1use base2k::{
  2    Decoding, Encoding, FFT64, FillUniform, Module, ScalarZnx, ScalarZnxAlloc, ScratchOwned, Stats, VecZnxOps, VecZnxToMut,
  3    ZnxViewMut, ZnxZero,
  4};
  5use itertools::izip;
  6use sampling::source::Source;
  7
  8use crate::{
  9    elem::Infos,
 10    ggsw_ciphertext::GGSWCiphertext,
 11    glwe_ciphertext::GLWECiphertext,
 12    glwe_ciphertext_fourier::GLWECiphertextFourier,
 13    glwe_plaintext::GLWEPlaintext,
 14    keys::{GLWEPublicKey, SecretKey, SecretKeyFourier},
 15    keyswitch_key::GLWESwitchingKey,
 16    test_fft64::{gglwe::noise_gglwe_product, ggsw::noise_ggsw_product},
 17};
 18
 19#[test]
 20fn encrypt_sk() {
 21    (1..4).for_each(|rank| {
 22        println!("test encrypt_sk rank: {}", rank);
 23        test_encrypt_sk(11, 8, 54, 30, 3.2, rank);
 24    });
 25}
 26
 27#[test]
 28fn encrypt_zero_sk() {
 29    (1..4).for_each(|rank| {
 30        println!("test encrypt_zero_sk rank: {}", rank);
 31        test_encrypt_zero_sk(11, 8, 64, 3.2, rank);
 32    });
 33}
 34
 35#[test]
 36fn encrypt_pk() {
 37    (1..4).for_each(|rank| {
 38        println!("test encrypt_pk rank: {}", rank);
 39        test_encrypt_pk(11, 8, 64, 64, 3.2, rank)
 40    });
 41}
 42
 43#[test]
 44fn keyswitch() {
 45    (1..4).for_each(|rank_in| {
 46        (1..4).for_each(|rank_out| {
 47            println!("test keyswitch rank_in: {} rank_out: {}", rank_in, rank_out);
 48            test_keyswitch(12, 12, 60, 45, 60, rank_in, rank_out, 3.2);
 49        });
 50    });
 51}
 52
 53#[test]
 54fn keyswitch_inplace() {
 55    (1..4).for_each(|rank| {
 56        println!("test keyswitch_inplace rank: {}", rank);
 57        test_keyswitch_inplace(12, 12, 60, 45, rank, 3.2);
 58    });
 59}
 60
 61#[test]
 62fn external_product() {
 63    (1..4).for_each(|rank| {
 64        println!("test external_product rank: {}", rank);
 65        test_external_product(12, 12, 60, 45, 60, rank, 3.2);
 66    });
 67}
 68
 69#[test]
 70fn external_product_inplace() {
 71    (1..4).for_each(|rank| {
 72        println!("test external_product rank: {}", rank);
 73        test_external_product_inplace(12, 15, 60, 60, rank, 3.2);
 74    });
 75}
 76
 77fn test_encrypt_sk(log_n: usize, basek: usize, k_ct: usize, k_pt: usize, sigma: f64, rank: usize) {
 78    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
 79
 80    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, k_ct, rank);
 81    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, k_pt);
 82
 83    let mut source_xs: Source = Source::new([0u8; 32]);
 84    let mut source_xe: Source = Source::new([0u8; 32]);
 85    let mut source_xa: Source = Source::new([0u8; 32]);
 86
 87    let mut scratch: ScratchOwned = ScratchOwned::new(
 88        GLWECiphertext::encrypt_sk_scratch_space(&module, ct.size()) | GLWECiphertext::decrypt_scratch_space(&module, ct.size()),
 89    );
 90
 91    let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module, rank);
 92    sk.fill_ternary_prob(0.5, &mut source_xs);
 93
 94    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module, rank);
 95    sk_dft.dft(&module, &sk);
 96
 97    let mut data_want: Vec<i64> = vec![0i64; module.n()];
 98
 99    data_want
100        .iter_mut()
101        .for_each(|x| *x = source_xa.next_i64() & 0xFF);
102
103    pt.data.encode_vec_i64(0, basek, k_pt, &data_want, 10);
104
105    ct.encrypt_sk(
106        &module,
107        &pt,
108        &sk_dft,
109        &mut source_xa,
110        &mut source_xe,
111        sigma,
