serai/crypto/dleq/src/cross_group/mod.rs

use thiserror::Error;

use rand_core::{RngCore, CryptoRng};
use digest::Digest;

use transcript::Transcript;

use group::{ff::{Field, PrimeField, PrimeFieldBits}, prime::PrimeGroup};
use multiexp::BatchVerifier;

use crate::Generators;

pub mod scalar;
use scalar::{scalar_convert, mutual_scalar_from_bytes};

pub(crate) mod schnorr;
use schnorr::SchnorrPoK;

pub(crate) mod aos;

mod bits;
use bits::{BitSignature, Bits};

#[cfg(feature = "serialize")]
use std::io::{Read, Write};

#[cfg(feature = "serialize")]
pub(crate) fn read_point<R: Read, G: PrimeGroup>(r: &mut R) -> std::io::Result<G> {
  let mut repr = G::Repr::default();
  r.read_exact(repr.as_mut())?;
  let point = G::from_bytes(&repr);
  if point.is_none().into() {
    Err(std::io::Error::new(std::io::ErrorKind::Other, "invalid point"))?;
  }
  Ok(point.unwrap())
}

#[derive(Error, PartialEq, Eq, Debug)]
pub enum DLEqError {
  #[error("invalid proof of knowledge")]
  InvalidProofOfKnowledge,
  #[error("invalid proof length")]
  InvalidProofLength,
  #[error("invalid challenge")]
  InvalidChallenge,
  #[error("invalid proof")]
  InvalidProof
}

// This should never be directly instantiated and uses a u8 to represent internal values
// Any external usage is likely invalid
#[doc(hidden)]
// Debug would be such a dump of data this likely isn't helpful, but at least it's available to
// anyone who wants it
#[derive(Clone, PartialEq, Eq, Debug)]
pub struct __DLEqProof<
  G0: PrimeGroup,
  G1: PrimeGroup,
  const SIGNATURE: u8,
  const RING_LEN: usize,
  const REMAINDER_RING_LEN: usize
> where G0::Scalar: PrimeFieldBits, G1::Scalar: PrimeFieldBits {
  bits: Vec<Bits<G0, G1, SIGNATURE, RING_LEN>>,
  remainder: Option<Bits<G0, G1, SIGNATURE, REMAINDER_RING_LEN>>,
  poks: (SchnorrPoK<G0>, SchnorrPoK<G1>)
}

macro_rules! dleq {
  ($name: ident, $signature: expr, $remainder: literal) => {
    pub type $name<G0, G1> = __DLEqProof<
      G0,
      G1,
      { $signature.to_u8() },
      { $signature.ring_len() },
      // There may not be a remainder, yet if there is one, it'll be just one bit
      // A ring for one bit has a RING_LEN of 2
      { if $remainder { 2 } else { 0 } }
    >;
  }
}

// Proves for 1-bit at a time with the signature form (e, s), as originally described in MRL-0010.
// Uses a merged challenge, unlike MRL-0010, for the ring signature, saving an element from each
// bit and removing a hash while slightly reducing challenge security. This security reduction is
// already applied to the scalar being proven for, a result of the requirement it's mutually valid
// over both scalar fields, hence its application here as well. This is mainly here as a point of
// reference for the following DLEq proofs, all which use merged challenges, and isn't performant
// in comparison to the others
dleq!(ClassicLinearDLEq, BitSignature::ClassicLinear, false);

// Proves for 2-bits at a time to save 3/7 elements of every other bit
// <9% smaller than CompromiseLinear, yet ~12% slower
dleq!(ConciseLinearDLEq, BitSignature::ConciseLinear, true);

// Uses AOS signatures of the form R, s, to enable the final step of the ring signature to be
// batch verified, at the cost of adding an additional element per bit
dleq!(EfficientLinearDLEq, BitSignature::EfficientLinear, false);

// Proves for 2-bits at a time while using the R, s form. This saves 3/7 elements of every other
// bit, while adding 1 element to every bit, and is more efficient than ConciseLinear yet less
// efficient than EfficientLinear due to having more ring signature steps which aren't batched
// >25% smaller than EfficientLinear and just 11% slower, making it the recommended option
dleq!(CompromiseLinearDLEq, BitSignature::CompromiseLinear, true);

impl<
  G0: PrimeGroup,
  G1: PrimeGroup,
  const SIGNATURE: u8,
  const RING_LEN: usize,
  const REMAINDER_RING_LEN: usize
> __DLEqProof<G0, G1, SIGNATURE, RING_LEN, REMAINDER_RING_LEN> where
  G0::Scalar: PrimeFieldBits, G1::Scalar: PrimeFieldBits {

