lm_ots.cpp

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/**
 * LM-OTS - Leighton-Micali One-Time Signatures
 * (C) 2023 Jack Lloyd
 *     2023 Fabian Albert, Philippe Lieser - Rohde & Schwarz Cybersecurity GmbH
 *
 * Botan is released under the Simplified BSD License (see license.txt)
 */
 
#include <botan/internal/lm_ots.h>
 
#include <botan/exceptn.h>
#include <botan/strong_type.h>
#include <botan/internal/bit_ops.h>
#include <botan/internal/hss_lms_utils.h>
#include <botan/internal/int_utils.h>
 
namespace Botan {
 
namespace {
constexpr uint16_t D_PBLC = 0x8080;
constexpr uint16_t D_MESG = 0x8181;
/// For derivation of C as in https://github.com/cisco/hash-sigs
constexpr uint16_t C_INDEX = 0xFFFD;
 
class Chain_Generator {
   public:
      Chain_Generator(const LMS_Identifier& identifier, LMS_Tree_Node_Idx q) : m_gen(identifier) {
         m_gen.set_q(q.get());
      }
 
      void process(HashFunction& hash,
                   uint16_t chain_idx,
                   uint8_t start,
                   uint8_t end,
                   std::span<const uint8_t> in,
                   std::span<uint8_t> out) {
         BOTAN_ARG_CHECK(start <= end, "Start value is bigger than end value");
 
         copy_mem(out, in);
         m_gen.set_i(chain_idx);
 
         for(uint8_t j = start; j < end; ++j) {
            m_gen.set_j(j);
            m_gen.gen(out, hash, out);
         }
      }
 
   private:
      PseudorandomKeyGeneration m_gen;
};
 
// RFC 8554 3.1.1
uint8_t byte(std::span<const uint8_t> S, uint32_t i) {
   BOTAN_ARG_CHECK(i < S.size(), "Index out of range");
   return S[i];
}
 
// RFC 8554 3.1.3
uint8_t coef(std::span<const uint8_t> S, uint32_t i, const LMOTS_Params& params) {
   const uint8_t w_bit_mask = params.coef_max();
   const uint8_t coef_byte = byte(S, (i * params.w()) / 8);
   const uint8_t shift = 8 - (params.w() * (i % (8 / params.w())) + params.w());
 
   return w_bit_mask & (coef_byte >> shift);
}
 
// RFC 8554 4.4
uint16_t checksum(const LMOTS_Params& params, std::span<const uint8_t> S) {
   size_t sum = 0;
   for(uint32_t i = 0; i < (params.n() * 8 / params.w()); ++i) {
      sum += params.coef_max() - coef(S, i, params);
   }
   return checked_cast_to<uint16_t>(sum << params.ls());
}
 
std::vector<uint8_t> gen_Q_with_cksm(const LMOTS_Params& params,
                                     const LMS_Identifier& identifier,
                                     const LMS_Tree_Node_Idx& q,
                                     std::span<const uint8_t> C,
                                     const LMS_Message& msg) {
   std::vector<uint8_t> Q_with_cksm(params.n() + sizeof(uint16_t));
   BufferStuffer qwc_stuffer(Q_with_cksm);
   const auto hash = params.hash();
   hash->update(identifier);
   hash->update(store_be(q));
   hash->update(store_be(D_MESG));
   hash->update(C);
   hash->update(msg);
   auto Q_span = qwc_stuffer.next(params.n());
   hash->final(Q_span);
 
   qwc_stuffer.append(store_be(checksum(params, Q_span)));
 
