prac/bst.cpp

#include <functional>

#include "bst.hpp"

// Helper functions to reconstruct shared RegBS, RegAS or RegXS

bool reconstruct_RegBS(MPCTIO &tio, yield_t &yield, RegBS flag) {
    RegBS reconstructed_flag;
    if (tio.player() < 2) {
        RegBS peer_flag;
        tio.queue_peer(&flag, 1);
        tio.queue_server(&flag, 1);
        yield();
        tio.recv_peer(&peer_flag, 1);
        reconstructed_flag = flag;
        reconstructed_flag ^= peer_flag;
    } else {
        RegBS p0_flag, p1_flag;
        yield();
        tio.recv_p0(&p0_flag, 1);
        tio.recv_p1(&p1_flag, 1);
        reconstructed_flag = p0_flag;
        reconstructed_flag ^= p1_flag;
    }
    return reconstructed_flag.bshare;
}

size_t reconstruct_RegAS(MPCTIO &tio, yield_t &yield, RegAS variable) {
    RegAS reconstructed_var;
    if (tio.player() < 2) {
        RegAS peer_var;
        tio.queue_peer(&variable, sizeof(variable));
        tio.queue_server(&variable, sizeof(variable));
        yield();
        tio.recv_peer(&peer_var, sizeof(variable));
        reconstructed_var = variable;
        reconstructed_var += peer_var;
    } else {
        RegAS p0_var, p1_var;
        yield();
        tio.recv_p0(&p0_var, sizeof(variable));
        tio.recv_p1(&p1_var, sizeof(variable));
        reconstructed_var = p0_var;
        reconstructed_var += p1_var;
    }
    return reconstructed_var.ashare;
}

size_t reconstruct_RegXS(MPCTIO &tio, yield_t &yield, RegXS variable) {
    RegXS reconstructed_var;
    if (tio.player() < 2) {
        RegXS peer_var;
        tio.queue_peer(&variable, sizeof(variable));
        tio.queue_server(&variable, sizeof(variable));
        yield();
        tio.recv_peer(&peer_var, sizeof(variable));
        reconstructed_var = variable;
        reconstructed_var ^= peer_var;
    } else {
        RegXS p0_var, p1_var;
        yield();
        tio.recv_p0(&p0_var, sizeof(variable));
        tio.recv_p1(&p1_var, sizeof(variable));
        reconstructed_var = p0_var;
        reconstructed_var ^= p1_var;
    }
    return reconstructed_var.xshare;
}

std::tuple<RegBS, RegBS> compare_keys(MPCTIO tio, yield_t &yield, Node n1, Node n2) {
    CDPF cdpf = tio.cdpf(yield);
    auto [lt, eq, gt] = cdpf.compare(tio, yield, n2.key - n1.key, tio.aes_ops());
    RegBS lteq = lt^eq;
    return {lteq, gt};
}

// Assuming pointer of 64 bits is split as:
// - 32 bits Left ptr
// - 32 bits Right ptr
// < Left, Right>

inline RegXS extractLeftPtr(RegXS pointer){ 
    return ((pointer&(0xFFFFFFFF00000000))>>32); 
}

inline RegXS extractRightPtr(RegXS pointer){
    return (pointer&(0x00000000FFFFFFFF)); 
}

inline void setLeftPtr(RegXS &pointer, RegXS new_ptr){ 
    pointer&=(0x00000000FFFFFFFF);
    pointer+=(new_ptr<<32);
}

inline void setRightPtr(RegXS &pointer, RegXS new_ptr){
    pointer&=(0xFFFFFFFF00000000);
    pointer+=(new_ptr);
}

