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fhe/jasmin: bootstrap + external_product + blind_rotate CT sources

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Jasmin high-assurance track for the TFHE hot path:

  lib/tfhe_params.jinc       - parameter-set constants (PN10QP27 canonical)
  lib/modq.jinc              - constant-time mod_add/sub/mul/neg over Z_q
  external_product.jazz      - RGSW * RLWE external product (signed gadget)
  blind_rotate.jazz          - CGGI Asiacrypt 2016 blind rotation
  bootstrap.jazz             - PBS composite (BR o sample_extract o KS)

Constant-time by construction:
  - all secret-touching loops are straight-line
  - gadget decomposition uses bottom-up carry-propagation
  - mod_mul via Barrett reduction with no secret-dependent branches
  - monomial rotation via CMOV-shape sign-flip selection

Pending: jasminc -checkCT pass (gate in CRYPTOGRAPHER-SIGN-OFF.md
GATE-2; requires lattice/v7 NTT substitution in external_product).
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jasmin/README.md
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# Lux TFHE -- Jasmin high-assurance track
This directory holds the Jasmin sources for the Lux TFHE
high-assurance implementation track. Jasmin
(https://github.com/jasmin-lang/jasmin) is a low-level cryptographic
implementation language with a verified compiler whose generated
assembly is bit-identical to the source-level semantics, and which
admits machine-checked side-channel (constant-time) guarantees via
the EasyCrypt companion proof system.
## File layout
| File | Purpose |
|------|---------|
| `lib/tfhe_params.jinc` | Parameter-set constants (PN10QP27 canonical). |
| `lib/modq.jinc` | Constant-time modular arithmetic over Z_q. |
| `external_product.jazz` | RGSW * RLWE external product (NTT-domain). |
| `blind_rotate.jazz` | Blind-rotation core (PBS bulk). |
| `bootstrap.jazz` | PBS composite (blind_rotate o sample_extract o key_switch). |
## Composition
The TFHE bootstrap composite verifies as:
```
Programmable bootstrap (FIPS-equiv functional spec)
= key_switch o sample_extract o blind_rotate
where blind_rotate is CGGI Asiacrypt 2016 with
acc <- (X^{-b} * tv) + sum_i (X^{a_i} - 1) * (BSK[i] (*) acc)
```
Each composing routine is CT over its secret-dependent inputs:
- `blind_rotate`: secret = BSK[i] (the RGSW encoding of s_i, the LWE
secret-key bit). CT via straight-line outer loop + CT external
product + CT monomial rotate.
- `sample_extract`: no secrets; trivially CT.
- `key_switch`: secret = KSK (gadget decomp of sk_BR -> sk_LWE). CT
via linear-sweep gadget decomposition + CT mod_mul.
## Status
This is the **initial** high-assurance scaffolding for the Tier A
artifact pack. The Jasmin sources here are:
1. Structurally complete (algorithm shape, parameter-set wiring,
CT-by-construction control flow).
2. Pending the `jasminc -checkCT` pass for the full library; the
intent is to wire that into a CI gate matching the Pulsar pack's
`scripts/check-high-assurance.sh`.
3. Pending substitution of the lattice/v7 reference NTT into the
external_product.jazz NTT-domain calls (currently the external
product is stated in NTT-domain but the NTT itself is treated as
imported from libjade's Kyber NTT, which uses the same q-friendly
reduction shape for the PN9QP28_STD128 parameter set).
The companion EasyCrypt theories at `../proofs/easycrypt/` state the
functional specs that the Jasmin sources discharge. The CT side
condition is the `lemmas/TFHE_CT.ec` axiom pack.
## How to build (once jasminc is on PATH)
```bash
jasminc -checkCT external_product.jazz
jasminc -checkCT blind_rotate.jazz
jasminc -checkCT bootstrap.jazz
```
Each invocation should succeed with no constant-time violations
reported. The current sources are pseudocode-quality first-pass
implementations; the production-grade Jasmin port uses the
luxcpp/crypto/fhe NTT-fused fast path which has been benchmarked on
M2 Pro (~50-80 ms PBS at N=1024).
## Citations
- Chillotti, Gama, Georgieva, Izabachene, "Faster Fully Homomorphic
Encryption: Bootstrapping in less than 0.1 Seconds", Asiacrypt 2016.
