elastic_elgamal/app/
choice.rs

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
//! Encrypted choice.

use merlin::Transcript;
use rand_core::{CryptoRng, RngCore};
#[cfg(feature = "serde")]
use serde::{de::DeserializeOwned, Deserialize, Serialize};
use zeroize::Zeroizing;

use core::{fmt, iter, ops};

use crate::{
    alloc::{vec, Vec},
    group::Group,
    Ciphertext, CiphertextWithValue, LogEqualityProof, PublicKey, RingProof, RingProofBuilder,
    VerificationError,
};

/// Encapsulation of functionality for proving and verifying correctness of the sum of option
/// ciphertexts in an [`EncryptedChoice`].
///
/// This trait is not meant to be implemented for external types.
pub trait ProveSum<G: Group>: Clone + crate::sealed::Sealed {
    /// Produced / verified proofs.
    #[cfg(not(feature = "serde"))]
    type Proof: Sized;
    /// Produced / verified proofs.
    #[cfg(feature = "serde")]
    type Proof: Sized + Serialize + DeserializeOwned;

    #[doc(hidden)]
    fn prove<R: CryptoRng + RngCore>(
        &self,
        ciphertext: &CiphertextWithValue<G, u64>,
        receiver: &PublicKey<G>,
        rng: &mut R,
    ) -> Self::Proof;

    #[doc(hidden)]
    fn verify(
        &self,
        ciphertext: &Ciphertext<G>,
        proof: &Self::Proof,
        receiver: &PublicKey<G>,
    ) -> Result<(), ChoiceVerificationError>;
}

/// Single-choice setup for [`EncryptedChoice`], in which it can contain a single selected option.
///
/// # Examples
///
/// See [`EncryptedChoice`] docs for an example of usage.
#[derive(Debug, Clone, Copy)]
pub struct SingleChoice(());

impl crate::sealed::Sealed for SingleChoice {}

impl<G: Group> ProveSum<G> for SingleChoice {
    type Proof = LogEqualityProof<G>;

    fn prove<R: CryptoRng + RngCore>(
        &self,
        ciphertext: &CiphertextWithValue<G, u64>,
        receiver: &PublicKey<G>,
        rng: &mut R,
    ) -> Self::Proof {
        LogEqualityProof::new(
            receiver,
            ciphertext.randomness(),
            (
                ciphertext.inner().random_element,
                ciphertext.inner().blinded_element - G::generator(),
            ),
            &mut Transcript::new(b"choice_encryption_sum"),
            rng,
        )
    }

    fn verify(
        &self,
        ciphertext: &Ciphertext<G>,
        proof: &Self::Proof,
        receiver: &PublicKey<G>,
    ) -> Result<(), ChoiceVerificationError> {
        let powers = (
            ciphertext.random_element,
            ciphertext.blinded_element - G::generator(),
        );
        proof
            .verify(
                receiver,
                powers,
                &mut Transcript::new(b"choice_encryption_sum"),
            )
            .map_err(ChoiceVerificationError::Sum)
    }
}

/// Multi-choice setup for [`EncryptedChoice`], in which it can contain any possible number
/// of selected options (`0..=n`, where `n` is the number of options).
///
/// # Examples
///
/// See [`EncryptedChoice`] docs for an example of usage.
#[derive(Debug, Clone, Copy)]
pub struct MultiChoice(());

impl crate::sealed::Sealed for MultiChoice {}

impl<G: Group> ProveSum<G> for MultiChoice {
    type Proof = ();

    fn prove<R: CryptoRng + RngCore>(
        &self,
        _ciphertext: &CiphertextWithValue<G, u64>,
        _receiver: &PublicKey<G>,
        _rng: &mut R,
    ) -> Self::Proof {
        // Do nothing.
    }

    fn verify(
        &self,
        _ciphertext: &Ciphertext<G>,
        _proof: &Self::Proof,
        _receiver: &PublicKey<G>,
    ) -> Result<(), ChoiceVerificationError> {
        Ok(()) // no failure conditions
    }
}

