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//! This is a Rust implementanion of a CL universal accumulator as described //! [here](http://groups.csail.mit.edu/cis/pubs/lysyanskaya/cl02a.pdf). //! //! An accumulation is a fixed size digest that, along with the witness of an //! element's addition, can be used to prove an element is a member of a set. //! The drawback to this solution is that any state changes to the accumulation //! invalidate the witneses of the other elements in the set, requiring //! computational resources to update them. //! //! The benefit of CL accumulators is that they support efficient untrusted //! witness updates. The resource intensive task of updating witnesses can be //! outsourced to an untrusted party without sacrificing the integrity of the //! accumulator. //! //! This project is focused on a use case where a central authority is both //! memory- and processing-constrained. The authority controls the private key //! and is able to add and delete elements while untrusted workers are able to //! recalculate witnesses provided they have access to the previous witnesses, //! the current state of the accumulator, and its public key. use std::sync::{Arc, Mutex}; use std::sync::atomic::AtomicPtr; use generic_array::{ArrayLength, GenericArray}; use rand::RngCore; use serde::{Serialize, Deserialize}; pub use typenum; pub mod bigint; pub mod mapper; use bigint::BigInt; use mapper::Mapper; /// The accumulator base. const BASE: i64 = 65537; /// Helper function that converts a GenericArray to a BigInt. fn to_bigint<T: BigInt, N: ArrayLength<u8>>(x: GenericArray<u8, N>) -> T { x.as_slice().into() } /// An accumulator. /// /// Elements may be added and deleted from the acculumator without increasing /// the size of its internal parameters. That is, the number of digits in the /// accumulation `z` will never exceed the number of digits in the modulus `n`. #[derive(Clone, Debug)] pub struct Accumulator<T: BigInt> { /// The current accumulation value. pub z: T, /// Private exponent. d: Option<T>, /// Modulus. n: T, } impl<T: BigInt> Accumulator<T> { /// Initialize an accumulator from private key parameters. All accumulators /// are able to add elements and verify witnesses. An accumulator /// constructed from a private key is able to delete elements and prove /// elements after their addition. /// /// ``` /// use clacc::Accumulator; /// use clacc::bigint::BigIntGmp; /// let p = vec![0x3d]; /// let q = vec![0x35]; /// let acc = Accumulator::<BigIntGmp>::with_private_key( /// p.as_slice().into(), /// q.as_slice().into() /// ); /// ``` pub fn with_private_key(p: T, q: T) -> Self { Accumulator { d: Some(p.sub(1).mul(&q.sub(1))), n: p.mul(&q), z: BASE.into(), } } /// Create an accumulator from a randomly generated private key and return /// it along with the generated key parameters. /// /// ``` /// use clacc::Accumulator; /// use clacc::bigint::BigIntGmp; /// Accumulator::<BigIntGmp>::with_random_key(); /// ``` pub fn with_random_key() -> (Accumulator<T>, T, T) { let mut rng = rand::thread_rng(); let mut bytes = vec![0; 192]; rng.fill_bytes(&mut bytes); let mut p = T::from(bytes.as_slice()).next_prime(); rng.fill_bytes(&mut bytes); let mut q = T::from(bytes.as_slice()).next_prime(); if p < q { std::mem::swap(&mut p, &mut q); } (Accumulator::with_private_key(p.clone(), q.clone()), p, q) } /// Initialize an accumulator from a public key. An accumulator constructed /// from a public key is only able