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Add Double Decomposition (bivariate representation) infrastructure
Implement foundational support for the Double Decomposition technique from "Revisiting Key Decomposition Techniques for FHE" (ePrint 2023/771). Changes: - Add auxiliary decomposition parameters (l̅, l̅ₐ, B̅gbit, B̅gₐbit) to all parameter structs with trivial default values (l̅=1, B̅g=2^digits) - Update TRGSW type definitions to use k*lₐ*l̅ₐ + l*l̅ row structure - Add h̅gen() and nonceh̅gen() for auxiliary h value generation - Modify trgswhadd, halftrgswhadd, trgswhoneadd for double decomposition - Update ApplyFFT2trgsw, ApplyNTT2trgsw, ApplyRAINTT2trgsw loop bounds With trivial values, behavior is unchanged (h̅[0]=1, sizes identical). 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
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5 files changed

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‎include/params.hpp‎

Lines changed: 6 additions & 6 deletions
Original file line numberDiff line numberDiff line change
@@ -138,17 +138,17 @@ template <class P>
138138
using TRLWERAINTT = std::array<PolynomialRAINTT<P>, P::k + 1>;
139139

140140
template <class P>
141-
using TRGSW = std::array<TRLWE<P>, P::k * P::lₐ + P::l>;
141+
using TRGSW = std::array<TRLWE<P>, P::k * P::lₐ * P::l̅ₐ + P::l * P::l̅>;
142142
template <class P>
143-
using HalfTRGSW = std::array<TRLWE<P>, P::l>;
143+
using HalfTRGSW = std::array<TRLWE<P>, P::l * P::l̅>;
144144
template <class P>
145-
using TRGSWFFT = aligned_array<TRLWEInFD<P>, P::k * P::lₐ + P::l>;
145+
using TRGSWFFT = aligned_array<TRLWEInFD<P>, P::k * P::lₐ * P::l̅ₐ + P::l * P::l̅>;
146146
template <class P>
147-
using HalfTRGSWFFT = aligned_array<TRLWEInFD<P>, P::l>;
147+
using HalfTRGSWFFT = aligned_array<TRLWEInFD<P>, P::l * P::l̅>;
148148
template <class P>
149-
using TRGSWNTT = std::array<TRLWENTT<P>, P::k * P::lₐ + P::l>;
149+
using TRGSWNTT = std::array<TRLWENTT<P>, P::k * P::lₐ * P::l̅ₐ + P::l * P::l̅>;
150150
template <class P>
151-
using TRGSWRAINTT = std::array<TRLWERAINTT<P>, P::k * P::lₐ + P::l>;
151+
using TRGSWRAINTT = std::array<TRLWERAINTT<P>, P::k * P::lₐ * P::l̅ₐ + P::l * P::l̅>;
152152

153153
#ifdef USE_KEY_BUNDLE
154154
template <class P>

‎include/params/128bit.hpp‎

Lines changed: 31 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -62,6 +62,13 @@ struct lvl1param {
6262
static constexpr double Δ =
6363
static_cast<double>(1ULL << std::numeric_limits<T>::digits) /
6464
plain_modulus;
65+
// Double Decomposition (bivariate representation) parameters
66+
// For now, set to trivial values (no actual second decomposition)
67+
static constexpr std::uint32_t l̅ = 1; // auxiliary decomposition levels
68+
static constexpr std::uint32_t l̅ₐ = l̅;
69+
static constexpr std::uint32_t B̅gbit =
70+
std::numeric_limits<T>::digits; // full coefficient width
71+
static constexpr std::uint32_t B̅gₐbit = B̅gbit;
6572
};
6673

6774
struct AHlvl1param {
@@ -83,6 +90,11 @@ struct AHlvl1param {
8390
static constexpr std::make_signed_t<T> μ = baseP::μ;
8491
static constexpr uint32_t plain_modulus = baseP::plain_modulus;
8592
static constexpr double Δ = baseP::Δ;
93+
// Double Decomposition parameters inherited from baseP
94+
static constexpr std::uint32_t l̅ = baseP::l̅;
95+
static constexpr std::uint32_t l̅ₐ = baseP::l̅ₐ;
96+
static constexpr std::uint32_t B̅gbit = baseP::B̅gbit;
97+
static constexpr std::uint32_t B̅gₐbit = baseP::B̅gₐbit;
8698
};
8799