// Pretty-print a reconstructed BST, rooted at node. is_left_child and
// is_right_child indicate whether node is a left or right child of its
// parent.  They cannot both be true, but the root of the tree has both
// of them false.
void BST::pretty_print(const std::vector<Node> &R, value_t node,
    const std::string &prefix = "", bool is_left_child = false,
    bool is_right_child = false)
{
    if (node == 0) {
        // NULL pointer
        if (is_left_child) {
            printf("%s\xE2\x95\xA7\n", prefix.c_str()); // ╧
        } else if (is_right_child) {
            printf("%s\xE2\x95\xA4\n", prefix.c_str()); // ╤
        } else {
            printf("%s\xE2\x95\xA2\n", prefix.c_str()); // ╢
        }
        return;
    }
    const Node &n = R[node];
    value_t left_ptr = extractLeftPtr(n.pointers).xshare;
    value_t right_ptr = extractRightPtr(n.pointers).xshare;
    std::string rightprefix(prefix), leftprefix(prefix),
        nodeprefix(prefix);
    if (is_left_child) {
        rightprefix.append("\xE2\x94\x82"); // │
        leftprefix.append(" ");
        nodeprefix.append("\xE2\x94\x94"); // └
    } else if (is_right_child) {
        rightprefix.append(" ");
        leftprefix.append("\xE2\x94\x82"); // │
        nodeprefix.append("\xE2\x94\x8C"); // ┌
    } else {
        rightprefix.append(" ");
        leftprefix.append(" ");
        nodeprefix.append("\xE2\x94\x80"); // ─
    }
    pretty_print(R, right_ptr, rightprefix, false, true);
    printf("%s\xE2\x94\xA4", nodeprefix.c_str()); // ┤
    n.dump();
    printf("\n");
    pretty_print(R, left_ptr, leftprefix, true, false);
}

void BST::print_oram(MPCTIO &tio, yield_t &yield) {
    auto A = oram->flat(tio, yield);
    auto R = A.reconstruct();

    for(size_t i=0;i<R.size();++i) {
        printf("\n%04lx ", i);
        R[i].dump();
    }
    printf("\n");
}

void BST::pretty_print(MPCTIO &tio, yield_t &yield) {
    RegXS peer_root;
    RegXS reconstructed_root = root;
    if (tio.player() == 1) {
        tio.queue_peer(&root, sizeof(root));
    } else {
        RegXS peer_root;
        tio.recv_peer(&peer_root, sizeof(peer_root));
        reconstructed_root += peer_root;
    }

    auto A = oram->flat(tio, yield);
    auto R = A.reconstruct();
    if(tio.player()==0) {
        pretty_print(R, reconstructed_root.xshare);
    }
}

// Check the BST invariant of the tree (that all keys to the left are
// less than or equal to this key, all keys to the right are strictly
// greater, and this is true recursively).  Returns a
// tuple<bool,address_t>, where the bool says whether the BST invariant
// holds, and the address_t is the height of the tree (which will be
// useful later when we check AVL trees).
std::tuple<bool, address_t> BST::check_bst(const std::vector<Node> &R,
    value_t node, value_t min_key = 0, value_t max_key = ~0)
{
    //printf("node = %ld\n", node);
    if (node == 0) {
        return { true, 0 };
    }
    const Node &n = R[node];
    value_t key = n.key.ashare;
    value_t left_ptr = extractLeftPtr(n.pointers).xshare;
    value_t right_ptr = extractRightPtr(n.pointers).xshare;
    auto [leftok, leftheight ] = check_bst(R, left_ptr, min_key, key);
    auto [rightok, rightheight ] = check_bst(R, right_ptr, key+1, max_key);
    address_t height = leftheight;
    if (rightheight > height) {
        height = rightheight;
    }
    height += 1;
    //printf("node = %ld, leftok = %d, rightok = %d\n", node, leftok, rightok);
    return { leftok && rightok && key >= min_key && key <= max_key,
        height };
}

void BST::check_bst(MPCTIO &tio, yield_t &yield) {
    auto A = oram->flat(tio, yield);
    auto R = A.reconstruct();

    RegXS rec_root = this->root;
    if (tio.player() == 1) {
        tio.queue_peer(&(this->root), sizeof(this->root));
    } else {
        RegXS peer_root;
        tio.recv_peer(&peer_root, sizeof(peer_root));
        rec_root+= peer_root;
    }
    if (tio.player() == 0) {
      auto [ ok, height ] = check_bst(R, rec_root.xshare);
      printf("BST structure %s\nBST height = %u\n",
          ok ? "ok" : "NOT OK", height);
    }
}

void newnode(Node &a) {
    a.key.randomize(8);
    a.pointers.set(0);
    a.value.randomize();
}

void BST::initialize(int num_players, size_t size) {
    this->MAX_SIZE = size;
    oram = new Duoram<Node>(num_players, size);
}


std::tuple<RegXS, RegBS> BST::insert(MPCTIO &tio, yield_t &yield, RegXS ptr,
    const Node &new_node, Duoram<Node>::Flat &A, int TTL, RegBS isDummy) {
    if(TTL==0) {
        RegBS zero;
        return {ptr, zero};
    }