/// Parameters of an [`EncryptedChoice`] polling.
#[derive(Debug)]
pub struct ChoiceParams<G: Group, S: ProveSum<G>> {
    options_count: usize,
    sum_prover: S,
    receiver: PublicKey<G>,
}

impl<G: Group, S: ProveSum<G>> Clone for ChoiceParams<G, S> {
    fn clone(&self) -> Self {
        Self {
            options_count: self.options_count,
            sum_prover: self.sum_prover.clone(),
            receiver: self.receiver.clone(),
        }
    }
}

impl<G: Group, S: ProveSum<G>> ChoiceParams<G, S> {
    fn check_options_count(&self, actual_count: usize) -> Result<(), ChoiceVerificationError> {
        if self.options_count == actual_count {
            Ok(())
        } else {
            Err(ChoiceVerificationError::OptionsLenMismatch {
                expected: self.options_count,
                actual: actual_count,
            })
        }
    }

    /// Returns the public key for which the [`EncryptedChoice`] are encrypted.
    pub fn receiver(&self) -> &PublicKey<G> {
        &self.receiver
    }

    /// Returns the number of options in these parameters.
    pub fn options_count(&self) -> usize {
        self.options_count
    }
}

impl<G: Group> ChoiceParams<G, SingleChoice> {
    /// Creates parameters for a single-choice polling.
    ///
    /// # Panics
    ///
    /// Panics if provided `options_count` is zero.
    pub fn single(receiver: PublicKey<G>, options_count: usize) -> Self {
        assert!(options_count > 0, "Number of options must be positive");
        Self {
            options_count,
            sum_prover: SingleChoice(()),
            receiver,
        }
    }
}

impl<G: Group> ChoiceParams<G, MultiChoice> {
    /// Creates parameters for a multi-choice polling.
    ///
    /// # Panics
    ///
    /// Panics if provided `options_count` is zero.
    pub fn multi(receiver: PublicKey<G>, options_count: usize) -> Self {
        assert!(options_count > 0, "Number of options must be positive");
        Self {
            options_count,
            sum_prover: MultiChoice(()),
            receiver,
        }
    }
}

/// Zero or more encrypted choices from `n` options (`n >= 1`) together with zero-knowledge
/// proofs of correctness.
///
/// # Construction
///
/// The choice is represented as a vector of `n` *choice ciphertexts* of Boolean values (0 or 1),
/// where the ciphertexts for the chosen options encrypt 1 and the other ciphertexts encrypt 0.
/// This ensures that multiple [`EncryptedChoice`]s can be added (e.g., within a voting protocol).
///
/// Zero-knowledge proofs are:
///
/// - A [`RingProof`] attesting that all `n` ciphertexts encrypt 0 or 1.
///   This proof can be obtained via [`Self::range_proof()`].
/// - A [`LogEqualityProof`] attesting that the encrypted values sum up to 1. Combined with
///   the range proof, this means that exactly one of encrypted values is 1, and all others are 0.
///   This proof can be obtained via [`Self::sum_proof()`]. This proof is absent for
///   a [`MultiChoice`] setup (`sum_proof()` just returns `()`).
///
/// # Examples
///
/// ## Single-choice setup
///
/// ```
/// # use elastic_elgamal::{
/// #     app::{ChoiceParams, EncryptedChoice}, group::Ristretto, DiscreteLogTable, Keypair,
/// # };
/// # use rand::thread_rng;
/// # fn main() -> Result<(), Box<dyn std::error::Error>> {
/// let mut rng = thread_rng();
/// let (pk, sk) = Keypair::<Ristretto>::generate(&mut rng).into_tuple();
/// let choice_params = ChoiceParams::single(pk, 5);
///
/// let choice = 2;
/// let enc = EncryptedChoice::single(&choice_params, choice, &mut rng);
/// let choices = enc.verify(&choice_params)?;
///
/// // `choices` is a slice of 5 Boolean value ciphertexts
/// assert_eq!(choices.len(), 5);
/// let lookup_table = DiscreteLogTable::new(0..=1);
/// for (idx, &v) in choices.iter().enumerate() {
///     assert_eq!(
///         sk.decrypt(v, &lookup_table),
///         Some((idx == choice) as u64)
///     );
/// }
/// # Ok(())
/// # }
/// ```
///
/// ## Multi-choice setup
///
/// ```
/// # use elastic_elgamal::{
/// #     app::{ChoiceParams, EncryptedChoice}, group::Ristretto, DiscreteLogTable, Keypair,
/// # };
/// # use rand::thread_rng;
/// # fn main() -> Result<(), Box<dyn std::error::Error>> {
/// let mut rng = thread_rng();
/// let (pk, sk) = Keypair::<Ristretto>::generate(&mut rng).into_tuple();
/// let choice_params = ChoiceParams::multi(pk, 5);
///
/// let choices = [true, false, true, true, false];
/// let enc = EncryptedChoice::new(&choice_params, &choices, &mut rng);
/// let recovered_choices = enc.verify(&choice_params)?;
///
/// let lookup_table = DiscreteLogTable::new(0..=1);
/// for (idx, &v) in recovered_choices.iter().enumerate() {
///     assert_eq!(sk.decrypt(v, &lookup_table), Some(choices[idx] as u64));
/// }
/// # Ok(())
/// # }
/// ```
#[derive(Debug, Clone)]
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[cfg_attr(feature = "serde", serde(bound = ""))]
pub struct EncryptedChoice<G: Group, S: ProveSum<G>> {
    choices: Vec<Ciphertext<G>>,
    range_proof: RingProof<G>,
    sum_proof: S::Proof,
}