  pub(crate) fn transcript<T: Transcript>(
    transcript: &mut T,
    generators: (Generators<G0>, Generators<G1>),
    keys: (G0, G1)
  ) {
    transcript.domain_separate(b"cross_group_dleq");
    generators.0.transcript(transcript);
    generators.1.transcript(transcript);
    transcript.domain_separate(b"points");
    transcript.append_message(b"point_0", keys.0.to_bytes().as_ref());
    transcript.append_message(b"point_1", keys.1.to_bytes().as_ref());
  }

  pub(crate) fn blinding_key<R: RngCore + CryptoRng, F: PrimeField>(
    rng: &mut R,
    total: &mut F,
    last: bool
  ) -> F {
    let blinding_key = if last {
      -*total
    } else {
      F::random(&mut *rng)
    };
    *total += blinding_key;
    blinding_key
  }

  fn reconstruct_keys(&self) -> (G0, G1) {
    let mut res = (
      self.bits.iter().map(|bit| bit.commitments.0).sum::<G0>(),
      self.bits.iter().map(|bit| bit.commitments.1).sum::<G1>()
    );

    if let Some(bit) = &self.remainder {
      res.0 += bit.commitments.0;
      res.1 += bit.commitments.1;
    }

    res
  }

  fn prove_internal<R: RngCore + CryptoRng, T: Clone + Transcript>(
    rng: &mut R,
    transcript: &mut T,
    generators: (Generators<G0>, Generators<G1>),
    f: (G0::Scalar, G1::Scalar)
  ) -> (Self, (G0::Scalar, G1::Scalar)) {
    Self::transcript(
      transcript,
      generators,
      ((generators.0.primary * f.0), (generators.1.primary * f.1))
    );

    let poks = (
      SchnorrPoK::<G0>::prove(rng, transcript, generators.0.primary, f.0),
      SchnorrPoK::<G1>::prove(rng, transcript, generators.1.primary, f.1)
    );

    let mut blinding_key_total = (G0::Scalar::zero(), G1::Scalar::zero());
    let mut blinding_key = |rng: &mut R, last| {
      let blinding_key = (
        Self::blinding_key(&mut *rng, &mut blinding_key_total.0, last),
        Self::blinding_key(&mut *rng, &mut blinding_key_total.1, last)
      );
      if last {
        debug_assert_eq!(blinding_key_total.0, G0::Scalar::zero());
        debug_assert_eq!(blinding_key_total.1, G1::Scalar::zero());
      }
      blinding_key
    };

    let capacity = usize::try_from(G0::Scalar::CAPACITY.min(G1::Scalar::CAPACITY)).unwrap();
    let bits_per_group = BitSignature::from(SIGNATURE).bits();

    let mut pow_2 = (generators.0.primary, generators.1.primary);

    let raw_bits = f.0.to_le_bits();
    let mut bits = Vec::with_capacity(capacity);
    let mut these_bits: u8 = 0;
    for (i, bit) in raw_bits.iter().enumerate() {
      if i == capacity {
        break;
      }

      let bit = *bit as u8;
      debug_assert_eq!(bit | 1, 1);

      // Accumulate this bit
      these_bits |= bit << (i % bits_per_group);
      if (i % bits_per_group) == (bits_per_group - 1) {
        let last = i == (capacity - 1);
        let blinding_key = blinding_key(&mut *rng, last);
        bits.push(
          Bits::prove(
            &mut *rng,
            transcript,
            generators,
            i / bits_per_group,
            &mut pow_2,
            these_bits,
            blinding_key
          )
        );
        these_bits = 0;
      }
    }
    debug_assert_eq!(bits.len(), capacity / bits_per_group);

    let mut remainder = None;
    if capacity != ((capacity / bits_per_group) * bits_per_group) {
      let blinding_key = blinding_key(&mut *rng, true);
      remainder = Some(
        Bits::prove(
          &mut *rng,
          transcript,
          generators,
          capacity / bits_per_group,
          &mut pow_2,
          these_bits,
          blinding_key
        )
      );
    }

    let proof = __DLEqProof { bits, remainder, poks };
    debug_assert_eq!(
      proof.reconstruct_keys(),
      (generators.0.primary * f.0, generators.1.primary * f.1)
    );
    (proof, f)
  }

  /// Prove the cross-Group Discrete Log Equality for the points derived from the scalar created as
  /// the output of the passed in Digest. Given the non-standard requirements to achieve
  /// uniformity, needing to be < 2^x instead of less than a prime moduli, this is the simplest way
  /// to safely and securely generate a Scalar, without risk of failure, nor bias
  /// It also ensures a lack of determinable relation between keys, guaranteeing security in the
  /// currently expected use case for this, atomic swaps, where each swap leaks the key. Knowing
  /// the relationship between keys would allow breaking all swaps after just one
  pub fn prove<R: RngCore + CryptoRng, T: Clone + Transcript, D: Digest>(
    rng: &mut R,
    transcript: &mut T,
    generators: (Generators<G0>, Generators<G1>),
    digest: D
  ) -> (Self, (G0::Scalar, G1::Scalar)) {
    Self::prove_internal(
      rng,
      transcript,
      generators,
      mutual_scalar_from_bytes(digest.finalize().as_ref())
    )
  }