    RegBS isNotDummy = isDummy ^ (tio.player());
    Node cnode = A[ptr];
    // Compare key
    auto [lteq, gt] = compare_keys(tio, yield, cnode, new_node);

    // Depending on [lteq, gt] select the next ptr/index as
    // upper 32 bits of cnode.pointers if lteq
    // lower 32 bits of cnode.pointers if gt 
    RegXS left = extractLeftPtr(cnode.pointers);
    RegXS right = extractRightPtr(cnode.pointers);
    
    RegXS next_ptr;
    mpc_select(tio, yield, next_ptr, gt, left, right, 32);

    CDPF dpf = tio.cdpf(yield);
    size_t &aes_ops = tio.aes_ops();
    // F_z: Check if this is last node on path
    RegBS F_z = dpf.is_zero(tio, yield, next_ptr, aes_ops);
    RegBS F_i;

    // F_i: If this was last node on path (F_z), and isNotDummy insert.
    mpc_and(tio, yield, F_i, (isNotDummy), F_z);
     
    isDummy^=F_i;
    auto [wptr, direction] = insert(tio, yield, next_ptr, new_node, A, TTL-1, isDummy);
    
    RegXS ret_ptr;
    RegBS ret_direction;
    // If we insert here (F_i), return the ptr to this node as wptr
    // and update direction to the direction taken by compare_keys
    mpc_select(tio, yield, ret_ptr, F_i, wptr, ptr);
    //ret_direction = direction + F_p(direction - gt)
    mpc_and(tio, yield, ret_direction, F_i, direction^gt);
    ret_direction^=direction;  

    return {ret_ptr, ret_direction};
}


// Insert(root, ptr, key, TTL, isDummy) -> (new_ptr, wptr, wnode, f_p)
void BST::insert(MPCTIO &tio, yield_t &yield, const Node &node, Duoram<Node>::Flat &A) {
    bool player0 = tio.player()==0;
    // If there are no items in tree. Make this new item the root.
    if(num_items==0) {
        Node zero;
        A[0] = zero;
        A[1] = node;
        (root).set(1*tio.player());
        num_items++;
        //printf("num_items == %ld!\n", num_items);
        return;
    } else {
        // Insert node into next free slot in the ORAM
        int new_id = 1 + num_items;
        int TTL = num_items++;
        A[new_id] = node;
        RegXS new_addr;
        new_addr.set(new_id * tio.player());
        RegBS isDummy;

        //Do a recursive insert
        auto [wptr, direction] = insert(tio, yield, root, node, A, TTL, isDummy);

        //Complete the insertion by reading wptr and updating its pointers
        RegXS pointers = A[wptr].NODE_POINTERS;
        RegXS left_ptr = extractLeftPtr(pointers);
        RegXS right_ptr = extractRightPtr(pointers);
        RegXS new_right_ptr, new_left_ptr;
        mpc_select(tio, yield, new_right_ptr, direction, right_ptr, new_addr);
        if(player0) {
            direction^=1;
        }
        mpc_select(tio, yield, new_left_ptr, direction, left_ptr, new_addr);
        setLeftPtr(pointers, new_left_ptr);
        setRightPtr(pointers, new_right_ptr);
        A[wptr].NODE_POINTERS = pointers;
        //printf("num_items == %ld!\n", num_items);
    } 
}


void BST::insert(MPCTIO &tio, yield_t &yield, Node &node) {
    auto A = oram->flat(tio, yield);
    auto R = A.reconstruct();

    insert(tio, yield, node, A);
    /*
    // To visualize database and tree after each insert:
    if (tio.player() == 0) {
        for(size_t i=0;i<R.size();++i) {
            printf("\n%04lx ", i);
            R[i].dump();
        }
        printf("\n");
    }
    pretty_print(R, 1);
    */
}

bool BST::del(MPCTIO &tio, yield_t &yield, RegXS ptr, RegAS del_key,
     Duoram<Node>::Flat &A, RegBS af, RegBS fs, int TTL, 
    del_return &ret_struct) {
    bool player0 = tio.player()==0;
    //printf("TTL = %d\n", TTL);
    if(TTL==0) {
        //Reconstruct and return af
        bool success = reconstruct_RegBS(tio, yield, af);
        //printf("Reconstructed flag = %d\n", success); 
        if(player0) 
          ret_struct.F_r^=1;
        return success;
    } else {
        bool player0 = tio.player()==0;
        Node node = A[ptr];
        // Compare key

