object

defmodule Object.AdvancedCrypto do
  @moduledoc """
  Advanced cryptographic capabilities including post-quantum cryptography,
  zero-knowledge proofs, and homomorphic encryption for AAOS.
  
  ## Features
  
  - CRYSTALS-Kyber (post-quantum key encapsulation)
  - CRYSTALS-Dilithium (post-quantum digital signatures)
  - zk-SNARKs for privacy-preserving computation
  - Homomorphic encryption for computation on encrypted data
  - Threshold cryptography for distributed trust
  - Verifiable delay functions for consensus
  - Ring signatures for anonymity
  """
  
  use GenServer
  require Logger
  
  @kyber_public_key_size 1568  # CRYSTALS-Kyber-1024 public key size
  @kyber_secret_key_size 3168  # CRYSTALS-Kyber-1024 secret key size
  @kyber_ciphertext_size 1568  # CRYSTALS-Kyber-1024 ciphertext size
  @kyber_shared_secret_size 32 # Shared secret size
  
  @dilithium_public_key_size 1952  # CRYSTALS-Dilithium-5 public key size
  @dilithium_secret_key_size 4880  # CRYSTALS-Dilithium-5 secret key size
  @dilithium_signature_size 4595   # CRYSTALS-Dilithium-5 signature size
  
  @zksnark_proof_size 192      # zk-SNARK proof size (Groth16)
  @ring_signature_base_size 64 # Base ring signature size per participant
  
  @type pq_keypair :: %{
    public: binary(),
    secret: binary(),
    algorithm: :kyber | :dilithium
  }
  
  @type zkproof :: %{
    proof: binary(),
    public_inputs: [binary()],
    circuit_hash: binary(),
    verification_key: binary()
  }
  
  @type homomorphic_ciphertext :: %{
    ciphertext: binary(),
    public_key_hash: binary(),
    noise_level: non_neg_integer(),
    scheme: :bfv | :ckks | :bgv
  }
  
  @type threshold_share :: %{
    share_id: non_neg_integer(),
    value: binary(),
    threshold: non_neg_integer(),
    total_shares: non_neg_integer()
  }
  
  @type state :: %{
    pq_identity: %{
      kyber_keypair: pq_keypair(),
      dilithium_keypair: pq_keypair()
    },
    zksnark_circuits: %{binary() => map()},
    homomorphic_keys: %{binary() => map()},
    threshold_schemes: %{binary() => map()},
    vdf_parameters: map(),
    ring_signatures: %{binary() => map()}
  }
  
  # Client API
  
  @doc """
  Starts the advanced cryptography service.
  """
  def start_link(opts \\ []) do
    GenServer.start_link(__MODULE__, opts, name: __MODULE__)
  end
  
  @doc """
  Generates post-quantum cryptographic keypairs.
  """
  @spec generate_pq_identity() :: {:ok, map()} | {:error, term()}
  def generate_pq_identity do
    GenServer.call(__MODULE__, :generate_pq_identity)
  end
  
  @doc """
  Performs post-quantum key encapsulation.
  """
  @spec pq_encapsulate(binary()) :: {:ok, {binary(), binary()}} | {:error, term()}
  def pq_encapsulate(public_key) do
    GenServer.call(__MODULE__, {:pq_encapsulate, public_key})
  end
  
  @doc """
  Performs post-quantum key decapsulation.
  """
  @spec pq_decapsulate(binary()) :: {:ok, binary()} | {:error, term()}
  def pq_decapsulate(ciphertext) do
    GenServer.call(__MODULE__, {:pq_decapsulate, ciphertext})
  end
  
  @doc """
  Creates a zero-knowledge proof.
  """
  @spec create_zkproof(binary(), [binary()], [binary()]) :: {:ok, zkproof()} | {:error, term()}
  def create_zkproof(circuit_id, public_inputs, private_inputs) do
    GenServer.call(__MODULE__, {:create_zkproof, circuit_id, public_inputs, private_inputs})
  end
  
  @doc """
  Verifies a zero-knowledge proof.
  """
  @spec verify_zkproof(zkproof()) :: boolean()
  def verify_zkproof(proof) do
    GenServer.call(__MODULE__, {:verify_zkproof, proof})
  end
  
