Add the INVPERM instruction

The IVMPERM instruction takes in a secret shared vector representing a permutation, and returns the corresponding secret shared inverse permutation.

Compiler/instructions.py

@@ -2501,6 +2501,26 @@ class delshuffle(base.Instruction):
     code = base.opcodes['DELSHUFFLE']
     arg_format = ['ci']
 
+class inverse_permutation(base.VectorInstruction, shuffle_base):
+    """ Calculate the inverse permutation of a secret permutation.
+
+    :param: destination (sint)
+    :param: source (sint)
+
+    """
+    __slots__ = []
+    code = base.opcodes['INVPERM']
+    arg_format = ['sw', 's']
+
+    def __init__(self, *args, **kwargs):
+        super(inverse_permutation, self).__init__(*args, **kwargs)
+        assert len(args[0]) == len(args[1])
+
+    def add_usage(self, req_node):
+        self.add_gen_usage(req_node, len(self.args[0]))
+        self.add_apply_usage(req_node, len(self.args[0]), 1)
+
+
 class check(base.Instruction):
     """
     Force MAC check in current thread and all idle thread if current

Compiler/instructions_base.py

@@ -111,6 +111,7 @@ opcodes = dict(
     GENSECSHUFFLE = 0xFB,
     APPLYSHUFFLE = 0xFC,
     DELSHUFFLE = 0xFD,
+    INVPERM = 0xFE,
     # Data access
     TRIPLE = 0x50,
     BIT = 0x51,

Compiler/types.py

@@ -2776,6 +2776,11 @@ class sint(_secret, _int):
         applyshuffle(res, self, unit_size, shuffle, reverse)
         return res
 
+    def inverse_permutation(self):
+        res = sint(size=self.size)
+        inverse_permutation(res, self)
+        return res
+
 class sintbit(sint):
     """ :py:class:`sint` holding a bit, supporting binary operations
     (``&, |, ^``). """

Processor/Instruction.h

@@ -113,6 +113,7 @@ enum
     GENSECSHUFFLE = 0xFB,
     APPLYSHUFFLE = 0xFC,
     DELSHUFFLE = 0xFD,
+    INVPERM = 0xFE,
     // Data access
     TRIPLE = 0x50,
     BIT = 0x51,

Processor/Instruction.hpp

@@ -283,6 +283,10 @@ void BaseInstruction::parse_operands(istream& s, int pos, int file_pos)
         n = get_int(s);
         get_vector(2, start, s);
         break;
+      // instructions with 2 register operands
+      case INVPERM:
+          get_vector(2, start, s);
+          break;
       // open instructions + read/write instructions with variable length args
       case OPEN:
       case GOPEN:
@@ -1076,6 +1080,9 @@ inline void Instruction::execute(Processor<sint, sgf2n>& Proc) const
       case DELSHUFFLE:
         Proc.Procp.delete_shuffle(Proc.read_Ci(r[0]));
         return;
+      case INVPERM:
+        Proc.Procp.inverse_permutation(*this);
+        return;
       case CHECK:
         {
           CheckJob job;

Processor/Processor.h

@@ -77,6 +77,7 @@ public:
   size_t generate_secure_shuffle(const Instruction& instruction);
   void apply_shuffle(const Instruction& instruction, int handle);
   void delete_shuffle(int handle);
+  void inverse_permutation(const Instruction& instruction);
 
   void input_personal(const vector<int>& args);
   void send_personal(const vector<int>& args);
@@ -101,6 +102,8 @@ public:
   {
     return C[i];
   }
+
+    void inverse_permutation(const Instruction &instruction, int handle);
 };
 
 class ArithmeticProcessor : public ProcessorBase

Processor/Processor.hpp

@@ -668,6 +668,12 @@ void SubProcessor<T>::delete_shuffle(int handle)
     shuffler.del(handle);
 }
 
+template<class T>
+void SubProcessor<T>::inverse_permutation(const Instruction& instruction) {
+    shuffler.inverse_permutation(S, instruction.get_size(), instruction.get_start()[0],
+                                 instruction.get_start()[1]);
+}
+
 template<class T>
 void SubProcessor<T>::input_personal(const vector<int>& args)
 {
@@ -686,6 +692,16 @@ void SubProcessor<T>::input_personal(const vector<int>& args)
       S[args[i + 2] + j] = input.finalize(args[i + 1]);
 }
 
+/**
+ *
+ * @tparam T
+ * @param args Args contains four arguments
+ *      a[0] = the size of the input (and output) vector
+ *      a[1] = the player to which to reveal the output
+ *      a[2] = the memory address of the input vector (sint) (i.e. the value to reveal)
+ *      a[3] = the memory address of the output vector (cint) (i.e. the register to store the revealed value)
+ * // TODO: When would there be multiple sets of arguments? (for ... i < args.size(); i += 4 ... )
+ */
 template<class T>
 void SubProcessor<T>::private_output(const vector<int>& args)
 {

Protocols/SecureShuffle.h

@@ -24,8 +24,28 @@ class SecureShuffle
     size_t n_shuffle;
     bool exact;
 
