elaborate non-interactive mpc example

examples/non_interactive_fheuint8.rs

@@ -2,77 +2,171 @@ use bin_rs::*;
 use itertools::Itertools;
 use rand::{thread_rng, Rng, RngCore};
 
-fn circuit(a: u8, b: u8, c: u8, d: u8) -> u8 {
+fn function1(a: u8, b: u8, c: u8, d: u8) -> u8 {
     ((a + b) * c) * d
 }
 
-fn fhe_circuit(a: &FheUint8, b: &FheUint8, c: &FheUint8, d: &FheUint8) -> FheUint8 {
+fn function1_fhe(a: &FheUint8, b: &FheUint8, c: &FheUint8, d: &FheUint8) -> FheUint8 {
     &(&(a + b) * c) * d
 }
 
-fn main() {
-    set_parameter_set(ParameterSelector::NonInteractiveLTE2Party);
+fn function2(a: u8, b: u8, c: u8, d: u8) -> u8 {
+    (a * b) + (c * d)
+}
 
-    // set CRS
+fn function2_fhe(a: &FheUint8, b: &FheUint8, c: &FheUint8, d: &FheUint8) -> FheUint8 {
+    &(a * b) + &(c * d)
+}
+
+fn main() {
+    set_parameter_set(ParameterSelector::NonInteractiveLTE4Party);
+
+    // set application's common reference seed
     let mut seed = [0u8; 32];
     thread_rng().fill_bytes(&mut seed);
     set_common_reference_seed(seed);
 
-    let no_of_parties = 2;
+    let no_of_parties = 4;
+
+    // Clide side //
 
     // Generate client keys
     let cks = (0..no_of_parties).map(|_| gen_client_key()).collect_vec();
 
-    // client 0 encrypts private input
+    // client 0 encrypts its private inputs
     let c0_a = thread_rng().gen::<u8>();
-    let c0_b = thread_rng().gen::<u8>();
-    let c0_batched_to_send = cks[0].encrypt(vec![c0_a, c0_b].as_slice());
+    // Clients encrypt their private inputs in a seeded batched ciphertext
+    let c0_enc = cks[0].encrypt(vec![c0_a].as_slice());
 
-    // client 1 encrypts private input
+    // client 1 encrypts its private inputs
     let c1_a = thread_rng().gen::<u8>();
-    let c1_b = thread_rng().gen::<u8>();
-    let c1_batch_to_send = cks[1].encrypt(vec![c1_a, c1_b].as_slice());
+    let c1_enc = cks[1].encrypt(vec![c1_a].as_slice());
 
-    // Both client indenpendently generate their server key shares
+    // client 2 encrypts its private inputs
+    let c2_a = thread_rng().gen::<u8>();
+    let c2_enc = cks[2].encrypt(vec![c2_a].as_slice());
+
+    // client 1 encrypts its private inputs
+    let c3_a = thread_rng().gen::<u8>();
+    let c3_enc = cks[3].encrypt(vec![c3_a].as_slice());
+
+    // Clients independently generate their server key shares
+    //
+    // We assign user_id 0 to client 0, user_id 1 to client 1, user_id 2 to client
+    // 2, user_id 3 to client 3.
     let server_key_shares = cks
         .iter()
         .enumerate()
         .map(|(id, k)| gen_server_key_share(id, no_of_parties, k))
         .collect_vec();
 
-    // Server side
+    // Each client uploads their server key shares and encrypted private inputs to
+    // the server in a single shot message.
 
-    // aggregates shares and generates server key
+    // Server side //
+
+    // Server receives server key shares from each client and proceeds to aggregate
+    // them to produce server key. After this point, server can use server key share
+    // to evaluate any arbitrary function on encrypted private inputs from the fixed
+    // set of clients
+
+    // aggregate shares and generates server key
     let server_key = aggregate_server_key_shares(&server_key_shares);
     server_key.set_server_key();
 
-    // extract a and b from client0 inputs
-    // let now = std::time::Instant::now();
-    let (ct_c0_a, ct_c0_b) = {
-        let ct = c0_batched_to_send.unseed::<Vec<Vec<u64>>>().key_switch(0);
-        (ct.extract_at(0), ct.extract_at(1))
-    };
-    // println!(
-    //     "Time to unseed, key switch, and extract 2 ciphertexts: {:?}",
-    //     now.elapsed()
-    // );
+    // Server proceeds to extract private inputs sent by clients
+    //
+    // To extract client 0's (with user_id=0) private inputs we first key switch
+    // client 0's private inputs from thei secret to ideal secret of the mpc
+    // protocol. To indicate we're key switching client 0's private input we
+    // supply client 0's user_id i.e. we call `key_switch(0)`. Then we extract
+    // the first ciphertext by calling `extract_at(0)`.
+    //
+    // Since client 0 only encrypted 1 input in batched ciphertext calling
+    // extract_at(index) for `index` > 0 will panic. If client 0 had more private
+    // inputs then we can either extract them all at once by `extract_all` or first
+    // `many` of them by `extract_many(many)`
+    let ct_c0_a = c0_enc.unseed::<Vec<Vec<u64>>>().key_switch(0).extract_at(0);
 