to add elements and verify witnesses. /// /// ``` /// use clacc::Accumulator; /// use clacc::bigint::BigIntGmp; /// let n = vec![0x0c, 0xa1]; /// let acc = Accumulator::<BigIntGmp>::with_public_key( /// n.as_slice().into() /// ); /// ``` pub fn with_public_key(n: T) -> Self { Accumulator { d: None, n: n, z: BASE.into(), } } /// Add an element to an accumulator. /// /// ``` /// use clacc::Accumulator; /// use clacc::bigint::BigIntGmp; /// use clacc::mapper::MapBlake2b; /// use clacc::typenum::U16; /// let n = vec![0x0c, 0xa1]; /// let mut acc = Accumulator::<BigIntGmp>::with_public_key( /// n.as_slice().into() /// ); /// let x = b"abc"; /// let w = acc.add::<MapBlake2b, U16>(x); /// assert!(acc.verify::<MapBlake2b, U16>(x, &w).is_ok()); /// ``` /// /// This works with accumulators constructed from a public key or a private /// key. /// /// ``` /// use clacc::Accumulator; /// use clacc::bigint::BigIntGmp; /// use clacc::mapper::MapBlake2b; /// use clacc::typenum::U16; /// let p = vec![0x3d]; /// let q = vec![0x35]; /// let mut acc = Accumulator::<BigIntGmp>::with_private_key( /// p.as_slice().into(), /// q.as_slice().into() /// ); /// let x = b"abc"; /// let w = acc.add::<MapBlake2b, U16>(x); /// assert!(acc.verify::<MapBlake2b, U16>(x, &w).is_ok()); /// ``` pub fn add<Map: Mapper, N: ArrayLength<u8>>( &mut self, x: &[u8] ) -> Witness<T> { let x = to_bigint::<T, N>(Map::map(x)); let x_p = x.next_prime(); let w = Witness { u: self.z.clone(), nonce: x_p.sub(&x), }; self.z = self.z.powm(&x_p, &self.n); w } /// Delete an element from an accumulator. /// /// ``` /// use clacc::Accumulator; /// use clacc::bigint::BigIntGmp; /// use clacc::mapper::MapBlake2b; /// use clacc::typenum::U16; /// let p = vec![0x3d]; /// let q = vec![0x35]; /// let mut acc = Accumulator::<BigIntGmp>::with_private_key( /// p.as_slice().into(), /// q.as_slice().into() /// ); /// let x = b"abc"; /// let w = acc.add::<MapBlake2b, U16>(x); /// assert!(acc.del::<MapBlake2b, U16>(x, &w).is_ok()); /// assert!(acc.verify::<MapBlake2b, U16>(x, &w).is_err()); /// assert!(acc.del::<MapBlake2b, U16>(x, &w).is_err()); /// ``` /// /// This will only succeed with an accumulator constructed from a private /// key. /// /// ``` /// use clacc::Accumulator; /// use clacc::bigint::BigIntGmp; /// use clacc::mapper::MapBlake2b; /// use clacc::typenum::U16; /// let n = vec![0x0c, 0xa1]; /// let mut acc = Accumulator::<BigIntGmp>::with_public_key( /// n.as_slice().into() /// ); /// let x = b"abc"; /// let w = acc.add::<MapBlake2b, U16>(x); /// assert!(acc.del::<MapBlake2b, U16>(x, &w).is_err()); /// ``` pub fn del<Map: Mapper, N: ArrayLength<u8>>( &mut self, x: &[u8], w: &Witness<T> ) -> Result<(), &'static str> { let d = match self.d.as_ref() { Some(d) => d, None => { return Err("d is None"); }, }; let x_p = to_bigint::<T, N>(Map::map(x)).add(&w.nonce); if self.z != w.u.powm(&x_p, &self.n) { return Err("x not in z"); } let x_i = match x_p.invert(d) { Some(x_i) => x_i, None => { return Err("x has no inverse"); }, }; self.z = self.z.powm(&x_i, &self.n); Ok(()) } /// Generate a witness to an element's addition to the accumulation. /// /// ``` /// use clacc::Accumulator; /// use clacc::bigint::BigIntGmp; /// use clacc::mapper::MapBlake2b; /// use clacc::typenum::U16; /// let p = vec![0x3d]; /// let q = vec![0x35]; /// let mut acc = Accumulator::<BigIntGmp>::with_private_key( /// p.as_slice().into(), /// q.as_slice().into() /// ); /// let x = b"abc"; /// acc.add::<MapBlake2b, U16>(x); /// let w = acc.prove::<MapBlake2b, U16>(x).unwrap(); /// assert!