        CDPF cdpf = tio.cdpf(yield);
        auto [lt, eq, gt] = cdpf.compare(tio, yield, del_key - node.key, tio.aes_ops());
      
        /*
        // Reconstruct and Debug Block 0
        bool lt_rec, eq_rec, gt_rec;
        lt_rec = reconstruct_RegBS(tio, yield, lt);
        eq_rec = reconstruct_RegBS(tio, yield, eq);
        gt_rec = reconstruct_RegBS(tio, yield, gt);
        size_t del_key_rec, node_key_rec;
        del_key_rec = reconstruct_RegAS(tio, yield, del_key);
        node_key_rec = reconstruct_RegAS(tio, yield, node.key);
        printf("node.key = %ld, del_key= %ld\n", node_key_rec, del_key_rec);
        printf("cdpf.compare results: lt = %d, eq = %d, gt = %d\n", lt_rec, eq_rec, gt_rec);
        */
        // c is the direction bit for next_ptr 
        // (c=0: go left or c=1: go right)
        RegBS c = gt;
        // lf = local found. We found the key to delete in this level.
        RegBS lf = eq;

        // Depending on [lteq, gt] select the next ptr/index as
        // upper 32 bits of cnode.pointers if lteq
        // lower 32 bits of cnode.pointers if gt 
        RegXS left = extractLeftPtr(node.pointers);
        RegXS right = extractRightPtr(node.pointers);
        
        CDPF dpf = tio.cdpf(yield);
        size_t &aes_ops = tio.aes_ops();
        // Check if left and right children are 0, and compute F_0, F_1, F_2
        RegBS l0 = dpf.is_zero(tio, yield, left, aes_ops);
        RegBS r0 = dpf.is_zero(tio, yield, right, aes_ops);
        RegBS F_0, F_1, F_2;
        // F_0 = l0 & r0
        mpc_and(tio, yield, F_0, l0, r0);
        // F_1 = l0 \xor r0
        F_1 = l0 ^ r0;
        // F_2 = !(F_0 + F_1) (Only 1 of F_0, F_1, and F_2 can be true)
        F_2 = F_0 ^ F_1;
        if(player0)
            F_2^=1;

        // We set next ptr based on c, but we need to handle three 
        // edge cases where we do not go by just the comparison result
        RegXS next_ptr;
        RegBS c_prime;
        // Case 1: found the node here (lf): we traverse down the lone child path.
        // or we are finding successor (fs) and there is no left child. 
        RegBS F_c1, F_c2, F_c3, F_c4;
        // Case 1: lf & F_1
        mpc_and(tio, yield, F_c1, lf, F_1);
        // Set c_prime for Case 1
        mpc_select(tio, yield, c_prime, F_c1, c, l0);

        /*
        // Reconstruct and Debug Block 1
        bool F_0_rec, F_1_rec, F_2_rec, c_prime_rec;
        F_0_rec = reconstruct_RegBS(tio, yield, F_0);
        F_1_rec = reconstruct_RegBS(tio, yield, F_1);
        F_2_rec = reconstruct_RegBS(tio, yield, F_2);
        c_prime_rec = reconstruct_RegBS(tio, yield, c_prime);
        printf("F_0 = %d, F_1 = %d, F_2 = %d, c_prime = %d\n", F_0_rec, F_1_rec, F_2_rec, c_prime_rec);
        */

        // s1: shares of 1 bit, s0: shares of 0 bit
        RegBS s1, s0;
        s1.set(tio.player()==1);
        // Case 2: found the node here (lf) and node has both children (F_2)
        // In find successor case, so find inorder successor
        // (Go right and then find leftmost child.)
        mpc_and(tio, yield, F_c2, lf, F_2);
        mpc_select(tio, yield, c_prime, F_c2, c_prime, s1);

        /*
        // Reconstruct and Debug Block 2
        bool F_c2_rec, s1_rec;
        F_c2_rec = reconstruct_RegBS(tio, yield, F_c2);
        s1_rec = reconstruct_RegBS(tio, yield, s1); 
        c_prime_rec = reconstruct_RegBS(tio, yield, c_prime); 
        printf("c_prime = %d, F_c2 = %d, s1 = %d\n", c_prime_rec, F_c2_rec, s1_rec);
        */


