1//! This module implements various low-level gadgets
  2use crate::traits::Group;
  3use bellperson::{
  4  gadgets::{
  5    boolean::{AllocatedBit, Boolean},
  6    num::AllocatedNum,
  7    Assignment,
  8  },
  9  ConstraintSystem, LinearCombination, SynthesisError,
 10};
 11use bellperson_nonnative::mp::bignat::{nat_to_limbs, BigNat};
 12use ff::{Field, PrimeField, PrimeFieldBits};
 13use rug::Integer;
 14
 15/// Gets as input the little indian representation of a number and spits out the number
 16#[allow(dead_code)]
 17pub fn le_bits_to_num<Scalar, CS>(
 18  mut cs: CS,
 19  bits: Vec<AllocatedBit>,
 20) -> Result<AllocatedNum<Scalar>, SynthesisError>
 21where
 22  Scalar: PrimeField + PrimeFieldBits,
 23  CS: ConstraintSystem<Scalar>,
 24{
 25  // We loop over the input bits and construct the constraint
 26  // and the field element that corresponds to the result
 27  let mut lc = LinearCombination::zero();
 28  let mut coeff = Scalar::one();
 29  let mut fe = Some(Scalar::zero());
 30  for bit in bits.iter() {
 31    lc = lc + (coeff, bit.get_variable());
 32    fe = bit.get_value().map(|val| {
 33      if val {
 34        fe.unwrap() + coeff
 35      } else {
 36        fe.unwrap()
 37      }
 38    });
 39    coeff = coeff.double();
 40  }
 41  let num = AllocatedNum::alloc(cs.namespace(|| "Field element"), || {
 42    fe.ok_or(SynthesisError::AssignmentMissing)
 43  })?;
 44  lc = lc - num.get_variable();
 45  cs.enforce(|| "compute number from bits", |lc| lc, |lc| lc, |_| lc);
 46  Ok(num)
 47}
 48
 49/// Allocate a variable that is set to zero
 50pub fn alloc_zero<F: PrimeField, CS: ConstraintSystem<F>>(
 51  mut cs: CS,
 52) -> Result<AllocatedNum<F>, SynthesisError> {
 53  let zero = AllocatedNum::alloc(cs.namespace(|| "alloc"), || Ok(F::zero()))?;
 54  cs.enforce(
 55    || "check zero is valid",
 56    |lc| lc,
 57    |lc| lc,
 58    |lc| lc + zero.get_variable(),
 59  );
 60  Ok(zero)
 61}
 62
 63/// Allocate a variable that is set to one
 64pub fn alloc_one<F: PrimeField, CS: ConstraintSystem<F>>(
 65  mut cs: CS,
 66) -> Result<AllocatedNum<F>, SynthesisError> {
 67  let one = AllocatedNum::alloc(cs.namespace(|| "alloc"), || Ok(F::one()))?;
 68  cs.enforce(
 69    || "check one is valid",
 70    |lc| lc + CS::one(),
 71    |lc| lc + CS::one(),
 72    |lc| lc + one.get_variable(),
 73  );
 74
 75  Ok(one)
 76}
 77
 78/// Allocate a scalar as a base. Only to be used is the scalar fits in base!
 79pub fn alloc_scalar_as_base<G, CS>(
 80  mut cs: CS,
 81  input: Option<G::Scalar>,
 82) -> Result<AllocatedNum<G::Base>, SynthesisError>
 83where
 84  G: Group,
 85  <G as Group>::Scalar: PrimeFieldBits,
 86  CS: ConstraintSystem<<G as Group>::Base>,
 87{
 88  AllocatedNum::alloc(cs.namespace(|| "allocate scalar as base"), || {
 89    let input_bits = input.get()?.clone().to_le_bits();
 90    let mut mult = G::Base::one();
 91    let mut val = G::Base::zero();
 92    for bit in input_bits {
 93      if bit {
 94        val += mult;
 95      }
 96      mult = mult + mult;
 97    }
 98    Ok(val)
 99  })
100}
101
102/// Allocate bignat a constant
103pub fn alloc_bignat_constant<F: PrimeField, CS: ConstraintSystem<F>>(
104  mut cs: CS,
105  val: &Integer,
106  limb_width: usize,
107  n_limbs: usize,
108) -> Result<BigNat<F>, SynthesisError> {
109  let limbs = nat_to_limbs(val, limb_width, n_limbs).unwrap();
110  let bignat = BigNat::alloc_from_limbs(
111    cs.namespace(|| "alloc bignat"),
112    || Ok(limbs.clone()),
113    None,
114    limb_width,
115    n_limbs,
116  )?;
117  // Now enforce that the limbs are all equal to the constants
118  #[allow(clippy::needless_range_loop)]
119  for i in 0..n_limbs {
120    cs.enforce(
121      || format!("check limb {}", i),
122      |lc| lc + &bignat.limbs[i],
123      |lc| lc + CS::one(),
124      |lc| lc + (limbs[i], CS::one()),
125    );
126  }
127  Ok(bignat)
128}
129
130/// Check that two numbers are equal and return a bit
131pub fn alloc_num_equals<F: PrimeField, CS: ConstraintSystem<F>>(
132  mut cs: CS,
133  a: &AllocatedNum<F>,
134  b: &AllocatedNum<F>,
135) -> Result<AllocatedBit, SynthesisError> {
136  // Allocate and constrain `r`: result boolean bit.