88100
struct lvl2param {
@@ -106,6 +118,13 @@ struct lvl2param {
106118
static constexpr uint32_t plain_modulus = 8;
107119
static constexpr double Δ =
108120
static_cast<double>(1ULL << (std::numeric_limits<T>::digits - 4));
121+
// Double Decomposition (bivariate representation) parameters
122+
// For now, set to trivial values (no actual second decomposition)
123+
static constexpr std::uint32_t l̅ = 1; // auxiliary decomposition levels
124+
static constexpr std::uint32_t l̅ₐ = l̅;
125+
static constexpr std::uint32_t B̅gbit =
126+
std::numeric_limits<T>::digits; // full coefficient width
127+
static constexpr std::uint32_t B̅gₐbit = B̅gbit;
109128
};
110129

111130
struct AHlvl2param {
@@ -127,6 +146,11 @@ struct AHlvl2param {
127146
static constexpr std::make_signed_t<T> μ = baseP::μ;
128147
static constexpr uint32_t plain_modulus = baseP::plain_modulus;
129148
static constexpr double Δ = baseP::Δ;
149+
// Double Decomposition parameters inherited from baseP
150+
static constexpr std::uint32_t l̅ = baseP::l̅;
151+
static constexpr std::uint32_t l̅ₐ = baseP::l̅ₐ;
152+
static constexpr std::uint32_t B̅gbit = baseP::B̅gbit;
153+
static constexpr std::uint32_t B̅gₐbit = baseP::B̅gₐbit;
130154
};
131155

132156
struct lvl3param {
@@ -150,6 +174,13 @@ struct lvl3param {
150174
static constexpr uint32_t plain_modulusbit = 31;
151175
static constexpr uint64_t plain_modulus = 1ULL << plain_modulusbit;
152176
static constexpr double Δ = 1ULL << (64 - plain_modulusbit - 1);
177+
// Double Decomposition (bivariate representation) parameters
178+
// For now, set to trivial values (no actual second decomposition)
179+
static constexpr std::uint32_t l̅ = 1; // auxiliary decomposition levels
180+
static constexpr std::uint32_t l̅ₐ = l̅;
181+
static constexpr std::uint32_t B̅gbit =
182+
std::numeric_limits<T>::digits; // full coefficient width
183+
static constexpr std::uint32_t B̅gₐbit = B̅gbit;
153184
};
154185

155186
// Key Switching parameters

‎include/params/CGGI16.hpp‎

Lines changed: 21 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -59,6 +59,13 @@ struct lvl1param {
5959
static constexpr double Δ =
6060
static_cast<double>(1ULL << std::numeric_limits<T>::digits) /
6161
plain_modulus;
62+
// Double Decomposition (bivariate representation) parameters
63+
// For now, set to trivial values (no actual second decomposition)
64+
static constexpr std::uint32_t l̅ = 1; // auxiliary decomposition levels
65+
static constexpr std::uint32_t l̅ₐ = l̅;
66+
static constexpr std::uint32_t B̅gbit =
67+
std::numeric_limits<T>::digits; // full coefficient width
68+
static constexpr std::uint32_t B̅gₐbit = B̅gbit;
6269
};
6370

6471
struct lvl2param {
@@ -80,6 +87,13 @@ struct lvl2param {
8087
static constexpr T μ = 1ULL << 61;
8188
static constexpr uint32_t plain_modulus = 8;
8289
static constexpr double Δ = μ;
90+
// Double Decomposition (bivariate representation) parameters
91+
// For now, set to trivial values (no actual second decomposition)
92+
static constexpr std::uint32_t l̅ = 1; // auxiliary decomposition levels
93+
static constexpr std::uint32_t l̅ₐ = l̅;
94+
static constexpr std::uint32_t B̅gbit =
95+
std::numeric_limits<T>::digits; // full coefficient width
96+
static constexpr std::uint32_t B̅gₐbit = B̅gbit;
8397
};
8498

8599
// Dummy
@@ -104,6 +118,13 @@ struct lvl3param {
104118
static constexpr uint32_t plain_modulusbit = 31;
105119
static constexpr uint64_t plain_modulus = 1ULL << plain_modulusbit;
106120
static constexpr double Δ = 1ULL << (64 - plain_modulusbit - 1);
121+
// Double Decomposition (bivariate representation) parameters
122+
// For now, set to trivial values (no actual second decomposition)
123+
static constexpr std::uint32_t l̅ = 1; // auxiliary decomposition levels
124+
static constexpr std::uint32_t l̅ₐ = l̅;
125+
static constexpr std::uint32_t B̅gbit =
126+
std::numeric_limits<T>::digits; // full coefficient width
127+
static constexpr std::uint32_t B̅gₐbit = B̅gbit;
107128
};
108129

