#Modulus
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thewassy153.bsky.social
just looked up both of them, and for some reason specifically the modulus longstrike has a threaded bolt??? at least that gives me a blaster to look for when thrifting lol
November 9, 2026 at 3:04 AM
eprint.ing.bot
Modulus Operandi: Round-Optimal Modulus Conversion for MPC and Threshold FHE (Ivan Damgård, Sebastian Hasler, Sebastian Kolby, Stanislas Pawlak) ia.cr/2026/2450
Abstract. In secure multiparty computation (MPC), modulus conversion turns a sharing of a value x modulo q into a sharing of the same value modulo t, without leaking anything about x. One important application of modulus conversion is in threshold decryption for lattice-based cryptosystems, where a sharing modulo the ciphertext modulus has to be moved to the plaintext modulus before it can be opened. The most efficient protocols so far (Damgård et al., Asiacrypt 2026) are in the preprocessing model, assume x is bounded away from q by a constant factor and take two rounds for a prime target modulus, three rounds for arbitrary moduli, and one round when all moduli are 2-powers. We improve upon this by constructing three new modulus conversion protocols in the preprocessing model: - Our first conversion protocol takes a single round for arbitrary moduli, consisting of just one opening. - Our second conversion protocol is a variant of the first protocol, where in the preprocessing most of the secure multiplications are replaced by private inputs, which are checked in a batch using fully linear interactive oracle proofs (FLIOPs). This makes the preprocessing cheaper (amortized over a batch of conversions) when the number N of parties is small. This comes at the cost of making the bound on x a factor N stronger. - Our third conversion protocol avoids the bound on x altogether but takes two rounds. All our protocols are stated in the arithmetic black box (ABB) model, so they can run on top of a wide variety of MPC protocols, inheriting their corruption threshold and security model. To allow the third conversion protocol to run in two rounds, we construct the first one-round comparison protocol in the ABB model for comparing a bitwise shared n-bit value against a public threshold with polynomial-size preprocessing. Concretely, the preprocessing size is 𝒪(n²) in general, and 𝒪(n²/log n) in our case where the secret value is fixed in preprocessing. We also construct constant-round ABB protocols without preprocessing for computing symmetric functions and comparisons of values shared bitwise modulo powers of arbitrary primes (e.g., 2^(k)), at communication quasi-linear in the number of input bits. Previously, this required either a sufficiently large prime or polynomially larger communication. Finally, we give an impossibility result for non-interactive modulus conversion, demonstrating that a single round is optimal: unless t divides q, every non-interactive conversion for inputs x < q/β is incorrect with probability at least  ≈ 1/(4β). Image showing part 2 of abstract. Image showing part 3 of abstract.
November 9, 2026 at 1:42 AM
astroarxiv.bsky.social
A possible connection between the ridge and hypotenuse in the bispectrum of black hole X-ray binaries through quasi-periodic modulation. Pei Jin et. al. https://arxiv.org/abs/2611.09635
Bispectral modulus along the fundamental QPO ridge of MAXI~J1820$+$070. The plotted quantities and color scheme are the same as those used in Fig.~ {fig:qpo_ridge_J1727 Bispectral modulus along the second harmonic ridge of MAXI~J1820$+$070. The plotted quantities and color scheme are the same as those used in Fig.~ {fig:harmonic_ridge_J1727 Modulus of the bispectra along the fundamental QPO ridge for the three NICER observations of Swift~J1727.8$-$1613. The green points show the bispectral modulus, \(|B( , )|\), after subtracting the average value over the 30--50~Hz frequency range, \( |B( , )| { =30-50~Hz Modulus of the bispectra along the second harmonic ridge for the three NICER observations of Swift~J1727.8$-$1613. The green points show the bispectral modulus, \(|B(2 , )|\), after subtracting the average value over the 30--50~Hz frequency range, \( |B(2 , )| { =30-50~Hz
November 9, 2026 at 9:15 AM
onmyouj.in
Time for another One-Shot Wednesday! Today, I'm playing Modulus... we buildin' robot factories in the sky!

🤖 twitch.tv/onmyoujin
Boston Dynamics Spot Robot Dog Dancing
ALT: Boston Dynamics Spot Robot Dog Dancing
static.klipy.com
November 5, 2026 at 3:16 AM
eprint.ing.bot
High-Precision CKKS with Focal Units (Jung Hee Cheon, Junho Lee) ia.cr/2026/2531
Abstract. In CKKS, higher precision requires a larger scaling factor, increasing modulus consumption during homomorphic arithmetic and leaving less modulus available after bootstrapping under the same modulus budget. We introduce Focused CKKS, which trades unused SIMD slots for precision through focused rescaling and key-switching based on cyclotomic units. These units reduce error in selected focus slots while allowing larger error in the background slots. Using only a 1/k fraction of the slots provides approximately k times as many bits of precision at the same scaling factor and CKKS parameter setting. Such a high-precision multiplication costs the same as an ordinary CKKS multiplication, with each focus slot supported by (k − 1) background slots. More generally, the construction supports different precision requirements across slots. We also construct a bootstrapping procedure tailored to Focused CKKS. Only the base modulus at the bottom level needs to grow with the target precision; the remaining bootstrapping computation maintains approximately the same modulus consumption by using fewer slots. By adapting the high-precision bootstrapping based on discrete CKKS and performing its error-cleaning step in Focused CKKS, we further reduce this base modulus by approximately the same factor k. Image showing part 2 of abstract.