137  // It equals `true` if `a` equals `b`, `false` otherwise
138  let r_value = match (a.get_value(), b.get_value()) {
139    (Some(a), Some(b)) => Some(a == b),
140    _ => None,
141  };
142
143  let r = AllocatedBit::alloc(cs.namespace(|| "r"), r_value)?;
144
145  let delta = AllocatedNum::alloc(cs.namespace(|| "delta"), || {
146    let a_value = *a.get_value().get()?;
147    let b_value = *b.get_value().get()?;
148
149    let mut delta = a_value;
150    delta.sub_assign(&b_value);
151
152    Ok(delta)
153  })?;
154
155  cs.enforce(
156    || "delta = (a - b)",
157    |lc| lc + a.get_variable() - b.get_variable(),
158    |lc| lc + CS::one(),
159    |lc| lc + delta.get_variable(),
160  );
161
162  let delta_inv = AllocatedNum::alloc(cs.namespace(|| "delta_inv"), || {
163    let delta = *delta.get_value().get()?;
164
165    if delta.is_zero().unwrap_u8() == 1 {
166      Ok(F::one()) // we can return any number here, it doesn't matter
167    } else {
168      Ok(delta.invert().unwrap())
169    }
170  })?;
171
172  // Allocate `t = delta * delta_inv`
173  // If `delta` is non-zero (a != b), `t` will equal 1
174  // If `delta` is zero (a == b), `t` cannot equal 1
175  let t = AllocatedNum::alloc(cs.namespace(|| "t"), || {
176    let mut tmp = *delta.get_value().get()?;
177    tmp.mul_assign(&(*delta_inv.get_value().get()?));
178
179    Ok(tmp)
180  })?;
181
182  // Constrain allocation:
183  // t = (a - b) * delta_inv
184  cs.enforce(
185    || "t = (a - b) * delta_inv",
186    |lc| lc + a.get_variable() - b.get_variable(),
187    |lc| lc + delta_inv.get_variable(),
188    |lc| lc + t.get_variable(),
189  );
190
191  // Constrain:
192  // (a - b) * (t - 1) == 0
193  // This enforces that correct `delta_inv` was provided,
194  // and thus `t` is 1 if `(a - b)` is non zero (a != b )
195  cs.enforce(
196    || "(a - b) * (t - 1) == 0",
197    |lc| lc + a.get_variable() - b.get_variable(),
198    |lc| lc + t.get_variable() - CS::one(),
199    |lc| lc,
200  );
201
202  // Constrain:
203  // (a - b) * r == 0
204  // This enforces that `r` is zero if `(a - b)` is non-zero (a != b)
205  cs.enforce(
206    || "(a - b) * r == 0",
207    |lc| lc + a.get_variable() - b.get_variable(),
208    |lc| lc + r.get_variable(),
209    |lc| lc,
210  );
211
212  // Constrain:
213  // (t - 1) * (r - 1) == 0
214  // This enforces that `r` is one if `t` is not one (a == b)
215  cs.enforce(
216    || "(t - 1) * (r - 1) == 0",
217    |lc| lc + t.get_variable() - CS::one(),
218    |lc| lc + r.get_variable() - CS::one(),
219    |lc| lc,
220  );
221
222  Ok(r)
223}
224
225/// If condition return a otherwise b
226pub fn conditionally_select<F: PrimeField, CS: ConstraintSystem<F>>(
227  mut cs: CS,
228  a: &AllocatedNum<F>,
229  b: &AllocatedNum<F>,
230  condition: &Boolean,
231) -> Result<AllocatedNum<F>, SynthesisError> {
232  let c = AllocatedNum::alloc(cs.namespace(|| "conditional select result"), || {