+    /**
+     * Generates and returns a newly generated random permutation. This permutation is generated locally.
+     *
+     * @param n The size of the permutation to generate.
+     * @return A vector representing a permutation, a shuffled array of integers 0 through n-1.
+     */
+    vector<int> generate_random_permutation(int n);
+
+    /**
+     * Configure a shared waksman network from a permutation known only to config_player.
+     * Note that although the configuration bits of the waksman network are secret shared,
+     * the player that generated the permutation (config_player) knows the value of these bits.
+     *
+     * A permutation is a mapping represented as a vector.
+     * Each item in the vector represents the output of mapping(i) where i is the index of that item.
+     *      e.g. [2, 4, 0, 3, 1] -> perm(1) = 4
+     *
+     * @param config_player The player tasked with generating the random permutation from which to configure the waksman network.
+     * @param n_shuffle The size of the permutation to generate.
+     */
+    void configure(int config_player, vector<int>* perm, int n);
     void player_round(int config_player);
-    void generate(int config_player, int n_shuffle);
 
     void waksman(vector<T>& a, int depth, int start);
     void cond_swap(T& x, T& y, const T& b);
@@ -44,9 +64,37 @@ public:
 
     int generate(int n_shuffle);
 
+    /**
+     *
+     * @param a The vector of registers representing the stack // TODO: Is this correct?
+     * @param n The size of the input vector to shuffle
+     * @param unit_size Determines how many vector items constitute a single block with regards to permutation:
+     *                  i.e. input vector [1,2,3,4] with <code>unit_size=2</code> under permutation map [1,0]
+     *                  would result in [3,4,1,2]
+     * @param output_base The starting address of the output vector (i.e. the location to write the inverted permutation to)
+     * @param input_base The starting address of the input vector (i.e. the location from which to read the permutation)
+     * @param handle The integer identifying the preconfigured waksman network (shuffle) to use. Such a handle can be obtained from calling
+     * @param reverse Boolean indicating whether to apply the inverse of the permutation
+     * @see SecureShuffle::generate for obtaining a shuffle handle
+     */
     void apply(vector<T>& a, size_t n, int unit_size, size_t output_base,
             size_t input_base, int handle, bool reverse);
 
+    /**
+     * Calculate the secret inverse permutation of stack given secret permutation.
+     *
+     * This method is given in [1], based on stack technique in [2]. It is used in the Compiler (high-level) implementation of Square-Root ORAM.
+     *
+     * [1] Samee Zahur, Xiao Wang, Mariana Raykova, Adrià Gascón, Jack Doerner, David Evans, and Jonathan Katz. 2016. Revisiting Square Root ORAM: Efficient Random Access in Multi-Party Computation. In IEEE S&P.
+     * [2] Ivan Damgård, Matthias Fitzi, Eike Kiltz, Jesper Buus Nielsen, and Tomas Toft. Unconditionally Secure Constant-rounds Multi-Party Computation for Equality, Comparison, Bits and Exponentiation. In Theory of Cryptography, 2006.
+     *
+     * @param stack The vector or registers representing the stack (?)
+     * @param n The size of the input vector for which to calculate the inverse permutation
+     * @param output_base The starting address of the output vector (i.e. the location to write the inverted permutation to)
+     * @param input_base The starting address of the input vector (i.e. the location from which to read the permutation)
+     */
+    void inverse_permutation(vector<T>& stack, size_t n, size_t output_base, size_t input_base);
+
     void del(int handle);
 };
 

Protocols/SecureShuffle.hpp

@@ -58,6 +58,82 @@ void SecureShuffle<T>::apply(vector<T>& a, size_t n, int unit_size, size_t outpu
     post(a, n, output_base);
 }
 