109130
struct lvl10param {

‎include/params/CGGI19.hpp‎

Lines changed: 21 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -59,6 +59,13 @@ struct lvl1param {
5959
static constexpr double Δ =
6060
static_cast<double>(1ULL << std::numeric_limits<T>::digits) /
6161
plain_modulus;
62+
// Double Decomposition (bivariate representation) parameters
63+
// For now, set to trivial values (no actual second decomposition)
64+
static constexpr std::uint32_t l̅ = 1; // auxiliary decomposition levels
65+
static constexpr std::uint32_t l̅ₐ = l̅;
66+
static constexpr std::uint32_t B̅gbit =
67+
std::numeric_limits<T>::digits; // full coefficient width
68+
static constexpr std::uint32_t B̅gₐbit = B̅gbit;
6269
};
6370

6471
struct lvl2param {
@@ -78,6 +85,13 @@ struct lvl2param {
7885
static constexpr T μ = 1ULL << 61;
7986
static constexpr uint32_t plain_modulus = 8;
8087
static constexpr double Δ = μ;
88+
// Double Decomposition (bivariate representation) parameters
89+
// For now, set to trivial values (no actual second decomposition)
90+
static constexpr std::uint32_t l̅ = 1; // auxiliary decomposition levels
91+
static constexpr std::uint32_t l̅ₐ = l̅;
92+
static constexpr std::uint32_t B̅gbit =
93+
std::numeric_limits<T>::digits; // full coefficient width
94+
static constexpr std::uint32_t B̅gₐbit = B̅gbit;
8195
};
8296

8397
// Dummy
@@ -102,6 +116,13 @@ struct lvl3param {
102116
static constexpr uint32_t plain_modulusbit = 31;
103117
static constexpr uint64_t plain_modulus = 1ULL << plain_modulusbit;
104118
static constexpr double Δ = 1ULL << (64 - plain_modulusbit - 1);
119+
// Double Decomposition (bivariate representation) parameters
120+
// For now, set to trivial values (no actual second decomposition)
121+
static constexpr std::uint32_t l̅ = 1; // auxiliary decomposition levels
122+
static constexpr std::uint32_t l̅ₐ = l̅;
123+
static constexpr std::uint32_t B̅gbit =
124+
std::numeric_limits<T>::digits; // full coefficient width
125+
static constexpr std::uint32_t B̅gₐbit = B̅gbit;
105126
};
106127