233    if *condition.get_value().get()? {
234      Ok(*a.get_value().get()?)
235    } else {
236      Ok(*b.get_value().get()?)
237    }
238  })?;
239
240  // a * condition + b*(1-condition) = c ->
241  // a * condition - b*condition = c - b
242  cs.enforce(
243    || "conditional select constraint",
244    |lc| lc + a.get_variable() - b.get_variable(),
245    |_| condition.lc(CS::one(), F::one()),
246    |lc| lc + c.get_variable() - b.get_variable(),
247  );
248
249  Ok(c)
250}
251
252/// If condition return a otherwise b where a and b are BigNats
253pub fn conditionally_select_bignat<F: PrimeField, CS: ConstraintSystem<F>>(
254  mut cs: CS,
255  a: &BigNat<F>,
256  b: &BigNat<F>,
257  condition: &Boolean,
258) -> Result<BigNat<F>, SynthesisError> {
259  assert!(a.limbs.len() == b.limbs.len());
260  let c = BigNat::alloc_from_nat(
261    cs.namespace(|| "conditional select result"),
262    || {
263      if *condition.get_value().get()? {
264        Ok(a.value.get()?.clone())
265      } else {
266        Ok(b.value.get()?.clone())
267      }
268    },
269    a.params.limb_width,
270    a.params.n_limbs,
271  )?;
272
273  // a * condition + b*(1-condition) = c ->
274  // a * condition - b*condition = c - b
275  for i in 0..c.limbs.len() {
276    cs.enforce(
277      || format!("conditional select constraint {}", i),
278      |lc| lc + &a.limbs[i] - &b.limbs[i],
279      |_| condition.lc(CS::one(), F::one()),
280      |lc| lc + &c.limbs[i] - &b.limbs[i],
281    );
282  }
283  Ok(c)
284}
285
286/// Same as the above but Condition is an AllocatedNum that needs to be
287/// 0 or 1. 1 => True, 0 => False
288pub fn conditionally_select2<F: PrimeField, CS: ConstraintSystem<F>>(
289  mut cs: CS,
290  a: &AllocatedNum<F>,
291  b: &AllocatedNum<F>,
292  condition: &AllocatedNum<F>,
293) -> Result<AllocatedNum<F>, SynthesisError> {
294  let c = AllocatedNum::alloc(cs.namespace(|| "conditional select result"), || {
295    if *condition.get_value().get()? == F::one() {
296      Ok(*a.get_value().get()?)
297    } else {
298      Ok(*b.get_value().get()?)
299    }
300  })?;
301
302  // a * condition + b*(1-condition) = c ->
303  // a * condition - b*condition = c - b
304  cs.enforce(
305    || "conditional select constraint",
306    |lc| lc + a.get_variable() - b.get_variable(),
307    |lc| lc + condition.get_variable(),
308    |lc| lc + c.get_variable() - b.get_variable(),
309  );
310
311  Ok(c)
312}
313
314/// If condition set to 0 otherwise a
315pub fn select_zero_or<F: PrimeField, CS: ConstraintSystem<F>>(
316  mut cs: CS,
317  a: &AllocatedNum<F>,
318  condition: &AllocatedNum<F>,
319) -> Result<AllocatedNum<F>, SynthesisError> {
320  let c = AllocatedNum::alloc(cs.namespace(|| "conditional select result"), || {
321    if *condition.get_value().get()? == F::one() {
322      Ok(F::zero())
323    } else {
324      Ok(*a.get_value().get()?)
325    }
326  })?;
327
328  // a * (1 - condition) = c
329  cs.enforce(
330    || "conditional select constraint",
331    |lc| lc + a.get_variable(),
332    |lc| lc + CS::one() - condition.get_variable(),
333    |lc| lc + c.get_variable(),
334  );
335
336  Ok(c)
337}
338
339/// If condition set to 1 otherwise a
340pub fn select_one_or<F: PrimeField, CS: ConstraintSystem<F>>(
341  mut cs: CS,
342  a: &AllocatedNum<F>,
343  condition: &AllocatedNum<F>,
344) -> Result<AllocatedNum<F>, SynthesisError> {
345  let c = AllocatedNum::alloc(cs.namespace(|| "conditional select result"), || {
346    if *condition.get_value().get()? == F::one() {
347      Ok(F::one())
348    } else {
349      Ok(*a.get_value().get()?)
350    }
351  })?;
352
353  cs.enforce(
354    || "conditional select constraint",
355    |lc| lc + CS::one() - a.get_variable(),
356    |lc| lc + condition.get_variable(),
357    |lc| lc + c.get_variable() - a.get_variable(),
358  );
359  Ok(c)
360}