-    // extract a and b from client1 inputs
-    let (ct_c1_a, ct_c1_b) = {
-        let ct = c1_batch_to_send.unseed::<Vec<Vec<u64>>>().key_switch(1);
-        (ct.extract_at(0), ct.extract_at(1))
-    };
+    let ct_c1_a = c1_enc.unseed::<Vec<Vec<u64>>>().key_switch(1).extract_at(0);
+    let ct_c2_a = c2_enc.unseed::<Vec<Vec<u64>>>().key_switch(2).extract_at(0);
+    let ct_c3_a = c3_enc.unseed::<Vec<Vec<u64>>>().key_switch(3).extract_at(0);
 
+    // After extracting each client's private inputs, server proceeds to evaluate
+    // the function1
     let now = std::time::Instant::now();
-    let c_out = fhe_circuit(&ct_c0_a, &ct_c1_a, &ct_c0_b, &ct_c1_b);
-    println!("Circuit Time: {:?}", now.elapsed());
+    let ct_out_f1 = function1_fhe(&ct_c0_a, &ct_c1_a, &ct_c2_a, &ct_c3_a);
+    println!("Function1 FHE evaluation time: {:?}", now.elapsed());
 
-    // decrypt c_out
+    // Server has finished running compute. Clients can proceed to decrypt the
+    // output ciphertext using multi-party decryption.
+
+    // Client side //
+
+    // In multi-party decryption, each client needs to come online, download output
+    // ciphertext from the server, produce decryption share, and send to other
+    // parties (either via p2p or via server). After receving decryption shares
+    // for output ciphertext from other parties, client can independently decrypt
+    // output ciphertext.
+
+    // each client produces decryption share
     let decryption_shares = cks
         .iter()
-        .map(|k| k.gen_decryption_share(&c_out))
+        .map(|k| k.gen_decryption_share(&ct_out_f1))
         .collect_vec();
-    let m_out = cks[0].aggregate_decryption_shares(&c_out, &decryption_shares);
-    let m_expected = circuit(c0_a, c1_a, c0_b, c1_b);
-    assert!(m_expected == m_out);
+
+    // With all decrytpion shares, client can aggregate the shares and decrypt the
+    // ciphertext
+    let out_f1 = cks[0].aggregate_decryption_shares(&ct_out_f1, &decryption_shares);
+
+    // we check that output is correct
+    let want_out_f1 = function1(c0_a, c1_a, c2_a, c3_a);
+    assert_eq!(out_f1, want_out_f1);
+
+    // -----------
+
+    // Server key can be re-used for different function with different private
+    // client inputs for same set of clients. Here we run `function2_fhe` for
+    // the same set of client but with new inputs. Client only have to upload their
+    // private inputs to the server this time.
+
+    // Each client encrypts their private input
+    let c0_a = thread_rng().gen::<u8>();
+    let c0_enc = cks[0].encrypt(vec![c0_a].as_slice());
+    let c1_a = thread_rng().gen::<u8>();
+    let c1_enc = cks[1].encrypt(vec![c1_a].as_slice());
+    let c2_a = thread_rng().gen::<u8>();
+    let c2_enc = cks[2].encrypt(vec![c2_a].as_slice());
+    let c3_a = thread_rng().gen::<u8>();
+    let c3_enc = cks[3].encrypt(vec![c3_a].as_slice());
+
+    // Client upload their private inputs to the server
+
+    // Server side //
+
+    // Server receives clients private inputs and extracts them
+    let ct_c0_a = c0_enc.unseed::<Vec<Vec<u64>>>().key_switch(0).extract_at(0);
+    let ct_c1_a = c1_enc.unseed::<Vec<Vec<u64>>>().key_switch(1).extract_at(0);
+    let ct_c2_a = c2_enc.unseed::<Vec<Vec<u64>>>().key_switch(2).extract_at(0);
+    let ct_c3_a = c3_enc.unseed::<Vec<Vec<u64>>>().key_switch(3).extract_at(0);
+
+    // Server proceeds to evaluate `function2_fhe`
+    let now = std::time::Instant::now();
+    let ct_out_f2 = function2_fhe(&ct_c0_a, &ct_c1_a, &ct_c2_a, &ct_c3_a);
+    println!("Function2 FHE evaluation time: {:?}", now.elapsed());
+
+    // Client side //
+
+    // Each client generates decrytion share for `ct_out_f2`
+    let decryption_shares = cks
+        .iter()
+        .map(|k| k.gen_decryption_share(&ct_out_f2))
+        .collect_vec();
+
+    // Client independently aggregate the shares and decrypt
+    let out_f2 = cks[0].aggregate_decryption_shares(&ct_out_f2, &decryption_shares);
+
+    // We check correctness of function2
+    let want_out_f2 = function2(c0_a, c1_a, c2_a, c3_a);
+    assert_eq!(out_f2, want_out_f2);
 }