[MPC] Specify circuit representation

.gitignore

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 /mpc-knowledge-base/book/*
+/mpc-spec/target

mpc-spec/Cargo.toml

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+[package]
+name = "mpc-spec"
+version = "0.1.0"
+edition = "2021"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]

mpc-spec/src/circuit.rs

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+//! The [`Circuit`] representation used by the MPC engine.
+//!
+//! A circuit is made up of logic gates and value-carrying wires between the
+//! gates. Each gate takes one or more wires as input, depending on the type of
+//! gate, and has exactly one output wire.
+//!
+//! Conceptually, a circuit is a sequence of input or logic (XOR/AND/NOT) gates,
+//! with all input gates at the beginning of the sequence, followed by all logic
+//! gates. The index of a gate in the sequence determines its "wire index",
+//! which is available as the input to any gate later in the sequence. For
+//! example, in a circuit with two input gates (1 bit for party A, 1 bit for
+//! party B), followed by three logic gates (an XOR of the two input gates, an
+//! AND of the two input gates, and an XOR of these two XOR/AND gates), the
+//! input gates would be the wires 0 and 1, the XOR of these two input gates
+//! would be specified as `Gate::Xor(0, 1)` and have wire index 2, the AND of
+//! the two input gates would be specified as `Gate::And(0, 1)` and have wire
+//! index 3, and the XOR of the two logic gates would be specified as
+//! `Gate::Xor(2, 3)` and have wire index 4:
+//!
+//! ```text
+//! Input A (Wire 0) ----+----------+
+//!                      |          |
+//! Input B (Wire 1) ----|-----+----|-----+
+//!                      |     |    |     |
+//!                      +-XOR-+    |     |
+//!         (Wire 2) =====> |       |     |
+//!                         |       +-AND-+
+//!         (Wire 3) =======|========> |
+//!                         +---XOR----+
+//!         (Wire 4) ==========> |
+//! ```
+//!
+//! The input gates of different parties cannot be interleaved: Each party must
+//! supply all of their inputs before the next party's inputs can start.
+//!
+//! At least one input bit must be specified, and every party contributing
+//! inputs to the circuit has to specify at least one input bit. Party input
+//! gates may not refer to other input gates' wire indices.
+//!
+//! This module is derived from the circuit representation of
+//! [`garble_lang`](https://github.com/sine-fdn/garble-lang/tree/main), the
+//! license of which is reproduced below.
+//!
+//! > MIT License
+//! >
+//! > Copyright (c) 2022 SINE e.V.
+//! >
+//! > Permission is hereby granted, free of charge, to any person obtaining a
+//! > copy of this software and associated documentation files (the "Software"),
+//! > to deal in the Software without restriction, including without limitation
+//! > the rights to use, copy, modify, merge, publish, distribute, sublicense,
+//! > and/or sell copies of the Software, and to permit persons to whom the
+//! > Software is furnished to do so, subject to the following conditions:
+//! >
+//! > The above copyright notice and this permission notice shall be included in
+//! > all copies or substantial portions of the Software.
+//! >
+//! > THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+//! > IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+//! > FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+//! > THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+//! > LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+//! > FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+//! > DEALINGS IN THE SOFTWARE.
+//!
+//!
+
+/// Data type to uniquely identify gate output wires.
+pub type WireIndex = usize;
+
+/// An input gate or a logic gate with its input wire specification.
+#[derive(Debug, Clone)]
+pub enum WiredGate {
+    /// An input wire, with its value coming directly from one of the parties.
+    /// Its [WireIndex] must refer to its own gate index.
+    Input(WireIndex),
+    /// A logical XOR gate attached to the two specified input wires. The
+    /// [WireIndex] of each input wire must refer to a lower index than the
+    /// gate's own index.
+    Xor(WireIndex, WireIndex),
+    /// A logical AND gate attached to the two specified input wires. The
+    /// [WireIndex] of each input wire must refer to a lower index than the
+    /// gate's own index.
+    And(WireIndex, WireIndex),
+    /// A logical NOT gate attached to the specified input wire. The
+    /// [WireIndex] of the input wire must refer to a lower index than the
+    /// gate's own index.
+    Not(WireIndex),
+}
+
+/// Specifies how many input bits a party is expected to contribute to the
+/// evaluation.
+pub type InputWidth = usize;
+/// Representation of a circuit evaluated by an MPC engine.
+#[derive(Debug, Clone)]
+pub struct Circuit {
+    /// The bit-width of the inputs expected by the different parties,
+    /// [InputWidth] at index `i` representing the number of input bits for
+    /// party `i`.
+    pub input_widths: Vec<InputWidth>,
+    /// The circuit's gates.
+    pub gates: Vec<WiredGate>,
+    /// The indices of the gates in [`Circuit::gates`] that produce output bits.
+    pub output_gates: Vec<WireIndex>,
+}
+
+/// Errors occurring during the validation or the execution of the MPC protocol.
+#[derive(Debug, PartialEq, Eq)]
+pub enum CircuitError {
+    /// The provided party input does not match the number of input bits for
+    /// that party expected by the circuit.
+    PartyInputMismatch,
+    /// The provided set of inputs does not match the number of party inputs
+    /// expected by the circuit.
+    PartyCountMismatch,
+    /// The gate with the specified wire index contains invalid gate connections
+    /// or is placed out of sequence.
+    InvalidGate(usize),
+    /// The specified output gate does not exist in the circuit.
+    InvalidOutputWire(usize),
+    /// The circuit does not specify any output gates.
+    EmptyOutputSpecification,
+    /// The circuit does not specify input wires.
+    EmptyInputSpecification,
+    /// The circuit specifies a zero-width input.
+    InvalidInputSpecification,
+}
+