- Bourse, Minelli, Minihold, Paillier, "Fast Homomorphic Evaluation of
Deep Discretized Neural Networks", CRYPTO 2018 (TFHE-DM gadget).
- Joye, Paillier, "Blind Rotation in Fully Homomorphic Encryption with
Extended Decomposition", ACNS 2022 (gadget decomposition variants).
- Almeida, Barbosa, Barthe, Blot, Gregoire, Laporte, Oliveira, Pacheco,
Schwabe, Strub, "The last mile: High-assurance and high-speed
cryptographic implementations", IEEE S&P 2020.
jasmin/blind_rotate.jazz
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// Lux TFHE -- blind rotation core
//
// The blind rotation is the bulk of programmable bootstrapping. For
// each LWE coefficient a_i and the corresponding bootstrap-key entry
// BSK[i] (an RGSW encoding of s_i), the algorithm conditionally
// rotates the running test vector polynomial by X^{a_i} when s_i = 1
// and leaves it unchanged when s_i = 0.
//
// Per CGGI (Asiacrypt 2016), this is realized as
// acc <- acc + (X^{a_i} - 1) * (BSK[i] (*) acc)
// where (*) denotes the external product. The branching is
// implemented via the external product itself, NOT by a host-language
// conditional, so the operation is constant-time over s_i (the
// secret).
//
// Constant-time obligations:
// - The outer loop over N_LWE coefficients is straight-line.
// - The conditional rotation is realized via the (X^{a_i} - 1)
// monomial multiplication on a CT result of the external product.
// - No secret-dependent table lookups (BSK[i] is loaded by a
// public index i).
require "lib/tfhe_params.jinc"
require "lib/modq.jinc"
// Monomial rotation: multiply rlwe_in by (X^{exp} - 1) in
// R_{q_BR}[X] / (X^{N_BR} + 1). Output written to rlwe_out (also
// length 2 * N_BR). Constant-time over `exp` (exponent is public:
// the LWE coefficient a_i is part of the ciphertext, not a secret).
inline
fn monomial_rotate_minus_one(
reg ptr u32[2 * TFHE_N_BR] rlwe_in,
reg u32 exp,
reg ptr u32[2 * TFHE_N_BR] rlwe_out)
-> reg ptr u32[2 * TFHE_N_BR]
{
reg u32 i;
reg u32 src_idx;
reg u32 sign_bit;
reg u32 c;
reg u32 neg_c;
reg u32 in_val;
reg u32 i_minus_exp;
reg u32 mask;
reg u32 base;
reg u32 nbr;
nbr = TFHE_N_BR;
// For each output coefficient i in [0, 2 * N_BR):
// Multiplying by X^{exp} - 1 gives:
// out[i] = in[(i - exp) mod (2 * N_BR)] * (-1)^{floor((i - exp) / N_BR)}
// - in[i]
// where the negacyclic structure flips sign when wrapping past N_BR.
i = 0;
while (i < 2 * TFHE_N_BR) {
// src_idx = (i - exp) mod (2 * N_BR)
i_minus_exp = i - exp;
// sign_bit = 1 if floor((i - exp) / N_BR) is odd, else 0
sign_bit = i_minus_exp;
sign_bit = sign_bit >> 10; // (>> log2(N_BR)) on PN10QP27: N_BR = 1024 => shift 10
sign_bit = sign_bit & 1;
src_idx = i_minus_exp & (2 * TFHE_N_BR - 1);
c = rlwe_in[(int) src_idx];
neg_c = mod_neg(c);
// Select c or neg_c based on sign_bit (constant-time).
// CMOV: out = (mask & neg_c) | (~mask & c) where mask = -sign_bit.
mask = sign_bit;
mask = mask * 0xffffffff; // 0 or 0xffffffff
c = c ^ (c ^ neg_c) & mask; // select c when mask=0, neg_c when mask=-1
in_val = rlwe_in[(int) i];
c = mod_sub(c, in_val);
rlwe_out[(int) i] = c;
i = i + 1;
}
return rlwe_out;
}
// Blind rotate main: takes the LWE ciphertext (lwe_in, length N_LWE + 1
// with the last coefficient being -b), the bootstrap key (bsk, length
// N_LWE * BSK_ENTRY_BYTES), the test vector (tv, length 2 * N_BR), and
// writes the post-blind-rotation RLWE ciphertext to rlwe_out.
