ark-r1cs-std/r1cs-std/src/bits/uint32.rs
r1cs-std/src/bits/uint32.rsRaw
1use algebra::{Field, FpParameters, PrimeField};
2
3use r1cs_core::{ConstraintSystem, LinearCombination, SynthesisError};
4
5use crate::{
6 boolean::{AllocatedBit, Boolean},
7 prelude::*,
8 Assignment, Vec,
9};
10
11/// Represents an interpretation of 32 `Boolean` objects as an
12/// unsigned integer.
13#[derive(Clone, Debug)]
14pub struct UInt32 {
15 // Least significant bit_gadget first
16 bits: Vec<Boolean>,
17 value: Option<u32>,
18}
19
20impl UInt32 {
21 /// Construct a constant `UInt32` from a `u32`
22 pub fn constant(value: u32) -> Self {
23 let mut bits = Vec::with_capacity(32);
24
25 let mut tmp = value;
26 for _ in 0..32 {
27 if tmp & 1 == 1 {
28 bits.push(Boolean::constant(true))
29 } else {
30 bits.push(Boolean::constant(false))
31 }
32
33 tmp >>= 1;
34 }
35
36 UInt32 {
37 bits,
38 value: Some(value),
39 }
40 }
41
42 /// Allocate a `UInt32` in the constraint system
43 pub fn alloc<ConstraintF, CS>(mut cs: CS, value: Option<u32>) -> Result<Self, SynthesisError>
44 where
45 ConstraintF: Field,
46 CS: ConstraintSystem<ConstraintF>,
47 {
48 let values = match value {
49 Some(mut val) => {
50 let mut v = Vec::with_capacity(32);
51
52 for _ in 0..32 {
53 v.push(Some(val & 1 == 1));
54 val >>= 1;
55 }
56
57 v
58 },
59 None => vec![None; 32],
60 };
61
62 let bits = values
63 .into_iter()
64 .enumerate()
65 .map(|(i, v)| {
66 Ok(Boolean::from(AllocatedBit::alloc(
67 cs.ns(|| format!("allocated bit_gadget {}", i)),
68 || v.get(),
69 )?))
70 })
71 .collect::<Result<Vec<_>, SynthesisError>>()?;
72
73 Ok(UInt32 { bits, value })
74 }
75
76 /// Turns this `UInt32` into its little-endian byte order representation.
77 pub fn to_bits_le(&self) -> Vec<Boolean> {
78 self.bits.clone()
79 }
80
81 /// Converts a little-endian byte order representation of bits into a
82 /// `UInt32`.
83 pub fn from_bits_le(bits: &[Boolean]) -> Self {
84 assert_eq!(bits.len(), 32);
85
86 let bits = bits.to_vec();
87
88 let mut value = Some(0u32);
89 for b in bits.iter().rev() {
90 value.as_mut().map(|v| *v <<= 1);
91
92 match b {
93 &Boolean::Constant(b) => {
94 if b {
95 value.as_mut().map(|v| *v |= 1);
96 }
97 },
98 &Boolean::Is(ref b) => match b.get_value() {
99 Some(true) => {
100 value.as_mut().map(|v| *v |= 1);
101 },
102 Some(false) => {},
103 None => value = None,
104 },
105 &Boolean::Not(ref b) => match b.get_value() {
106 Some(false) => {
107 value.as_mut().map(|v| *v |= 1);
108 },
109 Some(true) => {},
110 None => value = None,
111 },
112 }
113 }
114
115 Self { value, bits }
116 }
117
118 pub fn rotr(&self, by: usize) -> Self {
119 let by = by % 32;
120
121 let new_bits = self
122 .bits
123 .iter()
124 .skip(by)
125 .chain(self.bits.iter())
126 .take(32)
127 .cloned()
128 .collect();
129
130 UInt32 {
131 bits: new_bits,
132 value: self.value.map(|v| v.rotate_right(by as u32)),
133 }
134 }
135
136 /// XOR this `UInt32` with another `UInt32`
137 pub fn xor<ConstraintF, CS>(&self, mut cs: CS, other: &Self) -> Result<Self, SynthesisError>
138 where
139 ConstraintF: Field,
140 CS: ConstraintSystem<ConstraintF>,
141 {
142 let new_value = match (self.value, other.value) {
143 (Some(a), Some(b)) => Some(a ^ b),
144 _ => None,
145 };
146
147 let bits = self
148 .bits
149 .iter()
150 .zip(other.bits.iter())
151 .enumerate()
152 .map(|(i, (a, b))| Boolean::xor(cs.ns(|| format!("xor of bit_gadget {}", i)), a, b))
153 .collect::<Result<_, _>>()?;
154
155 Ok(UInt32 {
156 bits,
157 value: new_value,
158 })
159 }
160
161 /// Perform modular addition of several `UInt32` objects.
