits > 12) // really even 8 is too large ...
+      throw Invalid_Argument("Invalid window bits for Montgomery exponentiation");
 
-   if(window_bits > 12) // really even 8 is too large ...
-      throw Invalid_Argument("Montgomery window bits too large");
+   const size_t window_size = (1U << m_window_bits);
 
-   m_mod_prime = monty_inverse(m_p.word_at(0));
+   m_g.reserve(window_size);
 
-   const BigInt r = BigInt::power_of_2(m_p_words * BOTAN_MP_WORD_BITS);
-   m_R_mod = mod_p.reduce(r);
-   m_R2_mod = mod_p.square(m_R_mod);
+   m_g.push_back(Montgomery_Int(m_params, m_params->R1(), false));;
 
-   m_g.resize(1U << m_window_bits);
+   m_g.push_back(Montgomery_Int(m_params, g));
 
-   BigInt z(BigInt::Positive, 2 * (m_p_words + 1));
-   secure_vector<word> workspace(z.size());
+   const Montgomery_Int& monty_g = m_g[1];
 
-   m_g[0] = 1;
-
-   bigint_monty_mul(z, m_g[0], m_R2_mod,
-                    m_p.data(), m_p_words, m_mod_prime,
-                    workspace.data(), workspace.size());
-   m_g[0] = z;
+   for(size_t i = 2; i != window_size; ++i)
+      {
+      m_g.push_back(monty_g * m_g[i - 1]);
+      }
 
-   m_g[1] = mod_p.reduce(g);
+   // Resize each element to exactly p words
+   for(size_t i = 0; i != window_size; ++i)
+      {
+      m_g[i].fix_size();
+      }
+   }
 
-   bigint_monty_mul(z, m_g[1], m_R2_mod,
-                    m_p.data(), m_p_words, m_mod_prime,
-                    workspace.data(), workspace.size());
+namespace {
 
-   m_g[1] = z;
+void const_time_lookup(secure_vector<word>& output,
+                        const std::vector<Montgomery_Int>& g,
+                        size_t nibble)
+   {
+   const size_t words = output.size();
 
-   const BigInt& x = m_g[1];
+   clear_mem(output.data(), output.size());
 
-   for(size_t i = 2; i != m_g.size(); ++i)
+   for(size_t i = 0; i != g.size(); ++i)
       {
-      const BigInt& y = m_g[i-1];
+      const secure_vector<word>& vec = g[i].repr().get_word_vector();
+
+      BOTAN_ASSERT(vec.size() >= words,
+                   "Word size as expected in const_time_lookup");
 
-      bigint_monty_mul(z, x, y, m_p.data(), m_p_words, m_mod_prime,
-                       workspace.data(), workspace.size());
+      const word mask = CT::is_equal<word>(i, nibble);
 
-      m_g[i] = z;
-      m_g[i].shrink_to_fit();
-      m_g[i].grow_to(m_p_words);
+      for(size_t w = 0; w != words; ++w)
+         output[w] |= (mask & vec[w]);
       }
    }
 
-BigInt Montgomery_Exponentation_State::exponentiation(const BigInt& k) const
-   {
-   const size_t exp_nibbles = (k.bits() + m_window_bits - 1) / m_window_bits;
+}
 
-   BigInt x = m_R_mod;
+BigInt Montgomery_Exponentation_State::exponentiation(const BigInt& scalar) const
+   {
+   const size_t exp_nibbles = (scalar.bits() + m_window_bits - 1) / m_window_bits;
 
-   const size_t z_size = 2*(m_p_words + 1);
+   Montgomery_Int x(m_params, m_params->R1(), false);
 
-   BigInt z(BigInt::Positive, z_size);
-   secure_vector<word> workspace(z.size());
-   secure_vector<word> e(m_p_words);
+   secure_vector<word> e_bits(m_params->p_words());
 
    for(size_t i = exp_nibbles; i > 0; --i)
       {
       for(size_t j = 0; j != m_window_bits; ++j)
          {
-         bigint_monty_sqr(z, x, m_p.data(), m_p_words, m_mod_prime,
-                          workspace.data(), workspace.size());
-
-         x = z;
+         x.square_this();
          }
 
