diff options
author | Jack Lloyd <[email protected]> | 2020-03-06 06:57:46 -0500 |
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committer | Jack Lloyd <[email protected]> | 2020-03-06 08:23:29 -0500 |
commit | d2ada9892be75459f3080fe8f88ea9f6ef10ea1b (patch) | |
tree | c2e8e9804b54ad8412c7b8bd3ebda139dd2ba0ad /src | |
parent | 06a55af16fbee536cf3aa53370195b22327ca54f (diff) |
Optimize inverse_mod
About 25% faster
Diffstat (limited to 'src')
-rw-r--r-- | src/cli/speed.cpp | 40 | ||||
-rw-r--r-- | src/lib/math/numbertheory/mod_inv.cpp | 147 | ||||
-rw-r--r-- | src/lib/math/numbertheory/numthry.h | 3 |
3 files changed, 95 insertions, 95 deletions
diff --git a/src/cli/speed.cpp b/src/cli/speed.cpp index e876b7205..06c1e6ab9 100644 --- a/src/cli/speed.cpp +++ b/src/cli/speed.cpp @@ -1435,8 +1435,8 @@ class Speed final : public Command while(f_timer->under(runtime)) { - e_timer->run([&]() { Botan::power_mod(group.get_g(), random_e, group.get_p()); }); - f_timer->run([&]() { Botan::power_mod(group.get_g(), random_f, group.get_p()); }); + e_timer->run([&]() { group.power_g_p(random_e); }); + f_timer->run([&]() { group.power_g_p(random_f); }); } record_result(e_timer); @@ -1532,31 +1532,33 @@ class Speed final : public Command void bench_inverse_mod(const std::chrono::milliseconds runtime) { - - for(size_t bits : { 256, 384, 512 }) + for(size_t bits : { 256, 384, 512, 1024, 2048 }) { - const Botan::BigInt p = Botan::random_prime(rng(), bits); - const std::string bit_str = std::to_string(bits); - std::unique_ptr<Timer> monty_timer = make_timer("monty-" + bit_str); - std::unique_ptr<Timer> ct_invmod_timer = make_timer("ct-" + bit_str); + std::unique_ptr<Timer> timer = make_timer("inverse_mod-" + bit_str); - while(monty_timer->under(runtime)) + while(timer->under(runtime)) { - const Botan::BigInt x(rng(), p.bits() - 1); + const Botan::BigInt x(rng(), bits - 1); + Botan::BigInt mod(rng(), bits); - const Botan::BigInt x_inv1 = monty_timer->run( - [&] { return Botan::normalized_montgomery_inverse(x, p); }); + const Botan::BigInt x_inv = timer->run( + [&] { return Botan::inverse_mod(x, mod); }); - const Botan::BigInt x_inv2 = ct_invmod_timer->run( - [&] { return Botan::inverse_mod(x, p); }); - - BOTAN_ASSERT_EQUAL(x_inv1, x_inv2, "Same result"); + if(x_inv == 0) + { + const Botan::BigInt g = gcd(x, mod); + BOTAN_ASSERT(g != 1, "Inversion only fails if gcd(x, mod) > 1"); + } + else + { + const Botan::BigInt check = (x_inv*x) % mod; + BOTAN_ASSERT_EQUAL(check, 1, "Const time inversion correct"); + } } - record_result(monty_timer); - record_result(ct_invmod_timer); + record_result(timer); } } @@ -1856,6 +1858,8 @@ class Speed final : public Command std::unique_ptr<Botan::Private_Key> key(keygen_timer->run([&] { return Botan::create_private_key("RSA", rng(), std::to_string(keylen)); })); + + BOTAN_ASSERT(key->check_key(rng(), true), "Key is ok"); } record_result(keygen_timer); diff --git a/src/lib/math/numbertheory/mod_inv.cpp b/src/lib/math/numbertheory/mod_inv.cpp index 8a23707e0..8bc073d9c 100644 --- a/src/lib/math/numbertheory/mod_inv.cpp +++ b/src/lib/math/numbertheory/mod_inv.cpp @@ -8,6 +8,7 @@ #include <botan/divide.h> #include <botan/internal/ct_utils.h> #include <botan/internal/mp_core.h> +#include <botan/internal/rounding.h> namespace Botan { @@ -101,12 +102,11 @@ namespace { BigInt inverse_mod_odd_modulus(const BigInt& n, const BigInt& mod) { - if(n.is_negative() || mod.is_negative()) - throw