162 pub fn addmany<ConstraintF, CS>(mut cs: CS, operands: &[Self]) -> Result<Self, SynthesisError>
163 where
164 ConstraintF: PrimeField,
165 CS: ConstraintSystem<ConstraintF>,
166 {
167 // Make some arbitrary bounds for ourselves to avoid overflows
168 // in the scalar field
169 assert!(ConstraintF::Params::MODULUS_BITS >= 64);
170
171 assert!(operands.len() >= 1);
172 assert!(operands.len() <= 10);
173
174 if operands.len() == 1 {
175 return Ok(operands[0].clone());
176 }
177
178 // Compute the maximum value of the sum so we allocate enough bits for
179 // the result
180 let mut max_value = (operands.len() as u64) * u64::from(u32::max_value());
181
182 // Keep track of the resulting value
183 let mut result_value = Some(0u64);
184
185 // This is a linear combination that we will enforce to be "zero"
186 let mut lc = LinearCombination::zero();
187
188 let mut all_constants = true;
189
190 // Iterate over the operands
191 for op in operands {
192 // Accumulate the value
193 match op.value {
194 Some(val) => {
195 result_value.as_mut().map(|v| *v += u64::from(val));
196 },
197 None => {
198 // If any of our operands have unknown value, we won't
199 // know the value of the result
200 result_value = None;
201 },
202 }
203
204 // Iterate over each bit_gadget of the operand and add the operand to
205 // the linear combination
206 let mut coeff = ConstraintF::one();
207 for bit in &op.bits {
208 match *bit {
209 Boolean::Is(ref bit) => {
210 all_constants = false;
211
212 // Add coeff * bit_gadget
213 lc += (coeff, bit.get_variable());
214 },
215 Boolean::Not(ref bit) => {
216 all_constants = false;
217
218 // Add coeff * (1 - bit_gadget) = coeff * ONE - coeff * bit_gadget
219 lc = lc + (coeff, CS::one()) - (coeff, bit.get_variable());
220 },
221 Boolean::Constant(bit) => {
222 if bit {
223 lc += (coeff, CS::one());
224 }
225 },
226 }
227
228 coeff.double_in_place();
229 }
230 }
231
232 // The value of the actual result is modulo 2^32
233 let modular_value = result_value.map(|v| v as u32);
234
235 if all_constants && modular_value.is_some() {
236 // We can just return a constant, rather than
237 // unpacking the result into allocated bits.
238
239 return Ok(UInt32::constant(modular_value.unwrap()));
240 }
241
242 // Storage area for the resulting bits
243 let mut result_bits = vec![];
244
245 // Allocate each bit_gadget of the result
246 let mut coeff = ConstraintF::one();
247 let mut i = 0;
248 while max_value != 0 {
249 // Allocate the bit_gadget
250 let b = AllocatedBit::alloc(cs.ns(|| format!("result bit_gadget {}", i)), || {
251 result_value.map(|v| (v >> i) & 1 == 1).get()
252 })?;
253
254 // Subtract this bit_gadget from the linear combination to ensure the sums
255 // balance out
256 lc = lc - (coeff, b.get_variable());
257
258 result_bits.push(b.into());
259
260 max_value >>= 1;
261 i += 1;
262 coeff.double_in_place();
263 }
264
265 // Enforce that the linear combination equals zero
266 cs.enforce(|| "modular addition", |lc| lc, |lc| lc, |_| lc);
267
268 // Discard carry bits that we don't care about
269 result_bits.truncate(32);
270
271 Ok(UInt32 {
272 bits: result_bits,
273 value: modular_value,
274 })
275 }
276}
277
278impl<ConstraintF: Field> ToBytesGadget<ConstraintF> for UInt32 {
279 #[inline]