   return Q_with_cksm;
}
 
}  // namespace
 
LMOTS_Params LMOTS_Params::create_or_throw(LMOTS_Algorithm_Type type) {
   auto [hash_name, w] = [](const LMOTS_Algorithm_Type& lmots_type) -> std::pair<std::string_view, uint8_t> {
      switch(lmots_type) {
         case LMOTS_Algorithm_Type::SHA256_N32_W1:
            return {"SHA-256", 1};
         case LMOTS_Algorithm_Type::SHA256_N32_W2:
            return {"SHA-256", 2};
         case LMOTS_Algorithm_Type::SHA256_N32_W4:
            return {"SHA-256", 4};
         case LMOTS_Algorithm_Type::SHA256_N32_W8:
            return {"SHA-256", 8};
         case LMOTS_Algorithm_Type::SHA256_N24_W1:
            return {"Truncated(SHA-256,192)", 1};
         case LMOTS_Algorithm_Type::SHA256_N24_W2:
            return {"Truncated(SHA-256,192)", 2};
         case LMOTS_Algorithm_Type::SHA256_N24_W4:
            return {"Truncated(SHA-256,192)", 4};
         case LMOTS_Algorithm_Type::SHA256_N24_W8:
            return {"Truncated(SHA-256,192)", 8};
         case LMOTS_Algorithm_Type::SHAKE_N32_W1:
            return {"SHAKE-256(256)", 1};
         case LMOTS_Algorithm_Type::SHAKE_N32_W2:
            return {"SHAKE-256(256)", 2};
         case LMOTS_Algorithm_Type::SHAKE_N32_W4:
            return {"SHAKE-256(256)", 4};
         case LMOTS_Algorithm_Type::SHAKE_N32_W8:
            return {"SHAKE-256(256)", 8};
         case LMOTS_Algorithm_Type::SHAKE_N24_W1:
            return {"SHAKE-256(192)", 1};
         case LMOTS_Algorithm_Type::SHAKE_N24_W2:
            return {"SHAKE-256(192)", 2};
         case LMOTS_Algorithm_Type::SHAKE_N24_W4:
            return {"SHAKE-256(192)", 4};
         case LMOTS_Algorithm_Type::SHAKE_N24_W8:
            return {"SHAKE-256(192)", 8};
         case LMOTS_Algorithm_Type::RESERVED:
            throw Decoding_Error("Unsupported LMS algorithm type");
      }
      throw Decoding_Error("Unsupported LMS algorithm type");
   }(type);
 
   return LMOTS_Params(type, hash_name, w);
}
 
LMOTS_Params LMOTS_Params::create_or_throw(std::string_view hash_name, uint8_t w) {
   if(w != 1 && w != 2 && w != 4 && w != 8) {
      throw Decoding_Error("Invalid Winternitz parameter");
   }
   LMOTS_Algorithm_Type type = [](std::string_view hash, uint8_t w_p) -> LMOTS_Algorithm_Type {
      if(hash == "SHA-256") {
         switch(w_p) {
            case 1:
               return LMOTS_Algorithm_Type::SHA256_N32_W1;
            case 2:
               return LMOTS_Algorithm_Type::SHA256_N32_W2;
            case 4:
               return LMOTS_Algorithm_Type::SHA256_N32_W4;
            case 8:
               return LMOTS_Algorithm_Type::SHA256_N32_W8;
            default:
               throw Decoding_Error("Unsupported Winternitz parameter");
         }
      }
      if(hash == "Truncated(SHA-256,192)") {
         switch(w_p) {
            case 1:
               return LMOTS_Algorithm_Type::SHA256_N24_W1;
            case 2:
               return LMOTS_Algorithm_Type::SHA256_N24_W2;
            case 4:
               return LMOTS_Algorithm_Type::SHA256_N24_W4;
            case 8:
               return LMOTS_Algorithm_Type::SHA256_N24_W8;
            default:
               throw Decoding_Error("Unsupported Winternitz parameter");
         }
      }
      if(hash == "SHAKE-256(256)") {
         switch(w_p) {
            case 1:
               return LMOTS_Algorithm_Type::SHAKE_N32_W1;
            case 2:
               return LMOTS_Algorithm_Type::SHAKE_N32_W2;
            case 4:
               return LMOTS_Algorithm_Type::SHAKE_N32_W4;
            case 8:
               return LMOTS_Algorithm_Type::SHAKE_N32_W8;
            default:
               throw Decoding_Error("Unsupported Winternitz parameter");
         }
      }
      if(hash == "SHAKE-256(192)") {
         switch(w_p) {
            case 1:
               return LMOTS_Algorithm_Type::SHAKE_N24_W1;
            case 2:
               return LMOTS_Algorithm_Type::SHAKE_N24_W2;
            case 4:
               return LMOTS_Algorithm_Type::SHAKE_N24_W4;
            case 8:
               return LMOTS_Algorithm_Type::SHAKE_N24_W8;
            default:
               throw Decoding_Error("Unsupported Winternitz parameter");
         }
      }
      throw Decoding_Error("Unsupported hash function");
   }(hash_name, w);
 