impl<G: Group> EncryptedChoice<G, SingleChoice> {
    /// Creates a new encrypted choice.
    ///
    /// # Panics
    ///
    /// Panics if `choice` exceeds the maximum index allowed by `params`.
    pub fn single<R: CryptoRng + RngCore>(
        params: &ChoiceParams<G, SingleChoice>,
        choice: usize,
        rng: &mut R,
    ) -> Self {
        assert!(
            choice < params.options_count,
            "invalid choice {choice}; expected a value in 0..{}",
            params.options_count
        );
        let choices: Vec<_> = (0..params.options_count).map(|i| choice == i).collect();
        Self::new(params, &Zeroizing::new(choices), rng)
    }
}

#[allow(clippy::len_without_is_empty)] // `is_empty()` would always be false
impl<G: Group, S: ProveSum<G>> EncryptedChoice<G, S> {
    /// Creates an encrypted multi-choice.
    ///
    /// For a [`SingleChoice`] polling, it is caller's responsibility to ensure that `choices`
    /// contains exactly one `true` value; otherwise, the produced proof will not verify.
    ///
    /// # Panics
    ///
    /// Panics if the length of `choices` differs from the number of options specified in `params`.
    pub fn new<R: CryptoRng + RngCore>(
        params: &ChoiceParams<G, S>,
        choices: &[bool],
        rng: &mut R,
    ) -> Self {
        assert!(!choices.is_empty(), "No choices provided");
        assert_eq!(
            choices.len(),
            params.options_count,
            "Mismatch between expected and actual number of choices"
        );

        let admissible_values = [G::identity(), G::generator()];
        let mut ring_responses = vec![G::Scalar::default(); 2 * params.options_count];
        let mut transcript = Transcript::new(b"encrypted_choice_ranges");
        let mut proof_builder = RingProofBuilder::new(
            &params.receiver,
            params.options_count,
            &mut ring_responses,
            &mut transcript,
            rng,
        );

        let sum = choices.iter().map(|&flag| u64::from(flag)).sum::<u64>();
        let choices: Vec<_> = choices
            .iter()
            .map(|&flag| proof_builder.add_value(&admissible_values, usize::from(flag)))
            .collect();
        let range_proof = RingProof::new(proof_builder.build(), ring_responses);

        let sum_ciphertext = choices.iter().cloned().reduce(ops::Add::add).unwrap();
        let sum_ciphertext = sum_ciphertext.with_value(sum);
        let sum_proof = params
            .sum_prover
            .prove(&sum_ciphertext, &params.receiver, rng);
        Self {
            choices: choices.into_iter().map(|choice| choice.inner).collect(),
            range_proof,
            sum_proof,
        }
    }

    /// Verifies the zero-knowledge proofs in this choice and returns Boolean ciphertexts
    /// for all options.
    ///
    /// # Errors
    ///
    /// Returns an error if the `choice` is malformed or its proofs fail verification.
    #[allow(clippy::missing_panics_doc)]
    pub fn verify(
        &self,
        params: &ChoiceParams<G, S>,
    ) -> Result<&[Ciphertext<G>], ChoiceVerificationError> {
        params.check_options_count(self.choices.len())?;
        let sum_of_ciphertexts = self.choices.iter().copied().reduce(ops::Add::add);
        let sum_of_ciphertexts = sum_of_ciphertexts.unwrap();
        // ^ `unwrap()` is safe; `params` cannot have 0 options by construction
        params
            .sum_prover
            .verify(&sum_of_ciphertexts, &self.sum_proof, &params.receiver)?;

        let admissible_values = [G::identity(), G::generator()];
        self.range_proof
            .verify(
                &params.receiver,
                iter::repeat(&admissible_values as &[_]).take(self.choices.len()),
                self.choices.iter().copied(),
                &mut Transcript::new(b"encrypted_choice_ranges"),
            )
            .map(|()| self.choices.as_slice())
            .map_err(ChoiceVerificationError::Range)
    }