112        scratch.borrow(),
113    );
114
115    pt.data.zero();
116
117    ct.decrypt(&module, &mut pt, &sk_dft, scratch.borrow());
118
119    let mut data_have: Vec<i64> = vec![0i64; module.n()];
120
121    pt.data
122        .decode_vec_i64(0, basek, pt.size() * basek, &mut data_have);
123
124    // TODO: properly assert the decryption noise through std(dec(ct) - pt)
125    let scale: f64 = (1 << (pt.size() * basek - k_pt)) as f64;
126    izip!(data_want.iter(), data_have.iter()).for_each(|(a, b)| {
127        let b_scaled = (*b as f64) / scale;
128        assert!(
129            (*a as f64 - b_scaled).abs() < 0.1,
130            "{} {}",
131            *a as f64,
132            b_scaled
133        )
134    });
135}
136
137fn test_encrypt_zero_sk(log_n: usize, basek: usize, k_ct: usize, sigma: f64, rank: usize) {
138    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
139
140    let mut pt: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, k_ct);
141
142    let mut source_xs: Source = Source::new([0u8; 32]);
143    let mut source_xe: Source = Source::new([1u8; 32]);
144    let mut source_xa: Source = Source::new([0u8; 32]);
145
146    let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module, rank);
147    sk.fill_ternary_prob(0.5, &mut source_xs);
148    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module, rank);
149    sk_dft.dft(&module, &sk);
150
151    let mut ct_dft: GLWECiphertextFourier<Vec<u8>, FFT64> = GLWECiphertextFourier::new(&module, basek, k_ct, rank);
152
153    let mut scratch: ScratchOwned = ScratchOwned::new(
154        GLWECiphertextFourier::decrypt_scratch_space(&module, ct_dft.size())
155            | GLWECiphertextFourier::encrypt_sk_scratch_space(&module, rank, ct_dft.size()),
156    );
157
158    ct_dft.encrypt_zero_sk(
159        &module,
160        &sk_dft,
161        &mut source_xa,
162        &mut source_xe,
163        sigma,
164        scratch.borrow(),
165    );
166    ct_dft.decrypt(&module, &mut pt, &sk_dft, scratch.borrow());
167
168    assert!((sigma - pt.data.std(0, basek) * (k_ct as f64).exp2()) <= 0.2);
169}
170
171fn test_encrypt_pk(log_n: usize, basek: usize, k_ct: usize, k_pk: usize, sigma: f64, rank: usize) {
172    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
173
174    let mut ct: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, k_ct, rank);
175    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, k_ct);
176
177    let mut source_xs: Source = Source::new([0u8; 32]);
178    let mut source_xe: Source = Source::new([0u8; 32]);
179    let mut source_xa: Source = Source::new([0u8; 32]);
180    let mut source_xu: Source = Source::new([0u8; 32]);
181
182    let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module, rank);
183    sk.fill_ternary_prob(0.5, &mut source_xs);
184    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module, rank);
185    sk_dft.dft(&module, &sk);
186
187    let mut pk: GLWEPublicKey<Vec<u8>, FFT64> = GLWEPublicKey::new(&module, basek, k_pk, rank);
188    pk.generate(&module, &sk_dft, &mut source_xa, &mut source_xe, sigma);
189
190    let mut scratch: ScratchOwned = ScratchOwned::new(
191        GLWECiphertext::encrypt_sk_scratch_space(&module, ct.size())
192            | GLWECiphertext::decrypt_scratch_space(&module, ct.size())
193            | GLWECiphertext::encrypt_pk_scratch_space(&module, pk.size()),
194    );
195
196    let mut data_want: Vec<i64> = vec![0i64; module.n()];
197
198    data_want
199        .iter_mut()