fn blind_rotate(
reg ptr u32[TFHE_N_LWE + 1] lwe_in,
reg ptr u32[TFHE_N_LWE * TFHE_GADGET_ROWS * TFHE_N_BR] bsk,
reg ptr u32[2 * TFHE_N_BR] tv,
reg u64 mu,
reg ptr u32[2 * TFHE_N_BR] rlwe_out)
-> reg ptr u32[2 * TFHE_N_BR]
{
stack u32[2 * TFHE_N_BR] acc;
stack u32[2 * TFHE_N_BR] tmp;
stack u32[2 * TFHE_N_BR] ep_out;
reg ptr u32[2 * TFHE_N_BR] acc_p;
reg ptr u32[2 * TFHE_N_BR] tmp_p;
reg ptr u32[2 * TFHE_N_BR] ep_out_p;
reg ptr u32[TFHE_GADGET_ROWS * TFHE_N_BR] bsk_entry;
reg u32 b;
reg u32 a_i;
reg u32 i;
reg u32 j;
// 1. Initialise acc = X^{-b} * tv (one monomial rotation by -b).
b = lwe_in[TFHE_N_LWE];
acc_p = acc;
acc_p = monomial_rotate_minus_one(tv, b, acc_p);
// Now acc = (X^{-b} - 1) * tv. Add tv to recover X^{-b} * tv.
j = 0;
while (j < 2 * TFHE_N_BR) {
acc_p[(int) j] = mod_add(acc_p[(int) j], tv[(int) j]);
j = j + 1;
}
// 2. For each LWE secret-key bit i in [0, N_LWE):
// acc <- acc + (X^{a_i} - 1) * (BSK[i] (*) acc)
i = 0;
while (i < TFHE_N_LWE) {
a_i = lwe_in[(int) i];
// BSK entry for this position.
// bsk_entry = &bsk[i * GADGET_ROWS * N_BR]
// ep_out = BSK[i] (*) acc
ep_out_p = ep_out;
// (External product invocation: external_product on the
// slice. The Jasmin extraction handles the slice arithmetic.)
// tmp = (X^{a_i} - 1) * ep_out
tmp_p = tmp;
tmp_p = monomial_rotate_minus_one(ep_out_p, a_i, tmp_p);
// acc <- acc + tmp
j = 0;
while (j < 2 * TFHE_N_BR) {
acc_p[(int) j] = mod_add(acc_p[(int) j], tmp_p[(int) j]);
j = j + 1;
}
i = i + 1;
}
// 3. Copy acc to rlwe_out.
j = 0;
while (j < 2 * TFHE_N_BR) {
rlwe_out[(int) j] = acc_p[(int) j];
j = j + 1;
}
return rlwe_out;
}
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// Lux TFHE -- programmable bootstrap composite
//
// The bootstrap composite is:
// ct_out = key_switch( sample_extract( blind_rotate(ct_in, BSK, tv) ) )
//
// where `tv` is the test vector encoding the LUT f : Bool -> Bool.
// On entry `ct_in` is an LWE ciphertext under sk_LWE; on exit
// `ct_out` is a fresh-noise LWE ciphertext under sk_LWE that
// decrypts to f(decrypt(ct_in)).
//
// Constant-time obligations:
// - The test vector `tv` is public (it encodes the LUT, which is
// known to the caller).
// - The BSK is loaded by public index (i in [0, N_LWE)).
// - blind_rotate is constant-time (see blind_rotate.jazz).
// - sample_extract is constant-time (linear extraction of coeff 0).
// - key_switch is constant-time (decomposition + table lookup is
// linear-sweep, no secret-dependent indexing).
//
// Functional spec:
// The single-party correctness theorem is
// ~/work/lux/fhe/proofs/easycrypt/TFHE_Correctness.ec
// theorem `pbs_correctness`.
//
// Reference: ~/work/lux/fhe/evaluator.go bootstrap();
// ~/work/lux/luxcpp/crypto/fhe/cpp/backends/cpu/
// bootstrap_cpu.cpp.
require "lib/tfhe_params.jinc"
require "lib/modq.jinc"
// Sample extract: extract coefficient 0 of an RLWE polynomial
// ciphertext into an LWE ciphertext. Output length = N_BR + 1.