+
+template<class T>
+void SecureShuffle<T>::inverse_permutation(vector<T> &stack, size_t n, size_t output_base,
+                                           size_t input_base) {
+    int alice = 0;
+    int bob = 1;
+
+    auto &P = proc.P;
+    auto &input = proc.input;
+
+    // This method only supports two players
+    assert(proc.protocol.get_relevant_players().size() == 2);
+    // The current implementation assumes a semi-honest environment
+    assert(!T::malicious);
+
+    // We are dealing directly with permutations, so the unit_size will always be 1.
+    this->unit_size = 1;
+    // We need to account for sizes which are not a power of 2
+    size_t n_pow2 = (1u << int(ceil(log2(n))));
+
+    // Copy over the input registers
+    pre(stack, n, input_base);
+    // Alice generates stack local permutation and shares the waksman configuration bits secretly to Bob.
+    vector<int> perm_alice(n_pow2);
+    if (P.my_num() == alice)
+        perm_alice = generate_random_permutation(n);
+    configure(alice, &perm_alice, n);
+    // Apply perm_alice to perm_alice to get perm_bob,
+    // stack permutation that we can reveal to Bob without Bob learning anything about perm_alice (since it is masked by perm_a)
+    iter_waksman(true);
+    // Store perm_bob at stack[output_base]
+    post(stack, n, output_base);
+
+    // Reveal permutation perm_bob = perm_a * perm_alice
+    // Since this permutation is masked by perm_a, Bob learns nothing about perm
+    vector<int> perm_bob(n_pow2);
+    typename T::PrivateOutput output(proc);
+    for (size_t i = 0; i < n; i++)
+        output.prepare_sending(stack[output_base + i], bob);
+    output.exchange();
+    for (size_t i = 0; i < n_pow2; i++) {
+        // TODO: Is there a better way to convert a T::clear to int?
+        bigint val;
+        output.finalize(bob).to(val);
+        perm_bob[i] = (int) val.get_si();
+    }
+
+    vector<int> perm_bob_inv(n_pow2);
+    if (P.my_num() == bob) {
+        for (int i = 0; i < (int) n; i++)
+            perm_bob_inv[perm_bob[i]] = i;
+        // Pad the permutation to n_pow2
+        // Required when using waksman networks
+        for (int i = (int) n; i < (int) n_pow2; i++)
+            perm_bob_inv[i] = i;
+    }
+
+    // Alice secret shares perm_a with bob
+    // perm_a is stored in the stack at output_base
+    input.reset_all(P);
+    if (P.my_num() == alice) {
+        for (int i = 0; i < (int) n; i++)
+            input.add_mine(perm_alice[i]);
+    }
+    input.exchange();
+    for (int i = 0; i < (int) n; i++)
+        stack[output_base + i] = input.finalize(alice);
+
+    // The two parties now jointly compute perm_a * perm_bob_inv to obtain perm_inv
+    pre(stack, n, output_base);
+    configure(bob, &perm_bob_inv, n);
+    iter_waksman(true);
+    // perm_inv is written back to stack[output_base]
+    post(stack, n, output_base);
+}
+
 template<class T>
 void SecureShuffle<T>::del(int handle)
 {
@@ -129,9 +205,27 @@ void SecureShuffle<T>::post(vector<T>& a, size_t n, size_t output_base)
 }
 
 template<class T>
-void SecureShuffle<T>::player_round(int config_player)
-{
-    generate(config_player, n_shuffle);
+vector<int> SecureShuffle<T>::generate_random_permutation(int n) {
+    vector<int> perm;
+    int n_pow2 = 1 << int(ceil(log2(n)));
+    int shuffle_size = n;
+    for (int j = 0; j < n_pow2; j++)
+        perm.push_back(j);
+    SeededPRNG G;
+    for (int i = 0; i < shuffle_size; i++) {
+        int j = G.get_uint(shuffle_size - i);
+        swap(perm[i], perm[i + j]);
+    }
+
+    return perm;
+}
+
+template<class T>
+void SecureShuffle<T>::player_round(int config_player) {
+    vector<int> random_perm(n_shuffle);
+    if (proc.P.my_num() == config_player)
+        random_perm = generate_random_permutation(n_shuffle);
+    configure(config_player, &random_perm, n_shuffle);
     iter_waksman();
 }
 
@@ -142,9 +236,12 @@ int SecureShuffle<T>::generate(int n_shuffle)
     shuffles.push_back({});
     auto& shuffle = shuffles.back();
 
-    for (auto i : proc.protocol.get_relevant_players())
-    {
-        generate(i, n_shuffle);
+    for (auto i: proc.protocol.get_relevant_players()) {
+        vector<int> perm;
+        if (proc.P.my_num() == i)
+            perm = generate_random_permutation(n_shuffle);
+        configure(i, &perm, n_shuffle);
+
         shuffle.push_back(config);
     }
 
@@ -152,39 +249,27 @@ int SecureShuffle<T>::generate(int n_shuffle)
 }
 
 template<class T>
-void SecureShuffle<T>::generate(int config_player, int n)
-{
-    auto& P = proc.P;
-    auto& input = proc.input;
+void SecureShuffle<T>::configure(int config_player, vector<int> *perm, int n) {
+    auto &P = proc.P;
+    auto &input = proc.input;
     input.reset_all(P);
     int n_pow2 = 1 << int(ceil(log2(n)));
     Waksman waksman(n_pow2);
 
-    if (P.my_num() == config_player)
-    {
-        vector<int> perm;
-        int shuffle_size = n;
-        for (int j = 0; j < n_pow2; j++)
-            perm.push_back(j);
-        SeededPRNG G;
-        for (int i = 0; i < shuffle_size; i++)
-        {
-            int j = G.get_uint(shuffle_size - i);
-            swap(perm[i], perm[i + j]);
-        }
-
-        auto config_bits = waksman.configure(perm);
-        for (size_t i = 0; i < config_bits.size(); i++)
-        {
-            auto& x = config_bits[i];
+    // The player specified by config_player configures the shared waksman network
+    // using its personal permutation
+    if (P.my_num() == config_player) {
+        auto config_bits = waksman.configure(*perm);
+        for (size_t i = 0; i < config_bits.size(); i++) {
+            auto &x = config_bits[i];
             for (size_t j = 0; j < x.size(); j++)
                 if (waksman.matters(i, j))
                     input.add_mine(int(x[j]));
                 else
                     assert(x[j] == 0);
         }
-    }
-    else
+        // The other player waits for its share of the configured waksman network
+    } else
         for (size_t i = 0; i < waksman.n_bits(); i++)
             input.add_other(config_player);