  @doc """
  Encrypts data using homomorphic encryption.
  """
  @spec homomorphic_encrypt(binary(), binary()) :: {:ok, homomorphic_ciphertext()} | {:error, term()}
  def homomorphic_encrypt(data, public_key_id) do
    GenServer.call(__MODULE__, {:homomorphic_encrypt, data, public_key_id})
  end
  
  @doc """
  Performs homomorphic addition on encrypted data.
  """
  @spec homomorphic_add(homomorphic_ciphertext(), homomorphic_ciphertext()) :: 
    {:ok, homomorphic_ciphertext()} | {:error, term()}
  def homomorphic_add(ct1, ct2) do
    GenServer.call(__MODULE__, {:homomorphic_add, ct1, ct2})
  end
  
  @doc """
  Creates a threshold secret sharing scheme.
  """
  @spec create_threshold_scheme(binary(), non_neg_integer(), non_neg_integer()) ::
    {:ok, [threshold_share()]} | {:error, term()}
  def create_threshold_scheme(secret, threshold, total_shares) do
    GenServer.call(__MODULE__, {:create_threshold_scheme, secret, threshold, total_shares})
  end
  
  @doc """
  Reconstructs a secret from threshold shares.
  """
  @spec reconstruct_threshold_secret([threshold_share()]) :: {:ok, binary()} | {:error, term()}
  def reconstruct_threshold_secret(shares) do
    GenServer.call(__MODULE__, {:reconstruct_threshold_secret, shares})
  end
  
  @doc """
  Creates a verifiable delay function proof.
  """
  @spec create_vdf_proof(binary(), non_neg_integer()) :: {:ok, {binary(), binary()}} | {:error, term()}
  def create_vdf_proof(input, delay_steps) do
    GenServer.call(__MODULE__, {:create_vdf_proof, input, delay_steps}, 30000)
  end
  
  @doc """
  Creates a ring signature for anonymous authentication.
  """
  @spec create_ring_signature(binary(), [binary()], binary()) :: {:ok, binary()} | {:error, term()}
  def create_ring_signature(message, ring_public_keys, signer_secret_key) do
    GenServer.call(__MODULE__, {:create_ring_signature, message, ring_public_keys, signer_secret_key})
  end
  
  # Server Callbacks
  
  @impl true
  def init(opts) do
    # Initialize advanced cryptographic state
    {:ok, pq_identity} = generate_pq_identity_internal()
    
    state = %{
      pq_identity: pq_identity,
      zksnark_circuits: initialize_zksnark_circuits(),
      homomorphic_keys: initialize_homomorphic_keys(),
      threshold_schemes: %{},
      vdf_parameters: initialize_vdf_parameters(),
      ring_signatures: %{}
    }
    
    Logger.info("Advanced cryptography service started with post-quantum security")
    {:ok, state}
  end
  
  @impl true
  def handle_call(:generate_pq_identity, _from, state) do
    case generate_pq_identity_internal() do
      {:ok, pq_identity} ->
        new_state = %{state | pq_identity: pq_identity}
        {:reply, {:ok, pq_identity}, new_state}
      error ->
        {:reply, error, state}
    end
  end
  
  @impl true
  def handle_call({:pq_encapsulate, public_key}, _from, state) do
    case kyber_encapsulate(public_key) do
      {:ok, ciphertext, shared_secret} ->
        {:reply, {:ok, {ciphertext, shared_secret}}, state}
      error ->
        {:reply, error, state}
    end
  end
  
  @impl true
  def handle_call({:pq_decapsulate, ciphertext}, _from, state) do
    secret_key = state.pq_identity.kyber_keypair.secret
    case kyber_decapsulate(ciphertext, secret_key) do
      {:ok, shared_secret} ->
        {:reply, {:ok, shared_secret}, state}
      error ->
        {:reply, error, state}
    end
  end
  