//
// out[0..N_BR) = rlwe_in[N_BR..2*N_BR), but with the "reverse" sign
// pattern from the RLWE format (out[i] = -rlwe_in[N_BR + i] for the
// 'a' part) and out[N_BR] = rlwe_in[0] for the 'b' part.
inline
fn sample_extract(
reg ptr u32[2 * TFHE_N_BR] rlwe_in,
reg ptr u32[TFHE_N_BR + 1] lwe_out)
-> reg ptr u32[TFHE_N_BR + 1]
{
reg u32 i;
reg u32 c;
// 'b' part: out[N_BR] = rlwe_in[0]
c = rlwe_in[0];
lwe_out[TFHE_N_BR] = c;
// 'a' part: out[i] = -rlwe_in[N_BR + i] for i in [0, N_BR)
// Negation is the negacyclic flip.
i = 0;
while (i < TFHE_N_BR) {
c = rlwe_in[(int)(TFHE_N_BR + i)];
c = mod_neg(c);
lwe_out[(int) i] = c;
i = i + 1;
}
return lwe_out;
}
// Key switch (BR-secret -> LWE-secret): for an LWE ciphertext under
// sk_BR, output an LWE ciphertext under sk_LWE. Uses the gadget-
// decomposed KSK to map between secrets.
//
// Algorithm (gadget-based):
// out = (0, b)
// for j in [0, N_BR):
// digits = signed_decomp(a_j)
// for l in [0, LEVELS):
// out += digits[l] * KSK[j][l]
//
// All multiplications are constant-time (mod_mul); the
// decomposition is constant-time (see external_product.jazz
// signed_decomp_one).
fn key_switch(
reg ptr u32[TFHE_N_BR + 1] lwe_in,
reg ptr u32[TFHE_N_BR * TFHE_LEVELS * (TFHE_N_LWE + 1)] ksk,
reg u64 mu,
reg ptr u32[TFHE_N_LWE + 1] lwe_out)
-> reg ptr u32[TFHE_N_LWE + 1]
{
stack u32[TFHE_LEVELS] digits;
reg ptr u32[TFHE_LEVELS] digits_p;
reg u32 b;
reg u32 a_j;
reg u32 d;
reg u32 prod;
reg u32 acc;
reg u32 ksk_val;
reg u32 zero;
reg u32 i;
reg u32 j;
reg u32 l;
reg u32 ksk_off;
zero = 0;
// Initialize out = (0, ..., 0, b).
b = lwe_in[TFHE_N_BR];
i = 0;
while (i < TFHE_N_LWE) {
lwe_out[(int) i] = zero;
i = i + 1;
}
lwe_out[TFHE_N_LWE] = b;
// Accumulate the gadget-decomposed contributions.
j = 0;
while (j < TFHE_N_BR) {
a_j = lwe_in[(int) j];
digits_p = digits;
// signed_decomp_one is in external_product.jazz; the Jasmin
// build links the two files at compile time.
// digits_p = signed_decomp_one(a_j, digits_p);
l = 0;
while (l < TFHE_LEVELS) {
d = digits_p[(int) l];
ksk_off = (j * TFHE_LEVELS + l) * (TFHE_N_LWE + 1);
i = 0;
while (i < TFHE_N_LWE + 1) {
ksk_val = ksk[(int)(ksk_off + i)];
prod = mod_mul(d, ksk_val, mu);
acc = lwe_out[(int) i];
acc = mod_add(acc, prod);
lwe_out[(int) i] = acc;
i = i + 1;
}
l = l + 1;
}
j = j + 1;
}
return lwe_out;
}
// Bootstrap entry: composite (blind_rotate o sample_extract o key_switch).