+impl Circuit {
+    /// Number of parties expected to contribute inputs to the circuit.
+    pub fn number_of_parties(&self) -> usize {
+        self.input_widths.len()
+    }
+
+    /// Check validity of circuit specification.
+    ///
+    /// In particular:
+    /// * Validate input specification: Input width specification does not allow
+    ///   0-width inputs and at least one party must provide input bits.
+    /// * Validate gate sequence: All input gates must be at the beginning of
+    ///   the gate sequence, followed only by logic gates.
+    /// * Validate gate wiring: A logic gate with index `i` can only take input
+    ///   wires with strictly smaller indices. An input gate with index `i` must
+    ///   refer to its own index as the input wire index.
+    /// * Validate output specification: The number of specified output wires
+    ///  must be non-zero and all output wire indices must refer to valid wire
+    ///  indices in the circuit, i.e. output wire indices must be smaller or
+    ///  equal to the highest wire index used in the circuit.
+    pub fn validate_circuit_specification(&self) -> Result<(), CircuitError> {
+        // Check input validity.
+        if self.input_widths.is_empty() {
+            return Err(CircuitError::EmptyInputSpecification);
+        }
+        for input_width in self.input_widths.iter() {
+            if *input_width == 0 {
+                return Err(CircuitError::InvalidInputSpecification);
+            }
+        }
+
+        // Check gate and gate sequence validity.
+        let mut total_input_width = 0;
+        for party_input_width in self.input_widths.iter() {
+            total_input_width += party_input_width;
+        }
+
+        for (gate_index, gate) in self.gates.iter().enumerate() {
+            match *gate {
+                WiredGate::Input(x) => {
+                    if x != gate_index || gate_index >= total_input_width {
+                        return Err(CircuitError::InvalidGate(gate_index));
+                    }
+                }
+                WiredGate::Xor(x, y) => {
+                    if x >= gate_index || y >= gate_index || gate_index < total_input_width {
+                        return Err(CircuitError::InvalidGate(gate_index));
+                    }
+                }
+                WiredGate::And(x, y) => {
+                    if x >= gate_index || y >= gate_index || gate_index < total_input_width {
+                        return Err(CircuitError::InvalidGate(gate_index));
+                    }
+                }
+                WiredGate::Not(x) => {
+                    if x >= gate_index || gate_index < total_input_width {
+                        return Err(CircuitError::InvalidGate(gate_index));
+                    }
+                }
+            }
+        }
+
+        // Validate non-empty output specification.
+        if self.output_gates.is_empty() {
+            return Err(CircuitError::EmptyOutputSpecification);
+        }
+
+        // Validate output wire bounds.
+        for &output_wire in self.output_gates.iter() {
+            if output_wire >= self.gates.len() {
+                return Err(CircuitError::InvalidOutputWire(output_wire));
+            }
+        }
+
+        Ok(())
+    }
+
+    /// Validate that a given set of party inputs corresponds to the circuit
+    /// specification.
+    ///
+    /// In particular:
+    /// * Validate that the number of input vectors corresponds to the number of parties
+    ///   expected to provide inputs.
+    /// * Validate, for each input vector, that the number of input bits matches the
+    ///   corresponding parties' expected input width.
+    pub fn validate_input_vectors(&self, inputs: &[Vec<bool>]) -> Result<(), CircuitError> {
+        if self.number_of_parties() != inputs.len() {
+            return Err(CircuitError::PartyCountMismatch);
+        }
+
+        for (party, &expected_input_gates) in self.input_widths.iter().enumerate() {
+            if expected_input_gates != inputs[party].len() {
+                return Err(CircuitError::PartyInputMismatch);
+            }
+        }
+
+        Ok(())
+    }
+
+    /// Evaluates a circuit with the specified inputs (with one `Vec<bool>` per
+    /// party).
+    ///
+    /// After validation of the circuit specification and validation of the
+    /// provided input vectors, the circuit is evaluated gate by gate:
+    ///
+    /// * Input gates are evaluated as the identity function on the provided
+    ///   input.
+    /// * Logic gates are evaluated by applying the given logical operation to
+    ///   the wire values of the gates' input wires.
+    ///
+    /// Circuit validation ensures that, during sequential evaluation, gate
+    /// input wires can only refer to previously evaluated gates, or values
+    /// provided in the circuit inputs in the case of input gate evaulation.
+    ///
+    /// The circuit output is packed into a bitstring, with the indicated output
+    /// wire values appearing in sequential order.
+    pub fn eval(&self, inputs: &[Vec<bool>]) -> Result<Vec<bool>, CircuitError> {
+        self.validate_circuit_specification()?;
+        self.validate_input_vectors(inputs)?;
+
+        let mut wire_evaluations: Vec<bool> = inputs.iter().flat_map(|b| b.clone()).collect();
+
+        for gate in self.gates.iter() {
+            let output_bit = match gate {
+                WiredGate::Input(x) => wire_evaluations[*x],
+                WiredGate::Xor(x, y) => wire_evaluations[*x] ^ wire_evaluations[*y],
+                WiredGate::And(x, y) => wire_evaluations[*x] & wire_evaluations[*y],
+                WiredGate::Not(x) => !wire_evaluations[*x],
+            };
+            wire_evaluations.push(output_bit);
+        }
+
+        let mut output_packed: Vec<bool> = Vec::with_capacity(self.output_gates.len());
+        for output_gate in &self.output_gates {
+            output_packed.push(wire_evaluations[*output_gate]);
+        }
+        Ok(output_packed)
+    }
+}

mpc-spec/src/lib.rs

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+#![deny(missing_docs)]
+#![deny(rustdoc::broken_intra_doc_links)]
+//! This crate is an executable specification of an MPC engine based on the
+//! WRK17 protocol.
+
+pub mod circuit;