280 fn to_bytes<CS: ConstraintSystem<ConstraintF>>(
281 &self,
282 _cs: CS,
283 ) -> Result<Vec<UInt8>, SynthesisError> {
284 let value_chunks = match self.value.map(|val| {
285 use algebra::bytes::ToBytes;
286 let mut bytes = [0u8; 4];
287 val.write(bytes.as_mut()).unwrap();
288 bytes
289 }) {
290 Some(chunks) => [
291 Some(chunks[0]),
292 Some(chunks[1]),
293 Some(chunks[2]),
294 Some(chunks[3]),
295 ],
296 None => [None, None, None, None],
297 };
298 let mut bytes = Vec::new();
299 for (i, chunk8) in self.to_bits_le().chunks(8).enumerate() {
300 let byte = UInt8 {
301 bits: chunk8.to_vec(),
302 value: value_chunks[i],
303 };
304 bytes.push(byte);
305 }
306
307 Ok(bytes)
308 }
309
310 fn to_bytes_strict<CS: ConstraintSystem<ConstraintF>>(
311 &self,
312 cs: CS,
313 ) -> Result<Vec<UInt8>, SynthesisError> {
314 self.to_bytes(cs)
315 }
316}
317
318impl PartialEq for UInt32 {
319 fn eq(&self, other: &Self) -> bool {
320 self.value.is_some() && other.value.is_some() && self.value == other.value
321 }
322}
323
324impl Eq for UInt32 {}
325
326impl<ConstraintF: Field> ConditionalEqGadget<ConstraintF> for UInt32 {
327 fn conditional_enforce_equal<CS: ConstraintSystem<ConstraintF>>(
328 &self,
329 mut cs: CS,
330 other: &Self,
331 condition: &Boolean,
332 ) -> Result<(), SynthesisError> {
333 for (i, (a, b)) in self.bits.iter().zip(&other.bits).enumerate() {
334 a.conditional_enforce_equal(
335 &mut cs.ns(|| format!("uint32_equal_{}", i)),
336 b,
337 condition,
338 )?;
339 }
340 Ok(())
341 }
342
343 fn cost() -> usize {
344 32 * <Boolean as ConditionalEqGadget<ConstraintF>>::cost()
345 }
346}
347
348#[cfg(test)]
349mod test {
350 use super::UInt32;
351 use crate::{bits::boolean::Boolean, test_constraint_system::TestConstraintSystem, Vec};
352 use algebra::{bls12_381::Fr, One, Zero};
353 use r1cs_core::ConstraintSystem;
354 use rand::{Rng, SeedableRng};
355 use rand_xorshift::XorShiftRng;
356
357 #[test]
358 fn test_uint32_from_bits() {
359 let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
360
361 for _ in 0..1000 {
362 let v = (0..32)
363 .map(|_| Boolean::constant(rng.gen()))
364 .collect::<Vec<_>>();
365
366 let b = UInt32::from_bits_le(&v);
367
368 for (i, bit_gadget) in b.bits.iter().enumerate() {
369 match bit_gadget {
370 &Boolean::Constant(bit_gadget) => {
371 assert!(bit_gadget == ((b.value.unwrap() >> i) & 1 == 1));
372 },
373 _ => unreachable!(),
374 }
375 }
376
377 let expected_to_be_same = b.to_bits_le();
378
379 for x in v.iter().zip(expected_to_be_same.iter()) {
380 match x {
381 (&Boolean::Constant(true), &Boolean::Constant(true)) => {},
382 (&Boolean::Constant(false), &Boolean::Constant(false)) => {},
383 _ => unreachable!(),
384 }
385 }
386 }
387 }
388
389 #[test]
390 fn test_uint32_xor() {
391 let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
392
393 for _ in 0..1000 {
394 let mut cs = TestConstraintSystem::<Fr>::new();
395
396 let a: u32 = rng.gen();
397 let b: u32 = rng.gen();
398 let c: u32 = rng.gen();
399
400 let mut expected = a ^ b ^ c;
401
402 let a_bit = UInt32::alloc(cs.ns(|| "a_bit"), Some(a)).unwrap();
403 let b_bit = UInt32::constant(b);
404 let c_bit = UInt32::alloc(cs.ns(|| "c_bit"), Some(c)).unwrap();
405
406 let r = a_bit.xor(cs.ns(|| "first xor"), &b_bit).unwrap();
407 let r = r.xor(cs.ns(|| "second xor"), &c_bit).unwrap();