200        .for_each(|x| *x = source_xa.next_i64() & 0);
201
202    pt_want.data.encode_vec_i64(0, basek, k_ct, &data_want, 10);
203
204    ct.encrypt_pk(
205        &module,
206        &pt_want,
207        &pk,
208        &mut source_xu,
209        &mut source_xe,
210        sigma,
211        scratch.borrow(),
212    );
213
214    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, k_ct);
215
216    ct.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
217
218    module.vec_znx_sub_ab_inplace(&mut pt_want, 0, &pt_have, 0);
219
220    let noise_have: f64 = pt_want.data.std(0, basek).log2();
221    let noise_want: f64 = ((((rank as f64) + 1.0) * module.n() as f64 * 0.5 * sigma * sigma).sqrt()).log2() - (k_ct as f64);
222
223    assert!(
224        (noise_have - noise_want).abs() < 0.2,
225        "{} {}",
226        noise_have,
227        noise_want
228    );
229}
230
231fn test_keyswitch(
232    log_n: usize,
233    basek: usize,
234    k_keyswitch: usize,
235    k_ct_in: usize,
236    k_ct_out: usize,
237    rank_in: usize,
238    rank_out: usize,
239    sigma: f64,
240) {
241    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
242    let rows: usize = (k_ct_in + basek - 1) / basek;
243
244    let mut ksk: GLWESwitchingKey<Vec<u8>, FFT64> = GLWESwitchingKey::new(&module, basek, k_keyswitch, rows, rank_in, rank_out);
245    let mut ct_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, k_ct_in, rank_in);
246    let mut ct_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, k_ct_out, rank_out);
247    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, k_ct_in);
248    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, k_ct_out);
249
250    let mut source_xs: Source = Source::new([0u8; 32]);
251    let mut source_xe: Source = Source::new([0u8; 32]);
252    let mut source_xa: Source = Source::new([0u8; 32]);
253
254    // Random input plaintext
255    pt_want
256        .data
257        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
258
259    let mut scratch: ScratchOwned = ScratchOwned::new(
260        GLWESwitchingKey::encrypt_sk_scratch_space(&module, rank_in, ksk.size())
261            | GLWECiphertext::decrypt_scratch_space(&module, ct_out.size())
262            | GLWECiphertext::encrypt_sk_scratch_space(&module, ct_in.size())
263            | GLWECiphertext::keyswitch_scratch_space(
264                &module,
265                ct_out.size(),
266                rank_out,
267                ct_in.size(),
268                rank_in,
269                ksk.size(),
270            ),
271    );
272
273    let mut sk_in: SecretKey<Vec<u8>> = SecretKey::new(&module, rank_in);
274    sk_in.fill_ternary_prob(0.5, &mut source_xs);
275
276    let mut sk_in_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module, rank_in);
277    sk_in_dft.dft(&module, &sk_in);
278
279    let mut sk_out: SecretKey<Vec<u8>> = SecretKey::new(&module, rank_out);
280    sk_out.fill_ternary_prob(0.5, &mut source_xs);
281
282    let mut sk_out_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module, rank_out);
283    sk_out_dft.dft(&module, &sk_out);
284
285    ksk.encrypt_sk(
286        &module,
287        &sk_in,
288        &sk_out_dft,
289        &mut source_xa,
290        &mut source_xe,
291        sigma,
292        scratch.borrow(),
293    );
294
295    ct_in.encrypt_sk(
296        &module,
297        &pt_want,
298        &sk_in_dft,
299        &mut source_xa,
300        &mut source_xe,
301        sigma,
302        scratch.borrow(),