Invalid_Argument("inverse_mod_odd_modulus: arguments must be non-negative"); - if(mod < 3 || mod.is_even()) - throw Invalid_Argument("Bad modulus to inverse_mod_odd_modulus"); - if(n >= mod) - throw Invalid_Argument("inverse_mod_odd_modulus n >= mod not supported"); + // Caller should assure these preconditions: + BOTAN_DEBUG_ASSERT(n.is_positive()); + BOTAN_DEBUG_ASSERT(mod.is_positive()); + BOTAN_DEBUG_ASSERT(n < mod); + BOTAN_DEBUG_ASSERT(mod >= 3 && mod.is_odd()); /* This uses a modular inversion algorithm designed by Niels Möller @@ -127,98 +127,85 @@ BigInt inverse_mod_odd_modulus(const BigInt& n, const BigInt& mod) about it, and the reference to the paper. */ - // todo allow this to be pre-calculated and passed in as arg - BigInt mp1o2 = (mod + 1) >> 1; - const size_t mod_words = mod.sig_words(); BOTAN_ASSERT(mod_words > 0, "Not empty"); - BigInt a = n; - BigInt b = mod; - BigInt u = 1, v = 0; + secure_vector<word> tmp_mem(5*mod_words); + + word* v_w = &tmp_mem[0]; + word* u_w = &tmp_mem[1*mod_words]; + word* b_w = &tmp_mem[2*mod_words]; + word* a_w = &tmp_mem[3*mod_words]; + word* mp1o2 = &tmp_mem[4*mod_words]; - a.grow_to(mod_words); - u.grow_to(mod_words); - v.grow_to(mod_words); - mp1o2.grow_to(mod_words); + copy_mem(a_w, n.data(), std::min(n.size(), mod_words)); + copy_mem(b_w, mod.data(), std::min(mod.size(), mod_words)); + u_w[0] = 1; + // v_w = 0 - secure_vector<word>& a_w = a.get_word_vector(); - secure_vector<word>& b_w = b.get_word_vector(); - secure_vector<word>& u_w = u.get_word_vector(); - secure_vector<word>& v_w = v.get_word_vector(); + // compute (mod + 1) / 2 which [because mod is odd] is equal to + // (mod / 2) + 1 + copy_mem(mp1o2, mod.data(), std::min(mod.size(), mod_words)); + bigint_shr1(mp1o2, mod_words, 0, 1); + word carry = bigint_add2_nc(mp1o2, mod_words, u_w, 1); + BOTAN_ASSERT_NOMSG(carry == 0); - CT::poison(a_w.data(), a_w.size()); - CT::poison(b_w.data(), b_w.size()); - CT::poison(u_w.data(), u_w.size()); - CT::poison(v_w.data(), v_w.size()); + CT::poison(tmp_mem.data(), tmp_mem.size()); // Only n.bits() + mod.bits() iterations are required, but avoid leaking the size of n - size_t bits = 2 * mod.bits(); + size_t execs = 2 * mod.bits(); - while(bits--) + while(execs--) { - /* - const word odd = a.is_odd(); - a -= odd * b; - const word underflow = a.is_negative(); - b += a * underflow; - a.set_sign(BigInt::Positive); - - a >>= 1; - - if(underflow) - { - std::swap(u, v); - } - - u -= odd * v; - u += u.is_negative() * mod; - - const word odd_u = u.is_odd(); - - u >>= 1; - u += mp1o2 * odd_u; - */ - const word odd_a = a_w[0] & 1; //if(odd_a) a -= b - word underflow = bigint_cnd_sub(odd_a, a_w.data(), b_w.data(), mod_words); + word underflow = bigint_cnd_sub(odd_a, a_w, b_w, mod_words); //if(underflow) { b -= a; a = abs(a); swap(u, v); } - bigint_cnd_add(underflow, b_w.data(), a_w.data(), mod_words); - bigint_cnd_abs(underflow, a_w.data(), mod_words); - bigint_cnd_swap(underflow, u_w.data(), v_w.data(), mod_words); + bigint_cnd_add(underflow, b_w, a_w, mod_words); + bigint_cnd_abs(underflow, a_w, mod_words); + bigint_cnd_swap(underflow, u_w, v_w, mod_words); // a >>= 1 - bigint_shr1(a_w.data(), mod_words, 0, 1); + bigint_shr1(a_w, mod_words, 0, 1); //if(odd_a) u -= v; - word borrow = bigint_cnd_sub(odd_a, u_w.data(), v_w.data(), mod_words); + word borrow = bigint_cnd_sub(odd_a, u_w, v_w, mod_words); // if(borrow) u += p - bigint_cnd_add(borrow, u_w.data(), mod.data(), mod_words); + bigint_cnd_add(borrow, u_w, mod.data(), mod_words); const word odd_u = u_w[0] & 1; // u >>= 1 - bigint_shr1(u_w.data(), mod_words, 0, 1); + bigint_shr1(u_w, mod_words, 0, 1); //if(odd_u) u += mp1o2; - bigint_cnd_add(odd_u, u_w.data(), mp1o2.data(), mod_words); + bigint_cnd_add(odd_u, u_w, mp1o2, mod_words); } - CT::unpoison(a_w.data(), a_w.size()); - CT::unpoison(b_w.data(), b_w.size()); - CT::unpoison(u_w.data(), u_w.size()); - CT::unpoison(v_w.data(), v_w.size()); + auto a_is_0 = CT::Mask<word>::set(); + for(size_t i = 0; i != mod_words; ++i) + a_is_0 &= CT::Mask<word>::is_zero(a_w[i]); - BOTAN_ASSERT(a.is_zero(), "A is zero"); + auto b_is_1 = CT::Mask<word>::is_equal(b_w[0], 1); + for(size_t i = 1; i != mod_words; ++i) + b_is_1 &= CT::Mask<word>::is_zero(b_w[i]); - if(b != 1) - return 0; + BOTAN_ASSERT(a_is_0.is_set(), "A is zero"); + + // if b != 1 then gcd(n,mod) > 1 and inverse does not exist + // in which case zero out the result to indicate this + (~b_is_1).if_set_zero_out(v_w, mod_words); - return v; + clear_mem(&tmp_mem[mod_words], 4*mod_words); + + CT::unpoison(tmp_mem.data(), tmp_mem.size()); + + BigInt r; + r.swap_reg(tmp_mem); + return r; } BigInt inverse_mod_pow2(const BigInt& a1, size_t k) @@ -237,15 +224,25 @@ BigInt inverse_mod_pow2(const BigInt& a1, size_t k) BigInt b = 1; BigInt X = 0; - for(size_t i = 0; i != k; ++i) + const size_t a_words = 1 + a.sig_words(); + + /* + Hide the exact value of k. k is anyway known to word length + granularity because of the length of a, so no point in doing more + than this. + */ + const size_t iter = round_up(k, BOTAN_MP_WORD_BITS); + + for(size_t i = 0; i != iter; ++i) { const bool b0 = b.get_bit(0); - X.conditionally_set_bit(i, b0); - b -= a * b0; - b /= 2; + b.grow_to(a_words); + bigint_cnd_sub(b0, b.mutable_data(), b.size(), a.data(), a.sig_words()); + b >>= 1; } + X.mask_bits(k); return X; } @@ -257,9 +254,7 @@ BigInt inverse_mod(const BigInt& n, const BigInt& mod) throw BigInt::DivideByZero(); if(mod.is_negative() || n.is_negative()) throw Invalid_Argument("inverse_mod: arguments must be non-negative"); - if(n.is_zero()) - return 0; - if(n.is_even() && mod.is_even()) + if(n.is_zero() || (n.is_even() && mod.is_even())) return 0; if(mod.is_odd()) @@ -306,10 +301,10 @@ BigInt inverse_mod(const BigInt& n, const BigInt& mod) // Compute h = c*(inv_2k-inv_o) mod 2^k BigInt h = c * (inv_2k - inv_o); const bool h_neg = h.is_negative(); - h.mask_bits(mod_lz); h.set_sign(BigInt::Positive); - if(h_neg && h > 0) - h = BigInt::power_of_2(mod_lz) - h; + h.mask_bits(mod_lz); + const bool h_nonzero = h.is_nonzero(); + h.ct_cond_assign(h_nonzero && h_neg, BigInt::power_of_2(mod_lz) - h); // Return result inv_o + h * o h *= o; diff --git a/src/lib/math/numbertheory/numthry.h b/src/lib/math/numbertheory/numthry.h index b476db600..e818aa0bb 100644 --- a/src/lib/math/numbertheory/numthry.h +++ b/src/lib/math/numbertheory/numthry.h @@ -81,7 +81,8 @@ BigInt BOTAN_PUBLIC_API(2,0) square(const BigInt& x); * as long as x is less than modulus. It also avoids leaking * information about the modulus, except that it does leak which of 3 * categories the modulus is in: an odd integer, a power of 2, or some -* other even number. +* other even number, and if the modulus is even, leaks the power of 2 +* which divides the modulus. * * @param x a positive integer * @param modulus a positive integer |