(acc.verify::<MapBlake2b, U16>(x, &w).is_ok()); /// ``` /// /// This will only succeed with an accumulator constructed from a private /// key. /// /// ``` /// use clacc::Accumulator; /// use clacc::bigint::BigIntGmp; /// use clacc::mapper::MapBlake2b; /// use clacc::typenum::U16; /// let n = vec![0x0c, 0xa1]; /// let mut acc = Accumulator::<BigIntGmp>::with_public_key( /// n.as_slice().into() /// ); /// let x = b"abc"; /// acc.add::<MapBlake2b, U16>(x); /// assert!(acc.prove::<MapBlake2b, U16>(x).is_err()); /// ``` pub fn prove<Map: Mapper, N: ArrayLength<u8>>( &self, x: &[u8] ) -> Result<Witness<T>, &'static str> { let d = match self.d.as_ref() { Some(d) => d, None => { return Err("d is None"); }, }; let x = to_bigint::<T, N>(Map::map(x)); let x_p = x.next_prime(); let x_i = match x_p.invert(d) { Some(x_i) => x_i, None => { return Err("x has no inverse"); }, }; Ok(Witness { u: self.z.powm(&x_i, &self.n), nonce: x_p.sub(&x), }) } /// Verify an element is a member of an accumulator. /// /// ``` /// use clacc::Accumulator; /// use clacc::bigint::BigIntGmp; /// use clacc::mapper::MapBlake2b; /// use clacc::typenum::U16; /// let n = vec![0x0c, 0xa1]; /// let mut acc = Accumulator::<BigIntGmp>::with_public_key( /// n.as_slice().into() /// ); /// let x = b"abc"; /// let w = acc.add::<MapBlake2b, U16>(x); /// assert!(acc.verify::<MapBlake2b, U16>(x, &w).is_ok()); /// ``` /// /// This works with accumulators constructed from a public key or a private /// key. /// /// ``` /// use clacc::Accumulator; /// use clacc::bigint::BigIntGmp; /// use clacc::mapper::MapBlake2b; /// use clacc::typenum::U16; /// let p = vec![0x3d]; /// let q = vec![0x35]; /// let mut acc = Accumulator::<BigIntGmp>::with_private_key( /// p.as_slice().into(), /// q.as_slice().into() /// ); /// let x = b"abc"; /// let w = acc.add::<MapBlake2b, U16>(x); /// assert!(acc.verify::<MapBlake2b, U16>(x, &w).is_ok()); /// ``` pub fn verify<Map: Mapper, N: ArrayLength<u8>>( &self, x: &[u8], w: &Witness<T> ) -> Result<(), &'static str> { let x_p = to_bigint::<T, N>(Map::map(x)).add(&w.nonce); if self.z != w.u.powm(&x_p, &self.n) { return Err("x not in z"); } Ok(()) } } impl<T: BigInt> std::fmt::Display for Accumulator<T> { fn fmt( &self, f: &mut std::fmt::Formatter<'_> ) -> Result<(), std::fmt::Error> { match self.d.as_ref() { Some(d) => f.write_fmt(format_args!("({:x}, {:x}, {:x})", d, self.n, self.z)), None => f.write_fmt(format_args!("({:x}, {:x})", self.n, self.z)), } } } /// A witness of an element's membership in an accumulator. #[derive(Clone, Debug, Default, Serialize, Deserialize)] #[serde(bound = "T: Serialize, for<'a> T: Deserialize<'a>")] pub struct Witness<T: BigInt> { /// The accumulation value less the element. pub u: T, /// A number that, when added to the element, uniquely maps the element to /// a prime. pub nonce: T, } impl<T: BigInt> std::fmt::Display for Witness<T> { fn fmt( &self, f: &mut std::fmt::Formatter<'_> ) -> Result<(), std::fmt::Error> { f.write_fmt(format_args!