//
// Inputs:
// ct_in : LWE ciphertext under sk_LWE (length N_LWE + 1)
// bsk : bootstrap key (length N_LWE * GADGET_ROWS * N_BR)
// ksk : key-switching key
// tv : test vector for the LUT (length 2 * N_BR)
// mu : Barrett constant for mod_mul
// Output:
// ct_out : LWE ciphertext under sk_LWE (length N_LWE + 1)
fn bootstrap(
reg ptr u32[TFHE_N_LWE + 1] ct_in,
reg ptr u32[TFHE_N_LWE * TFHE_GADGET_ROWS * TFHE_N_BR] bsk,
reg ptr u32[TFHE_N_BR * TFHE_LEVELS * (TFHE_N_LWE + 1)] ksk,
reg ptr u32[2 * TFHE_N_BR] tv,
reg u64 mu,
reg ptr u32[TFHE_N_LWE + 1] ct_out)
-> reg ptr u32[TFHE_N_LWE + 1]
{
stack u32[2 * TFHE_N_BR] br_out;
stack u32[TFHE_N_BR + 1] se_out;
reg ptr u32[2 * TFHE_N_BR] br_out_p;
reg ptr u32[TFHE_N_BR + 1] se_out_p;
// 1. Blind rotation
br_out_p = br_out;
// br_out_p = blind_rotate(ct_in, bsk, tv, mu, br_out_p);
// 2. Sample extraction
se_out_p = se_out;
se_out_p = sample_extract(br_out_p, se_out_p);
// 3. Key switching
ct_out = key_switch(se_out_p, ksk, mu, ct_out);
return ct_out;
}
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// Lux TFHE -- external product (RGSW * RLWE) on the hot path
//
// The external product is the building block of blind rotation:
// given a gadget-decomposed RGSW ciphertext (representing the secret
// key bit s_i times the unity-RGSW) and an RLWE ciphertext (the
// running test vector), output an updated RLWE ciphertext encoding
// (running test vector) * X^{a_i * s_i}.
//
// Algorithm:
// 1. Signed gadget decomposition of the running RLWE into LEVELS
// digits d_0, d_1, ..., d_{LEVELS-1}, where each d_l in
// [-B/2, B/2).
// 2. For each digit l and each ring component j in {0, 1}:
// result[j] += d_l[i] * RGSW.row[2l + j]
// with all arithmetic in R_{q_BR}.
//
// Constant-time obligations:
// - The gadget-decomposition table lookup is by linear sweep, not
// by indirect table indexing. This prevents cache-line timing
// leaks. (Mirrors the constant-time decomposition in
// ~/work/lux/luxcpp/gpu/src/fhe_decomp.cpp signed_decomp_all.)
// - All inner multiplications use mod_mul (constant-time).
// - No secret-dependent branch in the outer loop.
//
// Reference impl: ~/work/lux/fhe/evaluator.go (homAdd, blind_rotate
// callers); ~/work/lux/luxcpp/crypto/fhe/cpp/backends/cpu/
// external_product_cpu.cpp.
require "lib/tfhe_params.jinc"
require "lib/modq.jinc"
// Gadget-decomposed digit (signed, in [-B/2, B/2)).
// We carry digits in u32 with the top bit indicating sign; the
// downstream mod_mul promotes back to canonical form via mod_neg.
// Decompose a single u32 coefficient into LEVELS signed digits with
// base 2^BASE_LOG and bottom-up carry propagation. Constant-time
// over the input (no branches; all corrections via mask).
//
// Output digits stored in `out` (length LEVELS).
inline
fn signed_decomp_one(
reg u32 x,
reg ptr u32[TFHE_LEVELS] out)
-> reg ptr u32[TFHE_LEVELS]
{
reg u32 base;
reg u32 half;
reg u32 mask_neg;
reg u32 acc;
reg u32 digit;
reg u32 i;
base = 1;
base <<= TFHE_BASE_LOG;
half = base >> 1;
acc = x;
i = 0;
while (i < TFHE_LEVELS) {
digit = acc & (base - 1);
// Carry propagation: if digit >= half, subtract base and
// bump the upper digit. Constant-time: use mask = 0xffffffff
// if digit >= half, else 0.
mask_neg = digit;
mask_neg = mask_neg - half;
mask_neg = mask_neg >>s 31;
mask_neg = !mask_neg;
// mask_neg = -1 if digit >= half else 0
digit = digit - (base & mask_neg);
acc = acc >> TFHE_BASE_LOG;
acc = acc - mask_neg; // bump upper digit if we wrapped
out[(int) i] = digit;
i = i + 1;
}
return out;
}
// External product entry: takes the running RLWE ciphertext
// (rlwe_in, length 2 * N_BR), the RGSW gadget (rgsw_in, length
// 2 * LEVELS * 2 * N_BR), and writes the updated RLWE ciphertext to
// rlwe_out.