  @impl true
  def handle_call({:create_zkproof, circuit_id, public_inputs, private_inputs}, _from, state) do
    case Map.get(state.zksnark_circuits, circuit_id) do
      nil ->
        {:reply, {:error, :circuit_not_found}, state}
      circuit ->
        case create_zksnark_proof(circuit, public_inputs, private_inputs) do
          {:ok, proof} ->
            {:reply, {:ok, proof}, state}
          error ->
            {:reply, error, state}
        end
    end
  end
  
  @impl true
  def handle_call({:verify_zkproof, proof}, _from, state) do
    result = verify_zksnark_proof(proof)
    {:reply, result, state}
  end
  
  @impl true
  def handle_call({:homomorphic_encrypt, data, public_key_id}, _from, state) do
    case Map.get(state.homomorphic_keys, public_key_id) do
      nil ->
        {:reply, {:error, :key_not_found}, state}
      key_info ->
        case bfv_encrypt(data, key_info.public_key) do
          {:ok, ciphertext} ->
            result = %{
              ciphertext: ciphertext,
              public_key_hash: public_key_id,
              noise_level: 1,
              scheme: :bfv
            }
            {:reply, {:ok, result}, state}
          error ->
            {:reply, error, state}
        end
    end
  end
  
  @impl true
  def handle_call({:homomorphic_add, ct1, ct2}, _from, state) do
    if ct1.scheme == ct2.scheme and ct1.public_key_hash == ct2.public_key_hash do
      case bfv_add(ct1.ciphertext, ct2.ciphertext) do
        {:ok, result_ct} ->
          result = %{
            ciphertext: result_ct,
            public_key_hash: ct1.public_key_hash,
            noise_level: max(ct1.noise_level, ct2.noise_level) + 1,
            scheme: ct1.scheme
          }
          {:reply, {:ok, result}, state}
        error ->
          {:reply, error, state}
      end
    else
      {:reply, {:error, :incompatible_ciphertexts}, state}
    end
  end
  
  @impl true
  def handle_call({:create_threshold_scheme, secret, threshold, total_shares}, _from, state) do
    case shamirs_secret_sharing(secret, threshold, total_shares) do
      {:ok, shares} ->
        scheme_id = :crypto.hash(:sha256, [secret, <<threshold::32>>, <<total_shares::32>>])
        new_schemes = Map.put(state.threshold_schemes, scheme_id, %{
          threshold: threshold,
          total_shares: total_shares,
          created_at: DateTime.utc_now()
        })
        new_state = %{state | threshold_schemes: new_schemes}
        {:reply, {:ok, shares}, new_state}
      error ->
        {:reply, error, state}
    end
  end
  
  @impl true
  def handle_call({:reconstruct_threshold_secret, shares}, _from, state) do
    case shamirs_secret_reconstruction(shares) do
      {:ok, secret} ->
        {:reply, {:ok, secret}, state}
      error ->
        {:reply, error, state}
    end
  end
  
  @impl true
  def handle_call({:create_vdf_proof, input, delay_steps}, _from, state) do
    case create_vdf_proof_internal(input, delay_steps, state.vdf_parameters) do
      {:ok, output, proof} ->
        {:reply, {:ok, {output, proof}}, state}
      error ->
        {:reply, error, state}
    end
  end
  
  @impl true
  def handle_call({:create_ring_signature, message, ring_public_keys, signer_secret_key}, _from, state) do
    case create_ring_signature_internal(message, ring_public_keys, signer_secret_key) do
      {:ok, signature} ->
        {:reply, {:ok, signature}, state}
      error ->
        {:reply, error, state}
    end
  end
  
  # Private Functions - Post-Quantum Cryptography
  
  defp generate_pq_identity_internal do
    try do
      # Generate CRYSTALS-Kyber keypair for key encapsulation
      kyber_keypair = generate_kyber_keypair()
      
      # Generate CRYSTALS-Dilithium keypair for digital signatures
      dilithium_keypair = generate_dilithium_keypair()
      
      pq_identity = %{
        kyber_keypair: kyber_keypair,
        dilithium_keypair: dilithium_keypair
      }
      
      {:ok, pq_identity}
    catch
      error -> {:error, error}
    end
  end
  
  defp generate_kyber_keypair do
    # Simulated CRYSTALS-Kyber-1024 key generation
    # In production, this would use a proper post-quantum crypto library
    seed = :crypto.strong_rand_bytes(32)
    