107128
// Dummy

‎include/trgsw.hpp‎

Lines changed: 59 additions & 27 deletions
Original file line numberDiff line numberDiff line change
@@ -353,7 +353,7 @@ template <class P>
353353
TRGSWFFT<P> ApplyFFT2trgsw(const TRGSW<P> &trgsw)
354354
{
355355
alignas(64) TRGSWFFT<P> trgswfft;
356-
for (int i = 0; i < P::k * P::lₐ + P::l; i++)
356+
for (int i = 0; i < P::k * P::lₐ * P::l̅ₐ + P::l * P::l̅; i++)
357357
for (int j = 0; j < (P::k + 1); j++)
358358
TwistIFFT<P>(trgswfft[i][j], trgsw[i][j]);
359359
return trgswfft;
@@ -362,7 +362,7 @@ TRGSWFFT<P> ApplyFFT2trgsw(const TRGSW<P> &trgsw)
362362
template <class P>
363363
void ApplyFFT2trgsw(TRGSWFFT<P> &trgswfft, const TRGSW<P> &trgsw)
364364
{
365-
for (int i = 0; i < P::k * P::lₐ + P::l; i++)
365+
for (int i = 0; i < P::k * P::lₐ * P::l̅ₐ + P::l * P::l̅; i++)
366366
for (int j = 0; j < (P::k + 1); j++)
367367
TwistIFFT<P>(trgswfft[i][j], trgsw[i][j]);
368368
}
@@ -371,7 +371,7 @@ template <class P>
371371
HalfTRGSWFFT<P> ApplyFFT2halftrgsw(const HalfTRGSW<P> &trgsw)
372372
{
373373
alignas(64) HalfTRGSWFFT<P> halftrgswfft;
374-
for (int i = 0; i < P::l; i++)
374+
for (int i = 0; i < P::l * P::l̅; i++)
375375
for (int j = 0; j < (P::k + 1); j++)
376376
TwistIFFT<P>(halftrgswfft[i][j], trgsw[i][j]);
377377
return halftrgswfft;
@@ -381,7 +381,7 @@ template <class P>
381381
TRGSWNTT<P> ApplyNTT2trgsw(const TRGSW<P> &trgsw)
382382
{
383383
TRGSWNTT<P> trgswntt;
384-
for (int i = 0; i < P::k * P::lₐ + P::l; i++)
384+
for (int i = 0; i < P::k * P::lₐ * P::l̅ₐ + P::l * P::l̅; i++)
385385
for (int j = 0; j < P::k + 1; j++)
386386
TwistINTT<P>(trgswntt[i][j], trgsw[i][j]);
387387
return trgswntt;
@@ -392,7 +392,7 @@ TRGSWRAINTT<P> ApplyRAINTT2trgsw(const TRGSW<P> &trgsw)
392392
{
393393
constexpr uint8_t remainder = ((P::nbit - 1) % 3) + 1;
394394
TRGSWRAINTT<P> trgswntt;
395-
for (int i = 0; i < P::k * P::lₐ + P::l; i++)
395+
for (int i = 0; i < P::k * P::lₐ * P::l̅ₐ + P::l * P::l̅; i++)
396396
for (int j = 0; j < P::k + 1; j++) {
397397
raintt::TwistINTT<typename P::T, P::nbit, true>(
398398
trgswntt[i][j], trgsw[i][j], (*raintttable)[1],
@@ -412,7 +412,7 @@ template <class P>
412412
TRGSWNTT<P> TRGSW2NTT(const TRGSW<P> &trgsw)
413413
{
414414
TRGSWNTT<P> trgswntt;
415-
for (int i = 0; i < P::k * P::lₐ + P::l; i++)
415+
for (int i = 0; i < P::k * P::lₐ * P::l̅ₐ + P::l * P::l̅; i++)
416416
for (int j = 0; j < P::k + 1; j++) {
417417
PolynomialNTT<P> temp;
418418
TwistINTT<P>(temp, trgsw[i][j]);
@@ -452,13 +452,38 @@ constexpr std::array<typename P::T, P::lₐ> noncehgen()
452452
return h;
453453
}
454454