   return LMOTS_Params(type, hash_name, w);
}
 
LMOTS_Params::LMOTS_Params(LMOTS_Algorithm_Type algorithm_type, std::string_view hash_name, uint8_t w) :
      m_algorithm_type(algorithm_type), m_w(w), m_hash_name(hash_name) {
   const auto hash = HashFunction::create_or_throw(m_hash_name);
   m_n = hash->output_length();
   // RFC 8553 Appendix B - Parameter Computation
   auto u = ceil_division<size_t>(8 * m_n, m_w);                         // ceil(8*n/w)
   auto v = ceil_division<size_t>(high_bit(((1 << m_w) - 1) * u), m_w);  // ceil((floor(lg[(2^w - 1) * u]) + 1) / w)
   m_ls = checked_cast_to<uint8_t>(16 - (v * w));
   m_p = checked_cast_to<uint16_t>(u + v);
}
 
LMOTS_Signature::LMOTS_Signature(LMOTS_Algorithm_Type lmots_type,
                                 std::vector<uint8_t> C,
                                 std::vector<uint8_t> y_buffer) :
      m_algorithm_type(lmots_type), m_C(std::move(C)), m_y_buffer(std::move(y_buffer)) {
   LMOTS_Params params = LMOTS_Params::create_or_throw(m_algorithm_type);
 
   BufferSlicer y_slicer(m_y_buffer);
   for(uint16_t i = 0; i < params.p(); ++i) {
      m_y.push_back(y_slicer.take<LMOTS_Node>(params.n()));
   }
   BOTAN_ASSERT_NOMSG(y_slicer.empty());
}
 
LMOTS_Signature LMOTS_Signature::from_bytes_or_throw(BufferSlicer& slicer) {
   size_t total_remaining_bytes = slicer.remaining();
   // Alg. 6a. 1. (last 4 bytes) / Alg. 4b. 1.
   if(total_remaining_bytes < sizeof(LMOTS_Algorithm_Type)) {
      throw Decoding_Error("Too few signature bytes while parsing LMOTS signature.");
   }
   // Alg. 6a. 2.b. / Alg. 4b. 2.a.
   auto algorithm_type = load_be<LMOTS_Algorithm_Type>(slicer.take<sizeof(LMOTS_Algorithm_Type)>());
 
   // Alg. 6a. 2.d. / Alg. 4b. 2.c.
   LMOTS_Params params = LMOTS_Params::create_or_throw(algorithm_type);
 
   if(total_remaining_bytes < size(params)) {
      throw Decoding_Error("Too few signature bytes while parsing LMOTS signature.");
   }
 
   // Alg. 4b. 2.d.
   auto C = slicer.copy_as_vector(params.n());
   // Alg. 4b. 2.e.
   auto m_y_buffer = slicer.copy_as_vector(params.p() * params.n());
 
   return LMOTS_Signature(algorithm_type, std::move(C), std::move(m_y_buffer));
}
 
LMOTS_Private_Key::LMOTS_Private_Key(const LMOTS_Params& params,
                                     const LMS_Identifier& identifier,
                                     LMS_Tree_Node_Idx q,
                                     const LMS_Seed& seed) :
      OTS_Instance(params, identifier, q), m_seed(seed) {
   PseudorandomKeyGeneration gen(identifier);
   const auto hash = params.hash();
 
   gen.set_q(q.get());
   gen.set_j(0xff);
 