408
409 assert!(cs.is_satisfied());
410
411 assert!(r.value == Some(expected));
412
413 for b in r.bits.iter() {
414 match b {
415 &Boolean::Is(ref b) => {
416 assert!(b.get_value().unwrap() == (expected & 1 == 1));
417 },
418 &Boolean::Not(ref b) => {
419 assert!(!b.get_value().unwrap() == (expected & 1 == 1));
420 },
421 &Boolean::Constant(b) => {
422 assert!(b == (expected & 1 == 1));
423 },
424 }
425
426 expected >>= 1;
427 }
428 }
429 }
430
431 #[test]
432 fn test_uint32_addmany_constants() {
433 let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
434
435 for _ in 0..1000 {
436 let mut cs = TestConstraintSystem::<Fr>::new();
437
438 let a: u32 = rng.gen();
439 let b: u32 = rng.gen();
440 let c: u32 = rng.gen();
441
442 let a_bit = UInt32::constant(a);
443 let b_bit = UInt32::constant(b);
444 let c_bit = UInt32::constant(c);
445
446 let mut expected = a.wrapping_add(b).wrapping_add(c);
447
448 let r = UInt32::addmany(cs.ns(|| "addition"), &[a_bit, b_bit, c_bit]).unwrap();
449
450 assert!(r.value == Some(expected));
451
452 for b in r.bits.iter() {
453 match b {
454 &Boolean::Is(_) => panic!(),
455 &Boolean::Not(_) => panic!(),
456 &Boolean::Constant(b) => {
457 assert!(b == (expected & 1 == 1));
458 },
459 }
460
461 expected >>= 1;
462 }
463 }
464 }
465
466 #[test]
467 fn test_uint32_addmany() {
468 let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
469
470 for _ in 0..1000 {
471 let mut cs = TestConstraintSystem::<Fr>::new();
472
473 let a: u32 = rng.gen();
474 let b: u32 = rng.gen();
475 let c: u32 = rng.gen();
476 let d: u32 = rng.gen();
477
478 let mut expected = (a ^ b).wrapping_add(c).wrapping_add(d);
479
480 let a_bit = UInt32::alloc(cs.ns(|| "a_bit"), Some(a)).unwrap();
481 let b_bit = UInt32::constant(b);
482 let c_bit = UInt32::constant(c);
483 let d_bit = UInt32::alloc(cs.ns(|| "d_bit"), Some(d)).unwrap();
484
485 let r = a_bit.xor(cs.ns(|| "xor"), &b_bit).unwrap();
486 let r = UInt32::addmany(cs.ns(|| "addition"), &[r, c_bit, d_bit]).unwrap();
487
488 assert!(cs.is_satisfied());
489
490 assert!(r.value == Some(expected));
491
492 for b in r.bits.iter() {
493 match b {
494 &Boolean::Is(ref b) => {
495 assert!(b.get_value().unwrap() == (expected & 1 == 1));
496 },
497 &Boolean::Not(ref b) => {
498 assert!(!b.get_value().unwrap() == (expected & 1 == 1));
499 },
500 &Boolean::Constant(_) => unreachable!(),
501 }
502
503 expected >>= 1;
504 }
505
506 // Flip a bit_gadget and see if the addition constraint still works
507 if cs.get("addition/result bit_gadget 0/boolean").is_zero() {
508 cs.set("addition/result bit_gadget 0/boolean", Fr::one());
509 } else {
510 cs.set("addition/result bit_gadget 0/boolean", Fr::zero());
511 }
512
513 assert!(!cs.is_satisfied());
514 }
515 }
516
517 #[test]
518 fn test_uint32_rotr() {
519 let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
520
521 let mut num = rng.gen();
522
523 let a = UInt32::constant(num);
524
525 for i in 0..32 {
526 let b = a.rotr(i);
527
528 assert!(b.value.unwrap() == num);
529
530 let mut tmp = num;
531 for b in &b.bits {
532 match b {
533 &Boolean::Constant(b) => {
534 assert_eq!(b, tmp & 1 == 1);
535 },
536 _ => unreachable!(),
537 }
538
539 tmp >>= 1;
540 }
541
542 num = num.rotate_right(1);
543 }
544 }
545}