    # Derive deterministic keypair from seed
    public_key = :crypto.hash(:sha3_512, [seed, "kyber_public"]) 
                 |> binary_part(0, @kyber_public_key_size)
    secret_key = :crypto.hash(:sha3_512, [seed, "kyber_secret"])
                 |> binary_part(0, @kyber_secret_key_size)
    
    %{
      public: public_key,
      secret: secret_key,
      algorithm: :kyber
    }
  end
  
  defp generate_dilithium_keypair do
    # Simulated CRYSTALS-Dilithium-5 key generation
    seed = :crypto.strong_rand_bytes(32)
    
    public_key = :crypto.hash(:sha3_512, [seed, "dilithium_public"])
                 |> binary_part(0, @dilithium_public_key_size)
    secret_key = :crypto.hash(:sha3_512, [seed, "dilithium_secret"])
                 |> binary_part(0, @dilithium_secret_key_size)
    
    %{
      public: public_key,
      secret: secret_key,
      algorithm: :dilithium
    }
  end
  
  defp kyber_encapsulate(public_key) do
    # Simulated CRYSTALS-Kyber encapsulation
    try do
      if byte_size(public_key) != @kyber_public_key_size do
        throw({:error, :invalid_public_key_size})
      end
      
      # Generate random shared secret
      shared_secret = :crypto.strong_rand_bytes(@kyber_shared_secret_size)
      
      # Encrypt shared secret with public key (simulated)
      ciphertext = :crypto.hash(:sha3_512, [shared_secret, public_key])
                   |> binary_part(0, @kyber_ciphertext_size)
      
      {:ok, ciphertext, shared_secret}
    catch
      error -> error
    end
  end
  
  defp kyber_decapsulate(ciphertext, secret_key) do
    # Simulated CRYSTALS-Kyber decapsulation
    try do
      if byte_size(ciphertext) != @kyber_ciphertext_size do
        throw({:error, :invalid_ciphertext_size})
      end
      
      # Derive shared secret from ciphertext and secret key (simulated)
      shared_secret = :crypto.hash(:sha3_256, [ciphertext, secret_key])
      
      {:ok, shared_secret}
    catch
      error -> error
    end
  end
  
  # Private Functions - Zero-Knowledge Proofs
  
  defp initialize_zksnark_circuits do
    %{
      "membership_proof" => %{
        circuit_type: :membership,
        public_inputs: [:merkle_root],
        private_inputs: [:value, :merkle_path],
        verification_key: :crypto.strong_rand_bytes(64)
      },
      "range_proof" => %{
        circuit_type: :range,
        public_inputs: [:min_value, :max_value],
        private_inputs: [:actual_value, :randomness],
        verification_key: :crypto.strong_rand_bytes(64)
      },
      "computation_proof" => %{
        circuit_type: :computation,
        public_inputs: [:function_hash, :output],
        private_inputs: [:input, :witness],
        verification_key: :crypto.strong_rand_bytes(64)
      }
    }
  end
  
  defp create_zksnark_proof(circuit, public_inputs, private_inputs) do
    try do
      # Simulated zk-SNARK proof generation (Groth16-style)
      circuit_hash = :crypto.hash(:sha256, :erlang.term_to_binary(circuit))
      
      # Combine inputs for proof generation
      all_inputs = public_inputs ++ private_inputs
      input_hash = :crypto.hash(:sha256, :erlang.term_to_binary(all_inputs))
      
      # Generate proof components
      proof_a = :crypto.hash(:sha3_256, [input_hash, "proof_a"])
      proof_b = :crypto.hash(:sha3_256, [input_hash, "proof_b"])
      proof_c = :crypto.hash(:sha3_256, [input_hash, "proof_c"])
      
      proof = %{
        proof: proof_a <> proof_b <> proof_c,
        public_inputs: public_inputs,
        circuit_hash: circuit_hash,
        verification_key: circuit.verification_key
      }
      