455+
// Auxiliary h generation for Double Decomposition (bivariate representation)
456+
template <class P>
457+
constexpr std::array<typename P::T, P::l̅> h̅gen()
458+
{
459+
std::array<typename P::T, P::l̅> h̅{};
460+
for (int i = 0; i < P::l̅; i++)
461+
h̅[i] = 1ULL << (std::numeric_limits<typename P::T>::digits -
462+
(i + 1) * P::B̅gbit);
463+
return h̅;
464+
}
465+
466+
template <class P>
467+
constexpr std::array<typename P::T, P::l̅ₐ> nonceh̅gen()
468+
{
469+
std::array<typename P::T, P::l̅ₐ> h̅{};
470+
for (int i = 0; i < P::l̅ₐ; i++)
471+
h̅[i] = 1ULL << (std::numeric_limits<typename P::T>::digits -
472+
(i + 1) * P::B̅gₐbit);
473+
return h̅;
474+
}
475+
455476
template <class P>
456477
inline void halftrgswhadd(HalfTRGSW<P> &halftrgsw, const Polynomial<P> &p)
457478
{
458479
constexpr std::array<typename P::T, P::l> h = hgen<P>();
480+
constexpr std::array<typename P::T, P::l̅> h̅ = h̅gen<P>();
459481
for (int i = 0; i < P::l; i++) {
460-
for (int j = 0; j < P::n; j++) {
461-
halftrgsw[i][P::k][j] += static_cast<typename P::T>(p[j]) * h[i];
482+
for (int ī = 0; ī < P::l̅; ī++) {
483+
for (int j = 0; j < P::n; j++) {
484+
halftrgsw[i * P::l̅ + ī][P::k][j] +=
485+
static_cast<typename P::T>(p[j]) * h[i] * h̅[ī];
486+
}
462487
}
463488
}
464489
}
@@ -467,19 +492,26 @@ template <class P>
467492
inline void trgswhadd(TRGSW<P> &trgsw, const Polynomial<P> &p)
468493
{
469494
constexpr std::array<typename P::T, P::lₐ> nonceh = noncehgen<P>();
495+
constexpr std::array<typename P::T, P::l̅ₐ> nonceh̅ = nonceh̅gen<P>();
470496
for (int i = 0; i < P::lₐ; i++) {
471-
for (int k = 0; k < P::k; k++) {
472-
for (int j = 0; j < P::n; j++) {
473-
trgsw[i + k * P::lₐ][k][j] +=
474-
static_cast<typename P::T>(p[j]) * nonceh[i];
497+
for (int ī = 0; ī < P::l̅ₐ; ī++) {
498+
for (int k = 0; k < P::k; k++) {
499+
for (int j = 0; j < P::n; j++) {
500+
trgsw[(i * P::l̅ₐ + ī) + k * P::lₐ * P::l̅ₐ][k][j] +=
501+
static_cast<typename P::T>(p[j]) * nonceh[i] *
502+
nonceh̅[ī];
503+
}
475504
}
476505
}
477506
}
478507
constexpr std::array<typename P::T, P::l> h = hgen<P>();
508+
constexpr std::array<typename P::T, P::l̅> h̅ = h̅gen<P>();
479509
for (int i = 0; i < P::l; i++) {
480-
for (int j = 0; j < P::n; j++) {
481-
trgsw[i + P::k * P::lₐ][P::k][j] +=
482-
static_cast<typename P::T>(p[j]) * h[i];
510+
for (int ī = 0; ī < P::l̅; ī++) {
511+
for (int j = 0; j < P::n; j++) {
512+
trgsw[(i * P::l̅ + ī) + P::k * P::lₐ * P::l̅ₐ][P::k][j] +=
513+
static_cast<typename P::T>(p[j]) * h[i] * h̅[ī];
514+
}
483515
}
484516
}
485517
}
@@ -488,11 +520,19 @@ template <class P>
488520
inline void trgswhoneadd(TRGSW<P> &trgsw)
489521
{
490522
constexpr std::array<typename P::T, P::lₐ> nonceh = noncehgen<P>();
523+
constexpr std::array<typename P::T, P::l̅ₐ> nonceh̅ = nonceh̅gen<P>();
491524
for (int i = 0; i < P::lₐ; i++)
492-
for (int k = 0; k < P::k; k++) trgsw[i + k * P::lₐ][k][0] += nonceh[i];
525+
for (int ī = 0; ī < P::l̅ₐ; ī++)
526+
for (int k = 0; k < P::k; k++)
527+
trgsw[(i * P::l̅ₐ + ī) + k * P::lₐ * P::l̅ₐ][k][0] +=
528+
nonceh[i] * nonceh̅[ī];
493529

494530
constexpr std::array<typename P::T, P::l> h = hgen<P>();
495-
for (int i = 0; i < P::l; i++) trgsw[i + P::k * P::lₐ][P::k][0] += h[i];
531+
constexpr std::array<typename P::T, P::l̅> h̅ = h̅gen<P>();
532+
for (int i = 0; i < P::l; i++)
533+
for (int ī = 0; ī < P::l̅; ī++)
534+
trgsw[(i * P::l̅ + ī) + P::k * P::lₐ * P::l̅ₐ][P::k][0] +=
535+
h[i] * h̅[ī];
496536
}
497537

498538
template <class P>
@@ -525,24 +565,16 @@ template <class P>
525565
void halftrgswSymEncrypt(HalfTRGSW<P> &halftrgsw, const Polynomial<P> &p,
526566
const double α, const Key<P> &key)
527567
{
528-
constexpr std::array<typename P::T, P::l> h = hgen<P>();
529-
530568
for (TRLWE<P> &trlwe : halftrgsw) trlweSymEncryptZero<P>(trlwe, α, key);
531-
for (int i = 0; i < P::l; i++)
532-
for (int j = 0; j < P::n; j++)
533-
halftrgsw[i][P::k][j] += static_cast<typename P::T>(p[j]) * h[i];
569+
halftrgswhadd<P>(halftrgsw, p);
534570
}
535571

536572
template <class P>
537573
void halftrgswSymEncrypt(HalfTRGSW<P> &halftrgsw, const Polynomial<P> &p,
538574
const uint η, const Key<P> &key)
539575
{
540-
constexpr std::array<typename P::T, P::l> h = hgen<P>();
541-
542576
for (TRLWE<P> &trlwe : halftrgsw) trlweSymEncryptZero<P>(trlwe, η, key);
543-
for (int i = 0; i < P::l; i++)
544-
for (int j = 0; j < P::n; j++)
545-
halftrgsw[i][P::k][j] += static_cast<typename P::T>(p[j]) * h[i];
577+
halftrgswhadd<P>(halftrgsw, p);
546578
}
547579

548580
template <class P>

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