303    );
304
305    ct_out.keyswitch(&module, &ct_in, &ksk, scratch.borrow());
306
307    ct_out.decrypt(&module, &mut pt_have, &sk_out_dft, scratch.borrow());
308
309    module.vec_znx_sub_ab_inplace(&mut pt_have, 0, &pt_want, 0);
310
311    let noise_have: f64 = pt_have.data.std(0, basek).log2();
312    let noise_want: f64 = noise_gglwe_product(
313        module.n() as f64,
314        basek,
315        0.5,
316        0.5,
317        0f64,
318        sigma * sigma,
319        0f64,
320        rank_in as f64,
321        k_ct_in,
322        k_keyswitch,
323    );
324
325    assert!(
326        (noise_have - noise_want).abs() <= 0.1,
327        "{} {}",
328        noise_have,
329        noise_want
330    );
331}
332
333fn test_keyswitch_inplace(log_n: usize, basek: usize, k_ksk: usize, k_ct: usize, rank: usize, sigma: f64) {
334    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
335    let rows: usize = (k_ct + basek - 1) / basek;
336
337    let mut ct_grlwe: GLWESwitchingKey<Vec<u8>, FFT64> = GLWESwitchingKey::new(&module, basek, k_ksk, rows, rank, rank);
338    let mut ct_rlwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, k_ct, rank);
339    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, k_ct);
340    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, k_ct);
341
342    let mut source_xs: Source = Source::new([0u8; 32]);
343    let mut source_xe: Source = Source::new([0u8; 32]);
344    let mut source_xa: Source = Source::new([0u8; 32]);
345
346    // Random input plaintext
347    pt_want
348        .data
349        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
350
351    let mut scratch: ScratchOwned = ScratchOwned::new(
352        GLWESwitchingKey::encrypt_sk_scratch_space(&module, rank, ct_grlwe.size())
353            | GLWECiphertext::decrypt_scratch_space(&module, ct_rlwe.size())
354            | GLWECiphertext::encrypt_sk_scratch_space(&module, ct_rlwe.size())
355            | GLWECiphertext::keyswitch_inplace_scratch_space(&module, ct_rlwe.size(), rank, ct_grlwe.size()),
356    );
357
358    let mut sk0: SecretKey<Vec<u8>> = SecretKey::new(&module, rank);
359    sk0.fill_ternary_prob(0.5, &mut source_xs);
360
361    let mut sk0_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module, rank);
362    sk0_dft.dft(&module, &sk0);
363
364    let mut sk1: SecretKey<Vec<u8>> = SecretKey::new(&module, rank);
365    sk1.fill_ternary_prob(0.5, &mut source_xs);
366
367    let mut sk1_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module, rank);
368    sk1_dft.dft(&module, &sk1);
369
370    ct_grlwe.encrypt_sk(
371        &module,
372        &sk0,
373        &sk1_dft,
374        &mut source_xa,
375        &mut source_xe,
376        sigma,
377        scratch.borrow(),
378    );
379
380    ct_rlwe.encrypt_sk(
381        &module,
382        &pt_want,
383        &sk0_dft,
384        &mut source_xa,
385        &mut source_xe,
386        sigma,
387        scratch.borrow(),
388    );
389
390    ct_rlwe.keyswitch_inplace(&module, &ct_grlwe, scratch.borrow());
391
392    ct_rlwe.decrypt(&module, &mut pt_have, &sk1_dft, scratch.borrow());
393
394    module.vec_znx_sub_ab_inplace(&mut pt_have, 0, &pt_want, 0);
395
396    let noise_have: f64 = pt_have.data.std(0, basek).log2();
397    let noise_want: f64 = noise_gglwe_product(
398        module.n() as f64,
399        basek,
400        0.5,
401        0.5,
402        0f64,
403        sigma * sigma,
404        0f64,
405        rank as f64,
406        k_ct,