-      const uint32_t nibble = k.get_substring(m_window_bits*(i-1), m_window_bits);
+      const uint32_t nibble = scalar.get_substring(m_window_bits*(i-1), m_window_bits);
 
-      BigInt::const_time_lookup(e, m_g, nibble);
+      const_time_lookup(e_bits, m_g, nibble);
 
-      bigint_mul(z.mutable_data(), z.size(),
-                 x.data(), x.size(), x.sig_words(),
-                 e.data(), m_p_words, m_p_words,
-                 workspace.data(), workspace.size());
-
-      bigint_monty_redc(z.mutable_data(),
-                        m_p.data(), m_p_words, m_mod_prime,
-                        workspace.data(), workspace.size());
-
-      x = z;
+      x *= e_bits;
       }
 
-   x.grow_to(2*m_p_words + 1);
-
-   bigint_monty_redc(x.mutable_data(),
-                     m_p.data(), m_p_words, m_mod_prime,
-                     workspace.data(), workspace.size());
-
-   return x;
+   return x.value();
    }
 
 std::shared_ptr<const Montgomery_Exponentation_State>
-monty_precompute(const BigInt& g,
-                 const BigInt& p,
-                 const Modular_Reducer& mod_p,
+monty_precompute(std::shared_ptr<const Montgomery_Params> params,
+                 const BigInt& g,
                  size_t window_bits)
    {
-   return std::make_shared<const Montgomery_Exponentation_State>(g, p, mod_p, window_bits);
+   return std::make_shared<const Montgomery_Exponentation_State>(params, g, window_bits);
    }
 
 BigInt monty_execute(const Montgomery_Exponentation_State& precomputed_state,
diff --git a/src/lib/math/numbertheory/monty_exp.h b/src/lib/math/numbertheory/monty_exp.h
index 65fc9ce4b..8c644d221 100644
--- a/src/lib/math/numbertheory/monty_exp.h
+++ b/src/lib/math/numbertheory/monty_exp.h
@@ -14,15 +14,16 @@ namespace Botan {
 class BigInt;
 class Modular_Reducer;
 
+class Montgomery_Params;
+
 class Montgomery_Exponentation_State;
 
 /*
 * Precompute for calculating values g^x mod p
 */
 std::shared_ptr<const Montgomery_Exponentation_State>
-monty_precompute(const BigInt& g,
-                 const BigInt& p,
-                 const Modular_Reducer& mod_p,
+monty_precompute(std::shared_ptr<const Montgomery_Params> params_p,
+                 const BigInt& g,
                  size_t window_bits);
 
 /*
diff --git a/src/lib/math/numbertheory/powm_mnt.cpp b/src/lib/math/numbertheory/powm_mnt.cpp
index 81102188b..5da91796f 100644
--- a/src/lib/math/numbertheory/powm_mnt.cpp
+++ b/src/lib/math/numbertheory/powm_mnt.cpp
@@ -8,7 +8,7 @@
 
 #include <botan/internal/def_powm.h>
 #include <botan/numthry.h>
-#include <botan/internal/mp_core.h>
+#include <botan/monty.h>
 #include <botan/internal/monty_exp.h>
 
 namespace Botan {
@@ -21,7 +21,7 @@ void Montgomery_Exponentiator::set_exponent(const BigInt& exp)
 void Montgomery_Exponentiator::set_base(const BigInt& base)
    {
    size_t window_bits = Power_Mod::window_bits(m_e.bits(), base.bits(), m_hints);
-   m_monty = monty_precompute(base, m_p, m_mod_p, window_bits);
+   m_monty = monty_precompute(m_monty_params, base, window_bits);
    }
 
 BigInt Montgomery_Exponentiator::execute() const
@@ -33,6 +33,7 @@ Montgomery_Exponentiator::Montgomery_Exponentiator(const BigInt& mod,
                                                    Power_Mod::Usage_Hints hints) :
    m_p(mod),
    m_mod_p(mod),
+   m_monty_params(std::make_shared<Montgomery_Params>(m_p, m_mod_p)),
    m_hints(hints)
    {
    }