        // Case 3: finding successor (fs) and node has both children (F_2)
        // Go left. 
        mpc_and(tio, yield, F_c3, fs, F_2);
        mpc_select(tio, yield, c_prime, F_c3, c_prime, s0);

        // Case 4: finding successor (fs) and node has no more left children (l0)
        // This is the successor node then.
        // Go left (to end the traversal without triggering flags on the real path to the right.
        mpc_and(tio, yield, F_c4, fs, l0);
        mpc_select(tio, yield, c_prime, F_c4, c_prime, l0);

        // Set next_ptr
        mpc_select(tio, yield, next_ptr, c_prime, left, right, 32);
        
        RegBS af_prime, fs_prime;
        mpc_or(tio, yield, af_prime, af, lf);

        // If in Case 2, set fs. We are now finding successor
        mpc_or(tio, yield, fs_prime, fs, F_c2);

        // If in Case 3. Successor found here already. Toggle fs off
        fs_prime=fs_prime^F_c4;

        bool key_found = del(tio, yield, next_ptr, del_key, A, af_prime, fs_prime, TTL-1, ret_struct);

        // If we didn't find the key, we can end here.
        if(!key_found)
          return 0;

        //printf("TTL = %d\n", TTL); 
        RegBS F_rs;
        // Flag here should be direction (c_prime) and F_r i.e. we need to swap return ptr in,
        // F_r needs to be returned in ret_struct
        mpc_and(tio, yield, F_rs, c_prime, ret_struct.F_r);
        mpc_select(tio, yield, right, F_rs, right, ret_struct.ret_ptr);
        if(player0)
            c_prime^=1; 
        mpc_and(tio, yield, F_rs, c_prime, ret_struct.F_r);
        mpc_select(tio, yield, left, F_rs, left, ret_struct.ret_ptr); 

        /*
        // Reconstruct and Debug Block 3
        bool F_rs_rec, F_ls_rec;
        size_t ret_ptr_rec;
        F_rs_rec = reconstruct_RegBS(tio, yield, F_rs);
        F_ls_rec = reconstruct_RegBS(tio, yield, F_rs);
        ret_ptr_rec = reconstruct_RegXS(tio, yield, ret_struct.ret_ptr);
        printf("F_rs_rec = %d, F_ls_rec = %d, ret_ptr_rec = %ld\n", F_rs_rec, F_ls_rec, ret_ptr_rec);
        */
        RegXS new_ptr;
        setLeftPtr(new_ptr, left);
        setRightPtr(new_ptr, right);
        A[ptr].NODE_POINTERS = new_ptr;

        // Update the return structure 
        RegBS F_nd, F_ns, F_r;
        mpc_or(tio, yield, ret_struct.F_ss, ret_struct.F_ss, F_c2);
        if(player0)
            af^=1;
        mpc_and(tio, yield, F_nd, lf, af);
        // F_ns = fs & l0 
        // Finding successor flag & no more left child
        F_ns = F_c4;
        // F_r = F_d.(!F_2)
        if(player0)
            F_2^=1;
        // If we have to delete here, and it doesn't have two children we have to
        // update child pointer in parent with the returned pointer
        mpc_and(tio, yield, F_r, F_nd, F_2);
        mpc_or(tio, yield, F_r, F_r, F_ns);
        ret_struct.F_r = F_r;

        mpc_select(tio, yield, ret_struct.N_d, F_nd, ret_struct.N_d, ptr);
        mpc_select(tio, yield, ret_struct.N_s, F_ns, ret_struct.N_s, ptr);
        mpc_select(tio, yield, ret_struct.ret_ptr, F_r, ptr, ret_struct.ret_ptr);
        //We don't empty the key and value of the node with del_key in the ORAM 
        return 1;
    }
}


bool BST::del(MPCTIO &tio, yield_t &yield, RegAS del_key) {
    if(num_items==0)
        return 0;
    if(num_items==1) {
        //Delete root
        auto A = oram->flat(tio, yield);
        Node zero;
        empty_locations.emplace_back(root);
        A[root] = zero;
        num_items--;
        return 1; 
    } else {
        int TTL = num_items;
        // Flags for already found (af) item to delete and find successor (fs)
        // if this deletion requires a successor swap
        RegBS af;
        RegBS fs;
        del_return ret_struct; 
        auto A = oram->flat(tio, yield);
        int success = del(tio, yield, root, del_key, A, af, fs, TTL, ret_struct); 
        printf ("Success =  %d\n", success); 
        if(!success){
            return 0;
        }
        else{
            num_items--;
            