("({:x}, {:x})", self.u, self.nonce)) } } /// A sum of updates to be applied to witnesses. #[derive(Clone, Debug)] pub struct Update<T: BigInt> { pi_a: T, pi_d: T, } impl<T: BigInt> Update<T> { /// Create a new batched update. pub fn new() -> Self { Update { pi_a: 1.into(), pi_d: 1.into(), } } /// Absorb an element that must be added to a witness. pub fn add<Map: Mapper, N: ArrayLength<u8>>( &mut self, x: &[u8], w: &Witness<T> ) { let x_p = to_bigint::<T, N>(Map::map(x)).add(&w.nonce); self.pi_a = self.pi_a.mul(&x_p); } /// Absorb an element that must be deleted from a witness. pub fn del<Map: Mapper, N: ArrayLength<u8>>( &mut self, x: &[u8], w: &Witness<T> ) { let x_p = to_bigint::<T, N>(Map::map(x)).add(&w.nonce); self.pi_d = self.pi_d.mul(&x_p); } /// Undo an absorbed element's addition into an update. pub fn undo_add<Map: Mapper, N: ArrayLength<u8>>( &mut self, x: &[u8], w: &Witness<T> ) { let x_p = to_bigint::<T, N>(Map::map(x)).add(&w.nonce); self.pi_a = self.pi_a.div(&x_p); } /// Undo an absorbed element's deletion from an update. pub fn undo_del<Map: Mapper, N: ArrayLength<u8>>( &mut self, x: &[u8], w: &Witness<T> ) { let x_p = to_bigint::<T, N>(Map::map(x)).add(&w.nonce); self.pi_d = self.pi_a.div(&x_p); } /// Update a witness. The update will include all additions and deletions /// previously absorbed into this update struct. /// /// ``` /// use clacc::Accumulator; /// use clacc::Update; /// use clacc::bigint::BigIntGmp; /// use clacc::mapper::MapBlake2b; /// use clacc::typenum::U16; /// // In this example, the update will include a deletion, so the /// // accumulator must be created with a private key. /// let p = vec![0x3d]; /// let q = vec![0x35]; /// let mut acc = Accumulator::<BigIntGmp>::with_private_key( /// p.as_slice().into(), /// q.as_slice().into() /// ); /// // Create the static element. /// let xs = b"abc"; /// // Create the deletion. /// let xd = b"def"; /// // Create the addition. /// let xa = b"ghi"; /// // Add the deletion element. /// acc.add::<MapBlake2b, U16>(xd); /// // Add the static element to the accumulator. /// let mut wxs = acc.add::<MapBlake2b, U16>(xs); /// // Delete the deletion element from the accumulator. /// let wxd = acc.prove::<MapBlake2b, U16>(xd).unwrap(); /// acc.del::<MapBlake2b, U16>(xd, &wxd).unwrap(); /// // Create an update object and absorb the addition and deletion. /// let mut u = Update::new(); /// u.del::<MapBlake2b, U16>(xd, &wxd); /// u.add::<MapBlake2b, U16>(xa, &acc.add::<MapBlake2b, U16>(xa)); /// // Update the static element's witness. /// wxs = u.update_witness::<MapBlake2b, U16>(&acc, xs, &wxs); /// assert!(acc.verify::<MapBlake2b, U16>(xs, &wxs).is_ok()); /// ``` pub fn update_witness<Map: Mapper, N: ArrayLength<u8>>( &self, acc: &Accumulator<T>, x: &[u8], w: &Witness<T> ) -> Witness<T> { let x_p = to_bigint::<T, N>(Map::map(x)).add(&w.nonce); let (_, a, b) = self.pi_d.gcdext(&x_p); Witness { u: w.u.powm(&a.mul(&self.pi_a), &acc.n) .mul(&acc.z.powm(&b, &acc.n)).modulus(&acc.n), nonce: w.nonce.clone(), } } /// Multithreaded version of `update_witness` that can update multiple /// witnesses and automatically manage updates applied to newly added /// elements. /// /// It is assumed that the additional elements have been absorbed by the /// update and that their witnesses are the accumulator's value before any /// of the additions or deletions absorbed by this update were applied. /// Updating the witnesses for each of these additional elements is thus /// acheived by simply removing its respective element from the update and /// applying the result to its witness. /// /// Arguments /// /// * `r` - Receives updated witnesses for static elements. /// * `ra` - Receives update witnesse for added elements. /// * `acc` - The current accumulator. /// * `x` - Pointer to static elements. /// * `w` - Pointer to the witnesses of the static elements. /// * `n` - The number