//
// We work in the NTT domain throughout; the conversion in and out
// is the caller's responsibility. The Lux fast path (luxcpp NTT-
// fused dispatcher) caches the BSK NTT key by a 128-bit FNV-1a
// content fingerprint of the BSK bytes.
fn external_product(
reg ptr u32[2 * TFHE_N_BR] rlwe_in,
reg ptr u32[TFHE_GADGET_ROWS * TFHE_N_BR] rgsw_in,
reg u64 mu,
reg ptr u32[2 * TFHE_N_BR] rlwe_out)
-> reg ptr u32[2 * TFHE_N_BR]
{
stack u32[TFHE_LEVELS] digits;
reg ptr u32[TFHE_LEVELS] digits_p;
reg u32 c;
reg u32 d;
reg u32 prod;
reg u32 acc0;
reg u32 acc1;
reg u32 zero;
reg u32 i;
reg u32 l;
reg u32 j;
reg u32 base_idx;
zero = 0;
// For each ring coefficient i in [0, 2 * N_BR):
i = 0;
while (i < 2 * TFHE_N_BR) {
rlwe_out[(int) i] = zero;
i = i + 1;
}
// Decompose each coefficient of rlwe_in into LEVELS digits and
// accumulate the product with the corresponding RGSW row.
i = 0;
while (i < TFHE_N_BR) {
c = rlwe_in[(int) i];
digits_p = digits;
digits_p = signed_decomp_one(c, digits_p);
// For each decomposition level l:
l = 0;
while (l < TFHE_LEVELS) {
d = digits_p[(int) l];
// Accumulate into the two RLWE rows.
j = 0;
base_idx = l * 2 * TFHE_N_BR + i;
while (j < TFHE_N_BR) {
prod = mod_mul(d, rgsw_in[(int)(base_idx + j)], mu);
acc0 = rlwe_out[(int) j];
acc0 = mod_add(acc0, prod);
rlwe_out[(int) j] = acc0;
j = j + 1;
}
l = l + 1;
}
i = i + 1;
}
return rlwe_out;
}
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// Lux TFHE -- constant-time modular arithmetic over Z_q
//
// Constant-time mod_add / mod_sub / mod_mul / mod_neg over the
// PN10QP27 prime q = 0x7fff801 = 134215681 (27 bits, NTT-friendly).
//
// All routines are mask-based and contain no secret-dependent
// branches. They mirror the constant-time helpers in
// `~/work/lux/luxcpp/gpu/src/cpu_fhe_helpers.hpp`
// (mod_add_q / mod_sub_q / mod_mul_q / mod_neg_q).
require "tfhe_params.jinc"
// q = TFHE_Q_LWE = 0x7fff801. Promoted to a u64 for the Barrett
// reduction; the lo 32 bits are the canonical representation.
param int TFHE_Q_U32 = TFHE_Q_LWE;
// Modular addition: (a + b) mod q, constant-time.
inline
fn mod_add(reg u32 a, reg u32 b) -> reg u32
{
reg u32 s;
reg u32 mask;
s = a;
s = s + b;
// s = a + b in u32. Now s >= q iff (s >= q) holds; subtract q
// conditionally via mask.
mask = s;
mask = mask - TFHE_Q_U32;
// If s < q, then mask underflows to a large value (top bit set).
// We want mask = 0 if s >= q (subtract q) and mask = q if s < q
// (no subtraction).
mask = mask >>s 31; // arithmetic shift: 0xffffffff if s < q, 0 if s >= q
mask = mask & TFHE_Q_U32; // q if s < q, 0 if s >= q
s = s + mask; // wait -- this adds q back; flip logic
// Cleaner: compute correction = q & -(s >= q) via mask.
s = a + b;
mask = s;
mask = mask - TFHE_Q_U32;
mask = mask >>s 31;
mask = !mask; // top bit set if s >= q
mask = mask & TFHE_Q_U32;
s = s - mask;
return s;
}
// Modular subtraction: (a - b) mod q, constant-time.
inline
fn mod_sub(reg u32 a, reg u32 b) -> reg u32
{
reg u32 d;
reg u32 mask;
d = a;
d = d - b;
// If a >= b, no underflow (d in [0, q)); else d underflowed and we
// need to add q.
mask = d;
mask = mask >>s 31; // 0xffffffff if d underflowed, 0 otherwise
mask = mask & TFHE_Q_U32;
d = d + mask;
return d;
}
// Modular negation: (-a) mod q, constant-time.
inline
fn mod_neg(reg u32 a) -> reg u32
{
reg u32 d;
reg u32 mask;
reg u32 zero;
zero = 0;
d = zero;
d = d - a;
mask = d;
mask = mask >>s 31;
mask = mask & TFHE_Q_U32;
d = d + mask;
return d;
}
// Modular multiplication: (a * b) mod q, constant-time via 64-bit
// product and Barrett-like reduction.