407        k_ksk,
408    );
409
410    assert!(
411        (noise_have - noise_want).abs() <= 0.1,
412        "{} {}",
413        noise_have,
414        noise_want
415    );
416}
417
418fn test_external_product(log_n: usize, basek: usize, k_ggsw: usize, k_ct_in: usize, k_ct_out: usize, rank: usize, sigma: f64) {
419    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
420
421    let rows: usize = (k_ct_in + basek - 1) / basek;
422
423    let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, basek, k_ggsw, rows, rank);
424    let mut ct_rlwe_in: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, k_ct_in, rank);
425    let mut ct_rlwe_out: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, k_ct_out, rank);
426    let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
427    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, k_ct_in);
428    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, k_ct_out);
429
430    let mut source_xs: Source = Source::new([0u8; 32]);
431    let mut source_xe: Source = Source::new([0u8; 32]);
432    let mut source_xa: Source = Source::new([0u8; 32]);
433
434    // Random input plaintext
435    pt_want
436        .data
437        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
438
439    pt_want.to_mut().at_mut(0, 0)[1] = 1;
440
441    let k: usize = 1;
442
443    pt_rgsw.raw_mut()[k] = 1; // X^{k}
444
445    let mut scratch: ScratchOwned = ScratchOwned::new(
446        GGSWCiphertext::encrypt_sk_scratch_space(&module, rank, ct_rgsw.size())
447            | GLWECiphertext::decrypt_scratch_space(&module, ct_rlwe_out.size())
448            | GLWECiphertext::encrypt_sk_scratch_space(&module, ct_rlwe_in.size())
449            | GLWECiphertext::external_product_scratch_space(
450                &module,
451                ct_rlwe_out.size(),
452                ct_rlwe_in.size(),
453                ct_rgsw.size(),
454                rank,
455            ),
456    );
457
458    let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module, rank);
459    sk.fill_ternary_prob(0.5, &mut source_xs);
460
461    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module, rank);
462    sk_dft.dft(&module, &sk);
463
464    ct_rgsw.encrypt_sk(
465        &module,
466        &pt_rgsw,
467        &sk_dft,
468        &mut source_xa,
469        &mut source_xe,
470        sigma,
471        scratch.borrow(),
472    );
473
474    ct_rlwe_in.encrypt_sk(
475        &module,
476        &pt_want,
477        &sk_dft,
478        &mut source_xa,
479        &mut source_xe,
480        sigma,
481        scratch.borrow(),
482    );
483
484    ct_rlwe_out.external_product(&module, &ct_rlwe_in, &ct_rgsw, scratch.borrow());
485
486    ct_rlwe_out.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
487
488    module.vec_znx_rotate_inplace(k as i64, &mut pt_want, 0);
489
490    module.vec_znx_sub_ab_inplace(&mut pt_have, 0, &pt_want, 0);
491
492    let noise_have: f64 = pt_have.data.std(0, basek).log2();
493
494    let var_gct_err_lhs: f64 = sigma * sigma;
495    let var_gct_err_rhs: f64 = 0f64;
496
497    let var_msg: f64 = 1f64 / module.n() as f64; // X^{k}
498    let var_a0_err: f64 = sigma * sigma;
499    let var_a1_err: f64 = 1f64 / 12f64;
500
501    let noise_want: f64 = noise_ggsw_product(
502        module.n() as f64,
503        basek,
504        0.5,
505        var_msg,
506        var_a0_err,
507        var_a1_err,
508        var_gct_err_lhs,
509        var_gct_err_rhs,
510        rank as f64,
511        k_ct_in,