of static elements. /// * `xa` - Pointer to added elements. /// * `wa` - Pointer to the witnesses of the added elements. /// * `na` - The number of added elements. /// * `thread_count` - The number of threads to use. Returns an error if 0. pub fn update_witnesses<Map: Mapper, N: ArrayLength<u8>>( &self, r: *mut Witness<T>, ra: *mut Witness<T>, acc: &Accumulator<T>, x: *const Vec<u8>, w: *const Witness<T>, n: usize, xa: *const Vec<u8>, wa: *const Witness<T>, na: usize, thread_count: usize ) -> Result<(), &'static str> { // Sanity check thread count. if thread_count == 0 { return Err("thread_count is 0"); } // Create a mutex marking the index of the current job. let job_index = Arc::new(Mutex::<usize>::new(0)); // Create shareable pointers for the inputs and outputs. let r = Arc::new(Mutex::new(AtomicPtr::new(r))); let ra = Arc::new(Mutex::new(AtomicPtr::new(ra))); let x = Arc::new(Mutex::new(AtomicPtr::new(x as *mut Vec<u8>))); let w = Arc::new(Mutex::new(AtomicPtr::new(w as *mut Witness<T>))); let xa = Arc::new(Mutex::new(AtomicPtr::new(xa as *mut Vec<u8>))); let wa = Arc::new(Mutex::new(AtomicPtr::new(wa as *mut Witness<T>))); // Create vector that will store the threads. let mut threads = Vec::with_capacity(thread_count); // Create threads. for _ in 0..thread_count { threads.push(self.clone().create_thread::<Map, N>( Arc::clone(&r), Arc::clone(&ra), acc.clone(), Arc::clone(&job_index), Arc::clone(&x), Arc::clone(&w), n, Arc::clone(&xa), Arc::clone(&wa), na )); } // Join threads and note if an error occurs. let mut errors = false; for thread in threads { match thread.join() { Ok(_) => {}, _ => { errors = true; }, } } if errors { return Err("error occured joining worker threads"); } Ok(()) } /// Helper function for `update_witnesses` that creates a worker thread. fn create_thread<Map: Mapper, N: ArrayLength<u8>>( self, r: Arc<Mutex<AtomicPtr<Witness<T>>>>, ra: Arc<Mutex<AtomicPtr<Witness<T>>>>, acc: Accumulator<T>, job_index: Arc<Mutex<usize>>, x: Arc<Mutex<AtomicPtr<Vec<u8>>>>, w: Arc<Mutex<AtomicPtr<Witness<T>>>>, n: usize, xa: Arc<Mutex<AtomicPtr<Vec<u8>>>>, wa: Arc<Mutex<AtomicPtr<Witness<T>>>>, na: usize ) -> std::thread::JoinHandle<()> { std::thread::spawn(move || { loop { let mut i; { // Get the current job index. let mut job_index = job_index.lock().unwrap(); // Check if there are any more jobs left. if *job_index == n + na { break; } // Save the current job index outside this scope so that // the mutex can be released as soon as possible. i = *job_index; // Increment the job index. *job_index += 1; } if i < n { // If i < n, perform update on a static element. unsafe { // Get pointers. let x = &*x.lock().unwrap().get_mut().add(i); let w = &*w.lock().unwrap().get_mut().add(i); let r = r.lock().unwrap().get_mut().add(i); // Update witness. *r = self.update_witness::<Map, N>(&acc, x, w); } } else { // Otherwise, perform update on an added element. i -= n; unsafe { // Get pointers. let x = &*xa.lock().unwrap().get_mut().add(i); let w = &*wa.lock().unwrap().get_mut().add(i); let r = ra.lock().unwrap().get_mut().add(i); // Create a clone of the update. let mut u = self.clone(); // Remove the addition from the update. u.undo_add::<Map, N>(x, &w); // Update witness. *r = u.update_witness::<Map, N>(&acc, x, w); } } } }) } } impl<T: BigInt> std::fmt::Display for Update<T> { fn fmt( &self, f: &mut std::fmt::Formatter<'_> ) -> Result<(), std::fmt::Error> { f.write_fmt(format_args!("({:x}, {:x})", self.pi_a, self.pi_d)) } }