            //Add deleted (empty) location into the empty_locations vector for reuse in next insert()
            empty_locations.emplace_back(ret_struct.N_d);

            /*
            printf("In delete's swap portion\n");
            Node del_node = A.reconstruct(A[ret_struct.N_d]);
            Node suc_node = A.reconstruct(A[ret_struct.N_s]);
            printf("del_node key = %ld, suc_node key = %ld\n",
                del_node.key.ashare, suc_node.key.ashare);
            printf("flag_s = %d\n", ret_struct.F_ss.bshare);
            */
            Node del_node = A[ret_struct.N_d];
            Node suc_node = A[ret_struct.N_s];
            RegAS zero_as; RegXS zero_xs;
            mpc_select(tio, yield, root, ret_struct.F_r, root, ret_struct.ret_ptr);
            mpc_select(tio, yield, del_node.key, ret_struct.F_ss, del_node.key, suc_node.key);
            mpc_select(tio, yield, del_node.value, ret_struct.F_ss, del_node.value, suc_node.value);           
            A[ret_struct.N_d].NODE_KEY = del_node.key;
            A[ret_struct.N_d].NODE_VALUE = del_node.value;
            A[ret_struct.N_s].NODE_KEY = zero_as;
            A[ret_struct.N_s].NODE_VALUE = zero_xs;
        }

      return 1;
    }
}

// Now we use the node in various ways.  This function is called by
// online.cpp.
void bst(MPCIO &mpcio,
    const PRACOptions &opts, char **args)
{
    nbits_t depth=4;

    if (*args) {
        depth = atoi(*args);
        ++args;
    }
    size_t items = (size_t(1)<<depth)-1;
    if (*args) {
        items = atoi(*args);
        ++args;
    }

    MPCTIO tio(mpcio, 0, opts.num_threads);
    run_coroutines(tio, [&tio, depth, items] (yield_t &yield) {
        size_t size = size_t(1)<<depth;
        BST tree(tio.player(), size);

        int insert_array[] = {10, 10, 13, 11, 14, 8, 15, 20, 17, 19, 7, 12};
        //int insert_array[] = {1, 2, 3, 4, 5, 6};
        size_t insert_array_size = 11;
        Node node; 
        for(size_t i = 0; i<=insert_array_size; i++) {
          newnode(node);
          node.key.set(insert_array[i] * tio.player());
          tree.insert(tio, yield, node);
        }
       
        tree.print_oram(tio, yield);
        tree.pretty_print(tio, yield);
         
        RegAS del_key;

        printf("\n\nDelete %x\n", 20);
        del_key.set(20 * tio.player());
        tree.del(tio, yield, del_key);
        tree.print_oram(tio, yield);
        tree.pretty_print(tio, yield);
        tree.check_bst(tio, yield);

        printf("\n\nDelete %x\n", 10);
        del_key.set(10 * tio.player());
        tree.del(tio, yield, del_key);
        tree.print_oram(tio, yield);
        tree.pretty_print(tio, yield);
        tree.check_bst(tio, yield);

        printf("\n\nDelete %x\n", 8);
        del_key.set(8 * tio.player());
        tree.del(tio, yield, del_key);
        tree.print_oram(tio, yield);
        tree.pretty_print(tio, yield);
        tree.check_bst(tio, yield);

        printf("\n\nDelete %x\n", 7);
        del_key.set(7 * tio.player());
        tree.del(tio, yield, del_key);
        tree.print_oram(tio, yield);
        tree.pretty_print(tio, yield);
        tree.check_bst(tio, yield);

        printf("\n\nDelete %x\n", 17);
        del_key.set(17 * tio.player());
        tree.del(tio, yield, del_key);
        tree.print_oram(tio, yield);
        tree.pretty_print(tio, yield);
        tree.check_bst(tio, yield);

        printf("\n\nDelete %x\n", 15);
        del_key.set(15 * tio.player());
        tree.del(tio, yield, del_key);
        tree.print_oram(tio, yield);
        tree.pretty_print(tio, yield);
        tree.check_bst(tio, yield);

        printf("\n\nDelete %x\n", 5);
        del_key.set(5 * tio.player());
        tree.del(tio, yield, del_key);
        tree.print_oram(tio, yield);
        tree.pretty_print(tio, yield);
        tree.check_bst(tio, yield);
    });
}