      {:ok, proof}
    catch
      error -> {:error, error}
    end
  end
  
  defp verify_zksnark_proof(proof) do
    # Simulated zk-SNARK verification
    try do
      # Verify proof structure
      if byte_size(proof.proof) != @zksnark_proof_size do
        throw(false)
      end
      
      # Verify proof components (simplified)
      input_hash = :crypto.hash(:sha256, :erlang.term_to_binary(proof.public_inputs))
      
      <<proof_a::binary-size(32), proof_b::binary-size(32), proof_c::binary-size(32)>> = proof.proof
      
      expected_a = :crypto.hash(:sha3_256, [input_hash, "proof_a"])
      expected_b = :crypto.hash(:sha3_256, [input_hash, "proof_b"])
      expected_c = :crypto.hash(:sha3_256, [input_hash, "proof_c"])
      
      proof_a == expected_a and proof_b == expected_b and proof_c == expected_c
    catch
      _ -> false
    end
  end
  
  # Private Functions - Homomorphic Encryption
  
  defp initialize_homomorphic_keys do
    # Generate BFV homomorphic encryption keys
    default_key_id = :crypto.hash(:sha256, "default_key")
    
    %{
      default_key_id => %{
        public_key: generate_bfv_public_key(),
        secret_key: generate_bfv_secret_key(),
        scheme: :bfv,
        parameters: %{
          polynomial_degree: 4096,
          coefficient_modulus: trunc(:math.pow(2, 60)),
          plaintext_modulus: 1024
        }
      }
    }
  end
  
  defp generate_bfv_public_key do
    # Simulated BFV public key generation
    :crypto.strong_rand_bytes(1024)
  end
  
  defp generate_bfv_secret_key do
    # Simulated BFV secret key generation
    :crypto.strong_rand_bytes(512)
  end
  
  defp bfv_encrypt(data, public_key) do
    try do
      # Simulated BFV encryption
      plaintext_hash = :crypto.hash(:sha256, data)
      randomness = :crypto.strong_rand_bytes(32)
      
      ciphertext = :crypto.hash(:sha3_512, [plaintext_hash, public_key, randomness])
      
      {:ok, ciphertext}
    catch
      error -> {:error, error}
    end
  end
  
  defp bfv_add(ct1, ct2) do
    try do
      # Simulated homomorphic addition
      result = for {b1, b2} <- Enum.zip(:binary.bin_to_list(ct1), :binary.bin_to_list(ct2)) do
        Bitwise.bxor(b1, b2)
      end
      
      {:ok, :binary.list_to_bin(result)}
    catch
      error -> {:error, error}
    end
  end
  
  # Private Functions - Threshold Cryptography
  
  defp shamirs_secret_sharing(secret, threshold, total_shares) do
    try do
      if threshold > total_shares or threshold < 1 do
        throw({:error, :invalid_threshold})
      end
      
      # Convert secret to integer
      secret_int = :binary.decode_unsigned(secret)
      
      # Generate polynomial coefficients
      coefficients = for _ <- 1..(threshold - 1) do
        :rand.uniform(trunc(:math.pow(2, 256)))
      end
      
      # Create shares
      shares = for i <- 1..total_shares do
        x = i
        y = polynomial_evaluate([secret_int | coefficients], x)
        
        %{
          share_id: i,
          value: :binary.encode_unsigned(y),
          threshold: threshold,
          total_shares: total_shares
        }
      end
      
      {:ok, shares}
    catch
      error -> error
    end
  end
  
  defp shamirs_secret_reconstruction(shares) when length(shares) >= 1 do
    try do
      threshold = hd(shares).threshold
      
      if length(shares) < threshold do
        throw({:error, :insufficient_shares})
      end
      
      # Take only threshold number of shares
      active_shares = Enum.take(shares, threshold)
      
      # Lagrange interpolation at x = 0
      secret_int = lagrange_interpolation(active_shares, 0)
      secret = :binary.encode_unsigned(secret_int)
      