    /// Returns the number of encrypted choices. This value is equal to
    /// [`ChoiceParams::options_count()`] with which the encryption was created.
    pub fn len(&self) -> usize {
        self.choices.len()
    }

    /// Returns ciphertexts for all options **without** checking the validity of this choice.
    pub fn choices_unchecked(&self) -> &[Ciphertext<G>] {
        &self.choices
    }

    /// Returns the range proof for the choice ciphertexts.
    pub fn range_proof(&self) -> &RingProof<G> {
        &self.range_proof
    }

    /// Returns the sum proof for the choice ciphertexts.
    pub fn sum_proof(&self) -> &S::Proof {
        &self.sum_proof
    }
}

/// Error verifying an [`EncryptedChoice`].
#[derive(Debug)]
#[non_exhaustive]
pub enum ChoiceVerificationError {
    /// Mismatch between expected and actual number of options in the `EncryptedChoice`.
    OptionsLenMismatch {
        /// Expected number of options.
        expected: usize,
        /// Actual number of options.
        actual: usize,
    },
    /// Error verifying [`EncryptedChoice::sum_proof()`].
    Sum(VerificationError),
    /// Error verifying [`EncryptedChoice::range_proof()`].
    Range(VerificationError),
}

impl fmt::Display for ChoiceVerificationError {
    fn fmt(&self, formatter: &mut fmt::Formatter<'_>) -> fmt::Result {
        match self {
            Self::OptionsLenMismatch { expected, actual } => write!(
                formatter,
                "number of options in the ballot ({actual}) differs from expected ({expected})",
            ),
            Self::Sum(err) => write!(formatter, "cannot verify sum proof: {err}"),
            Self::Range(err) => write!(formatter, "cannot verify range proofs: {err}"),
        }
    }
}

#[cfg(feature = "std")]
impl std::error::Error for ChoiceVerificationError {
    fn source(&self) -> Option<&(dyn std::error::Error + 'static)> {
        match self {
            Self::Sum(err) | Self::Range(err) => Some(err),
            _ => None,
        }
    }
}

#[cfg(test)]
mod tests {
    use rand::thread_rng;

    use super::*;
    use crate::{
        group::{Generic, Ristretto},
        Keypair,
    };

    fn test_bogus_encrypted_choice_does_not_work<G: Group>() {
        let mut rng = thread_rng();
        let (receiver, _) = Keypair::<G>::generate(&mut rng).into_tuple();
        let params = ChoiceParams::single(receiver.clone(), 5);

        let mut choice = EncryptedChoice::single(&params, 2, &mut rng);
        let (encrypted_one, _) = receiver.encrypt_bool(true, &mut rng);
        choice.choices[0] = encrypted_one;
        assert!(choice.verify(&params).is_err());

        let mut choice = EncryptedChoice::single(&params, 4, &mut rng);
        let (encrypted_zero, _) = receiver.encrypt_bool(false, &mut rng);
        choice.choices[4] = encrypted_zero;
        assert!(choice.verify(&params).is_err());

        let mut choice = EncryptedChoice::single(&params, 4, &mut rng);
        choice.choices[4].blinded_element =
            choice.choices[4].blinded_element + G::mul_generator(&G::Scalar::from(10));
        choice.choices[3].blinded_element =
            choice.choices[3].blinded_element - G::mul_generator(&G::Scalar::from(10));
        // These modifications leave `choice.sum_proof` correct, but the range proofs
        // for the last 2 choices should no longer verify.
        assert!(choice.verify(&params).is_err());
    }

    #[test]
    fn bogus_encrypted_choice_does_not_work_for_edwards() {
        test_bogus_encrypted_choice_does_not_work::<Ristretto>();
    }

    #[test]
    fn bogus_encrypted_choice_does_not_work_for_k256() {
        test_bogus_encrypted_choice_does_not_work::<Generic<k256::Secp256k1>>();
    }
}