  /// Prove the cross-Group Discrete Log Equality for the points derived from the scalar passed in,
  /// failing if it's not mutually valid. This allows for rejection sampling externally derived
  /// scalars until they're safely usable, as needed
  pub fn prove_without_bias<R: RngCore + CryptoRng, T: Clone + Transcript>(
    rng: &mut R,
    transcript: &mut T,
    generators: (Generators<G0>, Generators<G1>),
    f0: G0::Scalar
  ) -> Option<(Self, (G0::Scalar, G1::Scalar))> {
    scalar_convert(f0).map(|f1| Self::prove_internal(rng, transcript, generators, (f0, f1)))
  }

  /// Verify a cross-Group Discrete Log Equality statement, returning the points proven for
  pub fn verify<R: RngCore + CryptoRng, T: Clone + Transcript>(
    &self,
    rng: &mut R,
    transcript: &mut T,
    generators: (Generators<G0>, Generators<G1>)
  ) -> Result<(G0, G1), DLEqError> {
    let capacity = usize::try_from(
      G0::Scalar::CAPACITY.min(G1::Scalar::CAPACITY)
    ).unwrap();
    let bits_per_group = BitSignature::from(SIGNATURE).bits();
    let has_remainder = (capacity % bits_per_group) != 0;

    // These shouldn't be possible, as locally created and deserialized proofs should be properly
    // formed in these regards, yet it doesn't hurt to check and would be problematic if true
    if (self.bits.len() != (capacity / bits_per_group)) || (
      (self.remainder.is_none() && has_remainder) || (self.remainder.is_some() && !has_remainder)
    ) {
      return Err(DLEqError::InvalidProofLength);
    }

    let keys = self.reconstruct_keys();
    Self::transcript(transcript, generators, keys);

    let batch_capacity = match BitSignature::from(SIGNATURE) {
      BitSignature::ClassicLinear => 3,
      BitSignature::ConciseLinear => 3,
      BitSignature::EfficientLinear => (self.bits.len() + 1) * 3,
      BitSignature::CompromiseLinear => (self.bits.len() + 1) * 3
    };
    let mut batch = (BatchVerifier::new(batch_capacity), BatchVerifier::new(batch_capacity));

    self.poks.0.verify(&mut *rng, transcript, generators.0.primary, keys.0, &mut batch.0);
    self.poks.1.verify(&mut *rng, transcript, generators.1.primary, keys.1, &mut batch.1);

    let mut pow_2 = (generators.0.primary, generators.1.primary);
    for (i, bits) in self.bits.iter().enumerate() {
      bits.verify(&mut *rng, transcript, generators, &mut batch, i, &mut pow_2)?;
    }
    if let Some(bit) = &self.remainder {
      bit.verify(&mut *rng, transcript, generators, &mut batch, self.bits.len(), &mut pow_2)?;
    }

    if (!batch.0.verify_vartime()) || (!batch.1.verify_vartime()) {
      Err(DLEqError::InvalidProof)?;
    }

    Ok(keys)
  }

  #[cfg(feature = "serialize")]
  pub fn serialize<W: Write>(&self, w: &mut W) -> std::io::Result<()> {
    for bit in &self.bits {
      bit.serialize(w)?;
    }
    if let Some(bit) = &self.remainder {
      bit.serialize(w)?;
    }
    self.poks.0.serialize(w)?;
    self.poks.1.serialize(w)
  }

  #[cfg(feature = "serialize")]
  pub fn deserialize<R: Read>(r: &mut R) -> std::io::Result<Self> {
    let capacity = usize::try_from(
      G0::Scalar::CAPACITY.min(G1::Scalar::CAPACITY)
    ).unwrap();
    let bits_per_group = BitSignature::from(SIGNATURE).bits();

    let mut bits = Vec::with_capacity(capacity / bits_per_group);
    for _ in 0 .. (capacity / bits_per_group) {
      bits.push(Bits::deserialize(r)?);
    }

    let mut remainder = None;
    if (capacity % bits_per_group) != 0 {
      remainder = Some(Bits::deserialize(r)?);
    }

    Ok(
      __DLEqProof {
        bits,
        remainder,
        poks: (SchnorrPoK::deserialize(r)?, SchnorrPoK::deserialize(r)?)
      }
    )
  }
}