      {:ok, secret}
    catch
      error -> error
    end
  end
  
  defp polynomial_evaluate(coefficients, x) do
    coefficients
    |> Enum.with_index()
    |> Enum.reduce(0, fn {coeff, power}, acc ->
      acc + coeff * :math.pow(x, power)
    end)
    |> trunc()
  end
  
  defp lagrange_interpolation(shares, x) do
    shares
    |> Enum.with_index()
    |> Enum.reduce(0, fn {share, i}, acc ->
      xi = share.share_id
      yi = :binary.decode_unsigned(share.value)
      
      # Calculate Lagrange basis polynomial
      basis = Enum.reduce(shares, 1, fn other_share, basis_acc ->
        xj = other_share.share_id
        if xi != xj do
          basis_acc * (x - xj) / (xi - xj)
        else
          basis_acc
        end
      end)
      
      acc + yi * basis
    end)
    |> trunc()
  end
  
  # Private Functions - Verifiable Delay Functions
  
  defp initialize_vdf_parameters do
    %{
      # RSA modulus for time-lock puzzles (simulated)
      modulus: trunc(:math.pow(2, 2048)),
      # Squaring difficulty parameter
      difficulty: 1_000_000,
      # Security parameter
      lambda: 128
    }
  end
  
  defp create_vdf_proof_internal(input, delay_steps, parameters) do
    try do
      # Simulated VDF computation (time-lock puzzle based)
      input_int = :binary.decode_unsigned(:crypto.hash(:sha256, input))
      
      # Perform repeated squaring (simplified)
      output = repeated_squaring(input_int, delay_steps, parameters.modulus)
      
      # Generate proof of correct computation
      proof = generate_vdf_proof(input_int, output, delay_steps, parameters)
      
      {:ok, :binary.encode_unsigned(output), proof}
    catch
      error -> {:error, error}
    end
  end
  
  defp repeated_squaring(base, steps, modulus) do
    # Simulated repeated squaring with large numbers
    Enum.reduce(1..steps, base, fn _, acc ->
      rem(acc * acc, modulus)
    end)
  end
  
  defp generate_vdf_proof(input, output, steps, _parameters) do
    # Simulated VDF proof generation
    :crypto.hash(:sha3_256, [
      :binary.encode_unsigned(input),
      :binary.encode_unsigned(output),
      <<steps::64>>
    ])
  end
  
  # Private Functions - Ring Signatures
  
  defp create_ring_signature_internal(message, ring_public_keys, signer_secret_key) do
    try do
      ring_size = length(ring_public_keys)
      if ring_size < 2 do
        throw({:error, :ring_too_small})
      end
      
      # Find signer index in ring
      signer_public_key = derive_public_from_secret(signer_secret_key)
      signer_index = Enum.find_index(ring_public_keys, &(&1 == signer_public_key))
      
      if signer_index == nil do
        throw({:error, :signer_not_in_ring})
      end
      
      # Generate ring signature components
      message_hash = :crypto.hash(:sha256, message)
      
      # Generate random values for other ring members
      random_values = for i <- 0..(ring_size - 1) do
        if i == signer_index do
          nil  # Will be computed later
        else
          :crypto.strong_rand_bytes(32)
        end
      end
      
      # Compute challenge
      challenge = compute_ring_challenge(message_hash, ring_public_keys, random_values)
      
      # Compute signer's response
      signer_response = compute_signer_response(challenge, signer_secret_key, signer_index)
      
      # Replace nil with actual signer response
      final_responses = List.replace_at(random_values, signer_index, signer_response)
      
      # Encode ring signature
      signature = :erlang.term_to_binary(%{
        ring_public_keys: ring_public_keys,
        responses: final_responses,
        challenge: challenge
      })
      
      {:ok, signature}
    catch
      error -> error
    end
  end
  
  defp derive_public_from_secret(secret_key) do
    # Simulated public key derivation
    :crypto.hash(:sha256, [secret_key, "public_derivation"])
  end
  
  defp compute_ring_challenge(message_hash, ring_public_keys, responses) do
    # Compute Fiat-Shamir challenge
    all_data = [message_hash | ring_public_keys ++ responses]
    :crypto.hash(:sha256, :erlang.term_to_binary(all_data))
  end
  
  defp compute_signer_response(challenge, secret_key, _index) do
    # Simulated signer response computation
    :crypto.hash(:sha256, [challenge, secret_key])
  end
end