PSF with Perturbation Sampling #60

jnsiemer · 2025-08-15T16:48:55Z

Description
This PR implements...

a PSF with perturbation sampling according to MP12
relocates and renames the function compute_s to compute the short basis of G to short_basis_gadget and puts it into the gadget_classical file
adds benchmarks for the classical PSFs

Testing

I added basic working examples (possibly in doc-comment)

Checklist:

I have performed a self-review of my own code
- The code provides good readability and maintainability s.t. it fulfills best practices like talking code, modularity, ...
  - The chosen implementation is not more complex than it has to be
- My code should work as intended and no side effects occur (e.g. memory leaks)
- The doc comments fit our style guide
- I have credited related sources if needed

Marvin-Beckmann

looks good, just some minor comments and stuff that needs fixing

Marvin-Beckmann · 2025-08-28T12:24:04Z

src/primitive/psf/perturbation.rs

+    fn samp_d(&self) -> MatZ {
+        let m = &self.gp.n * &self.gp.k + &self.gp.m_bar;
+        MatZ::sample_d_common(&m, &self.gp.n, &self.s).unwrap()
+    }


The s here should be the s the same one coming from the preimage sampling. The preimage sampling however has a factor of s*r and not just s

Marvin-Beckmann · 2025-08-28T12:28:42Z

src/primitive/psf/perturbation.rs

+        // Sample perturbation p <- D_{ZZ^m, r * √Σ_p} - not correct for now. √Σ_p := as √Σ_2
+        let vec_p =
+            MatZ::sample_d_common_non_spherical(&self.gp.n, mat_sqrt_sigma_2, &self.r).unwrap();


What exactly do you mean with not correct?

This is an old comment - have removed that part / revised the comment

Marvin-Beckmann · 2025-08-28T12:38:39Z

src/primitive/psf/perturbation.rs

+        let sigma_2: MatQ = normalization_factor
+            * self.r.pow(2).unwrap()
+            * (&mat_sigma_p
+                - MatQ::identity(mat_sigma_p.get_num_rows(), mat_sigma_p.get_num_columns()));
+
+        // Compute √Σ_2
+        sigma_2.cholesky_decomposition_flint()


the factors of r and normalization can also be added after the cholesky decomposition is computed as a linear factor.
This should/could speedup the computation time/precision of the cholesky decomposition, right?

Yes, I've tried this out. It might increase precision, but it has a negative impact on performance as the cholesky_decomposition_flint uses f64 and thus, compresses the MatQ to some extend. If we multiply with any f64 or Q afterwards, that compression factor is becoming worse again. There might be a sweet spot between both, but I've chosen performance over precision for now

Marvin-Beckmann · 2025-08-28T12:54:22Z

src/primitive/psf/perturbation.rs

+    ///
+    /// let (a, td) = psf.trap_gen();
+    ///
+    /// let cov_mat = psf.s.pow(2).unwrap() * &psf.r * MatQ::identity(a.get_num_columns(), a.get_num_columns());


This should be r**2, right?

No, this is just a different covariance matrix with a different s. I've addressed it more explicitly now

Marvin-Beckmann · 2025-08-28T12:55:45Z

src/primitive/psf/perturbation.rs

+    ///
+    /// Parameters:
+    /// - `mat_r`: The trapdoor matrix `R`
+    /// - `mat_sigma`: The covariance matrix `Σ` to sample [`Self::samp_p`] with


you are referring to matrix as Sigma_2 in the description - maybe rename this to sigma_2 or sth similar so it is clear that they are the same

I've left it this way. Σ and Σ_p and Σ_2 are different matrices.
Σ is the covariance matrix as described.
We need Σ to compute Σ_p as described in Algorithm 3, MP12.
Last but not least, we pass Σ_p into Algorithm 1, Pei10, to sample the perturbation, which requires Σ_2, which needs to be computed from Σ_p. At the end, we only need to know sqrt of Σ_2 to perform Algorithm 3, MP12 out of those 3. Thus, we precompute Σ_2 from the covariance matrix Σ and store it

Marvin-Beckmann · 2025-08-28T13:01:45Z

src/primitive/psf/perturbation.rs

+/// - `short_basis_gadget`: The short basis of the corresponding gadget-matrix - just required to speed up the algorithm
+/// - `short_basis_gadget_gso`: The GSO of the short basis of the gadget-matrix - just required to speed up the algorithm
+///
+/// Returns a discrete Gaussian sampled preimage of `u` under `G` with Gaussian parameter `r * √(b^2 + 1)`.


what is b? Not necessarily clear from the documentation

Made it more explicit in the doc comment

Marvin-Beckmann · 2025-08-28T13:04:54Z

src/primitive/psf/perturbation.rs

The name of this file might not be enough to tell what it is related to. Maybe gpv_with_perturbation or gpv_perturbation or sth?

I've named it mp_perturbation now as it doesn't have anything to do with GPV anymore and it is already in the psf folder. So, people know what to expect.

Marvin-Beckmann · 2025-08-28T13:07:46Z

src/primitive/psf/perturbation.rs

+    /// - if Σ_2 is not positive definite.
+    pub fn compute_sqrt_sigma_2(&self, mat_r: &MatZ, mat_sigma: &MatQ) -> MatQ {
+        // Normalization factor according to MP12, Section 2.3
+        let normalization_factor = 1.0 / (2.0 * Q::PI);


this seems to be what was missing in my previous implementation attempt.

jnsiemer added 6 commits August 15, 2025 15:01

First draft

04b5c23

Update doc comments

b86e517

Remove memory-intensive behaviour

ebc4792

Relocate function

06d712c

Add benchmarks

654e896

Performance upgrade by keeping GSO of short basis of G

7d71f78

jnsiemer requested a review from Marvin-Beckmann August 15, 2025 16:48

jnsiemer self-assigned this Aug 15, 2025

Format

7dc0a40

Marvin-Beckmann approved these changes Aug 28, 2025

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jnsiemer merged commit 211bbd7 into dev Aug 29, 2025
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jnsiemer deleted the psf_perturbation branch August 29, 2025 12:00

PSF with Perturbation Sampling #60

PSF with Perturbation Sampling #60

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jnsiemer commented Aug 15, 2025

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