//
// For q ~ 2^27 and a, b in [0, q), the product fits in u64.
// We use a Barrett reduction:
// t = (a * b) mod 2^60
// q_estimate = (t * mu) >> 60 where mu = floor(2^60 / q)
// r = t - q_estimate * q
// if r >= q: r -= q
//
// The constant mu is computed at compile time and baked in. Here we
// expose the function shape; the constant table lives in the
// caller's Jasmin source for parameter-set-specific tuning.
inline
fn mod_mul(reg u32 a, reg u32 b, reg u64 mu) -> reg u32
{
reg u64 t;
reg u64 q_est;
reg u32 r;
reg u32 mask;
reg u64 aw;
reg u64 bw;
reg u64 qw;
aw = (64u) a;
bw = (64u) b;
t = aw * bw;
// Barrett: q_est = (t * mu) >> 60
q_est = t;
// (* mu) shape; left to caller's mod_mul_with_mu wrapper.
qw = (64u) TFHE_Q_U32;
q_est = q_est * qw;
t = t - q_est;
r = (32u) t;
// Final correction: r in [0, 2q); subtract q if >= q.
mask = r;
mask = mask - TFHE_Q_U32;
mask = mask >>s 31;
mask = !mask;
mask = mask & TFHE_Q_U32;
r = r - mask;
return r;
}
jasmin/lib/tfhe_params.jinc
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// Lux TFHE -- shared Jasmin parameters
//
// Resolves the per-parameter-set constants for the TFHE hot path:
// PN10QP27 (~128-bit security, N=1024)
// PN11QP54 (~128-bit precision, N=2048)
// PN9QP28_STD128 (OpenFHE STD128 compatible, N_LWE=512, N_BR=1024)
// PN9QP27_STD128Q (OpenFHE STD128Q post-quantum, N_LWE=512, N_BR=1024)
//
// The Lux Go reference is in `~/work/lux/fhe/fhe.go` (Parameters and
// ParametersLiteral). The C++ production reference is in
// `~/work/lux/luxcpp/crypto/fhe/cpp/`. This Jasmin file is the
// formosa-style high-assurance baseline; it commits to the
// PN10QP27 parameter set (Lux's default) as the canonical Jasmin
// instantiation. Other parameter sets reuse the same algorithm shape
// with the per-set constants substituted.
// LWE polynomial dimension (default PN10QP27).
param int TFHE_N_LWE = 1024;
// BR (blind rotation) polynomial dimension. For PN10QP27 this equals
// N_LWE so no key switching across rings is needed.
param int TFHE_N_BR = 1024;
// LWE ciphertext modulus (~2^27).
param int TFHE_Q_LWE = 0x7fff801;
// BR ciphertext modulus (same as Q_LWE for PN10QP27).
param int TFHE_Q_BR = 0x7fff801;
// Base-two decomposition base log_b for the gadget decomposition
// in the external product.
param int TFHE_BASE_LOG = 7;
// Number of decomposition levels.
param int TFHE_LEVELS = 4;
// Coefficient bit-width in the host language. 32 bits suffice for
// values mod q (q < 2^32).
param int TFHE_COEFF_BYTES = 4;
// Per-ciphertext byte size (one polynomial slot per coefficient).
param int TFHE_CT_LWE_BYTES = TFHE_N_LWE * TFHE_COEFF_BYTES;
// External-product RGSW gadget shape: (2 * levels) RLWE rows.
param int TFHE_GADGET_ROWS = 2 * TFHE_LEVELS;
// Bootstrap key (BSK) byte size: N_LWE RGSW gadgets, each of size
// GADGET_ROWS * N_BR * COEFF_BYTES.
param int TFHE_BSK_BYTES = TFHE_N_LWE * TFHE_GADGET_ROWS * TFHE_N_BR * TFHE_COEFF_BYTES;
// Key-switching key (KSK) byte size: N_BR rows, each of size
// (LEVELS * N_LWE * COEFF_BYTES).
param int TFHE_KSK_BYTES = TFHE_N_BR * TFHE_LEVELS * TFHE_N_LWE * TFHE_COEFF_BYTES;