   for(uint16_t i = 0; i < params.p(); ++i) {
      gen.set_i(i);
      m_ots_sk.push_back(gen.gen<LMOTS_Node>(*hash, seed));
   }
}
 
void LMOTS_Private_Key::sign(StrongSpan<LMOTS_Signature_Bytes> out_sig, const LMS_Message& msg) const {
   BOTAN_ARG_CHECK(out_sig.size() == LMOTS_Signature::size(params()), "Invalid output buffer size");
   BufferStuffer sig_stuffer(out_sig);
   const auto hash = params().hash();
   sig_stuffer.append(store_be(params().algorithm_type()));
   const auto C = sig_stuffer.next(params().n());
 
   // Since we do not store the signatures of the lms trees in the HSS sk,
   // we need deterministic signatures to avoid reusing a OTS key to generate multiple signatures.
   // See also: https://github.com/cisco/hash-sigs/blob/b0631b8891295bf2929e68761205337b7c031726/lm_ots_sign.c#L110-L115
   derive_random_C(C, *hash);
 
   const auto Q_with_cksm = gen_Q_with_cksm(params(), identifier(), q(), C, msg);
 
   Chain_Generator chain_gen(identifier(), q());
   for(uint16_t i = 0; i < params().p(); ++i) {
      const auto y_i = sig_stuffer.next(params().n());
      const uint8_t a = coef(Q_with_cksm, i, params());
      chain_gen.process(*hash, i, 0, a, chain_input(i), y_i);
   }
   BOTAN_ASSERT_NOMSG(sig_stuffer.full());
}
 
void LMOTS_Private_Key::derive_random_C(std::span<uint8_t> out, HashFunction& hash) const {
   PseudorandomKeyGeneration gen(identifier());
 
   gen.set_q(q().get());
   gen.set_i(C_INDEX);
   gen.set_j(0xff);
 
   gen.gen(out, hash, m_seed);
}
 
LMOTS_Public_Key::LMOTS_Public_Key(const LMOTS_Private_Key& lmots_sk) : OTS_Instance(lmots_sk) {
   const auto pk_hash = lmots_sk.params().hash();
   pk_hash->update(lmots_sk.identifier());
   pk_hash->update(store_be(lmots_sk.q()));
   pk_hash->update(store_be(D_PBLC));
 
   Chain_Generator chain_gen(lmots_sk.identifier(), lmots_sk.q());
   const auto hash = lmots_sk.params().hash();
   LMOTS_Node tmp(lmots_sk.params().n());
   for(uint16_t i = 0; i < lmots_sk.params().p(); ++i) {
      chain_gen.process(*hash, i, 0, lmots_sk.params().coef_max(), lmots_sk.chain_input(i), tmp);
      pk_hash->update(tmp);
   }
 
   m_K = pk_hash->final<LMOTS_K>();
}
 
LMOTS_K lmots_compute_pubkey_from_sig(const LMOTS_Signature& sig,
                                      const LMS_Message& msg,
                                      const LMS_Identifier& identifier,
                                      LMS_Tree_Node_Idx q) {
   auto params = LMOTS_Params::create_or_throw(sig.algorithm_type());
 
   // Alg. 4b 3.
 
   const auto Q_with_cksm = gen_Q_with_cksm(params, identifier, q, sig.C(), msg);
 
   // Prefill the final hash object
   const auto pk_hash = params.hash();
   pk_hash->update(identifier);
   pk_hash->update(store_be(q));
   pk_hash->update(store_be(D_PBLC));
 
   Chain_Generator chain_gen(identifier, q);
   const auto hash = params.hash();
   LMOTS_Node tmp(params.n());
   for(uint16_t i = 0; i < params.p(); ++i) {
      const uint8_t a = coef(Q_with_cksm, i, params);
      chain_gen.process(*hash, i, a, params.coef_max(), sig.y(i), tmp);
      pk_hash->update(tmp);
   }
   // Alg. 4b 4.
   return pk_hash->final<LMOTS_K>();
}
 
}  // namespace Botan