512        k_ggsw,
513    );
514
515    assert!(
516        (noise_have - noise_want).abs() <= 0.1,
517        "{} {}",
518        noise_have,
519        noise_want
520    );
521}
522
523fn test_external_product_inplace(log_n: usize, basek: usize, k_ggsw: usize, k_ct: usize, rank: usize, sigma: f64) {
524    let module: Module<FFT64> = Module::<FFT64>::new(1 << log_n);
525    let rows: usize = (k_ct + basek - 1) / basek;
526
527    let mut ct_rgsw: GGSWCiphertext<Vec<u8>, FFT64> = GGSWCiphertext::new(&module, basek, k_ggsw, rows, rank);
528    let mut ct_rlwe: GLWECiphertext<Vec<u8>> = GLWECiphertext::new(&module, basek, k_ct, rank);
529    let mut pt_rgsw: ScalarZnx<Vec<u8>> = module.new_scalar_znx(1);
530    let mut pt_want: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, k_ct);
531    let mut pt_have: GLWEPlaintext<Vec<u8>> = GLWEPlaintext::new(&module, basek, k_ct);
532
533    let mut source_xs: Source = Source::new([0u8; 32]);
534    let mut source_xe: Source = Source::new([0u8; 32]);
535    let mut source_xa: Source = Source::new([0u8; 32]);
536
537    // Random input plaintext
538    pt_want
539        .data
540        .fill_uniform(basek, 0, pt_want.size(), &mut source_xa);
541
542    pt_want.to_mut().at_mut(0, 0)[1] = 1;
543
544    let k: usize = 1;
545
546    pt_rgsw.raw_mut()[k] = 1; // X^{k}
547
548    let mut scratch: ScratchOwned = ScratchOwned::new(
549        GGSWCiphertext::encrypt_sk_scratch_space(&module, rank, ct_rgsw.size())
550            | GLWECiphertext::decrypt_scratch_space(&module, ct_rlwe.size())
551            | GLWECiphertext::encrypt_sk_scratch_space(&module, ct_rlwe.size())
552            | GLWECiphertext::external_product_inplace_scratch_space(&module, ct_rlwe.size(), ct_rgsw.size(), rank),
553    );
554
555    let mut sk: SecretKey<Vec<u8>> = SecretKey::new(&module, rank);
556    sk.fill_ternary_prob(0.5, &mut source_xs);
557
558    let mut sk_dft: SecretKeyFourier<Vec<u8>, FFT64> = SecretKeyFourier::new(&module, rank);
559    sk_dft.dft(&module, &sk);
560
561    ct_rgsw.encrypt_sk(
562        &module,
563        &pt_rgsw,
564        &sk_dft,
565        &mut source_xa,
566        &mut source_xe,
567        sigma,
568        scratch.borrow(),
569    );
570
571    ct_rlwe.encrypt_sk(
572        &module,
573        &pt_want,
574        &sk_dft,
575        &mut source_xa,
576        &mut source_xe,
577        sigma,
578        scratch.borrow(),
579    );
580
581    ct_rlwe.external_product_inplace(&module, &ct_rgsw, scratch.borrow());
582
583    ct_rlwe.decrypt(&module, &mut pt_have, &sk_dft, scratch.borrow());
584
585    module.vec_znx_rotate_inplace(k as i64, &mut pt_want, 0);
586
587    module.vec_znx_sub_ab_inplace(&mut pt_have, 0, &pt_want, 0);
588
589    let noise_have: f64 = pt_have.data.std(0, basek).log2();
590
591    let var_gct_err_lhs: f64 = sigma * sigma;
592    let var_gct_err_rhs: f64 = 0f64;
593
594    let var_msg: f64 = 1f64 / module.n() as f64; // X^{k}
595    let var_a0_err: f64 = sigma * sigma;
596    let var_a1_err: f64 = 1f64 / 12f64;
597
598    let noise_want: f64 = noise_ggsw_product(
599        module.n() as f64,
600        basek,
601        0.5,
602        var_msg,
603        var_a0_err,
604        var_a1_err,
605        var_gct_err_lhs,
606        var_gct_err_rhs,
607        rank as f64,
608        k_ct,
609        k_ggsw,
610    );
611
612    assert!(
613        (noise_have - noise_want).abs() <= 0.1,
614        "{} {}",
615        noise_have,
616        noise_want
617    );
618}