November 9, 2026 at 1:51 AM
commseng.nature.com
A handheld tool for Young’s modulus characterization of soft materials: towards point-of-care tissue assessment
A handheld tool for Young’s modulus characterization of soft materials: towards point-of-care tissue assessment
Communications Engineering, Published online: 05 November 2026; doi:10.1038/s44172-026-00814-1A handheld tool for Young’s modulus characterization of soft materials: towards point-of-care tissue assessment
dlvr.it
November 6, 2026 at 7:21 AM
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High-Precision Bootstrapping for GCKKS (Shihe Ma, Jiaming Liu, Anyu Wang, Xiaoyun Wang) ia.cr/2026/2600
Abstract. Generalized CKKS (GCKKS) trades slot count for reduced modulus consumption in high-precision approximate arithmetic. However, designing a GCKKS bootstrapping algorithm with reduced modulus consumption throughout its computation remains a challenging problem. We construct high-precision bootstrapping for GCKKS using low-precision overflow extraction followed by iterative precision enhancement. Our main ingredient is a ciphertext-conversion framework for changing the decryption factor and slot count without requiring the factors to be units. A slot-aware analysis bounds unused-slot magnitudes proportionally to the corresponding evaluations of the decryption factor, which is essential to ensure the unused-slot values remain well-bounded after conversion. We combine precision doubling with ciphertext splitting and develop a joint evaluation procedure that produces two error-cleaned outputs at the cost of only one evaluation of the cleaning polynomial. We also give a useful-slot-preserving conversion from CKKS to GCKKS that simultaneously resets unused slots through component-wise re-encoding. Underlying these constructions, we also improve the construction of the decryption factors by searching directly in the canonical embedding and obtain depth-free conjugation with non-unit factors. For target encoding precision p and 2N/k useful slots in a ring of dimension N, the precision-dependent stages of the bootstrapping use O(k) homomorphic operations and consume O((p/k)log k) modulus bits. Image showing part 2 of abstract.
November 9, 2026 at 1:59 AM
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Homomorphic Encryption for High-precision Arithmetic of Approximate Numbers (Shihe Ma, Jiaming Liu, Anyu Wang, Xiaoyun Wang) ia.cr/2026/2524
Abstract. The CKKS fully homomorphic encryption scheme enables efficient arithmetic over complex numbers, but each homomorphic multiplication consumes a large modulus to ensure enough precision, limiting both the circuit depth and precision supported by CKKS. This work addresses this problem by proposing Generalized CKKS (GCKKS), a CKKS analogue of the GBFV scheme (EUROCRYPT 2025) that trades the number of slots for reduced modulus consumption. Despite its high-level similarity to GBFV, GCKKS faces new challenges caused by the different encoding and encryption structures of CKKS. We address these challenges with novel techniques not present in GBFV. Our plaintext encoding starts with an improved and SIMD version of Costache, Smart, and Vivek’s encoding in 2017. Namely, it rounds complex values to cyclotomic integers instead of Gaussian integers, and reduces the rounding problem to solving CVP instances. This encoding allows storing high-precision complex values in polynomials with small canonical norms. As an important observation, the encoding can be simplified to a sparse CKKS encoding followed by multiplication with a polynomial constructed from a short vector in the encoding lattice. We show that by integrating this encoding format into GCKKS decryption, most GCKKS homomorphic operations and the corresponding noise analyses reduce to their CKKS counterparts. This relieves GCKKS from any heavy computational or noise overhead. In experiments, GCKKS provides 7 levels with 1000-bit precision at ring dimension 2¹⁴, where each multiplication takes less than 30 ms. To our knowledge, this precision has never been achieved before. It can be used to preserve enough precision after noise flooding, a necessary ingredient for CKKS circuit privacy and a common approach to secure threshold CKKS and to provide IND-CPA^(D) security. Image showing part 2 of abstract.
November 9, 2026 at 1:51 AM
eprint.ing.bot
Exact Error Bootstrapping and Comb Bootstrapping in FHEW/TFHE (Philippe Chartier, Mohammed Lemou) ia.cr/2026/2630
Abstract. In FHEW and TFHE, bootstrapping evaluates the decryption function via a blind rotation, whose resolution limits the message space. We propose instead to bootstrap the . By rounding the ciphertext at a resolution that is a multiple of the message modulus, we preserve the message exactly. Reduction modulo a small integer then yields a noise-free encryption of the error, which a single blind rotation lifts exactly before it is subtracted. The message modulus is thus constrained solely by the noise and can be much larger than in standard TFHE. Since the error takes far fewer distinct values than the ring degree, a single blind rotation can also refresh several ciphertexts simultaneously. We call this procedure the comb bootstrap. Between refreshes, an integer remains encrypted in a single ciphertext, allowing additions modulo the message modulus and multiplications without programmable bootstrapping. Built on TFHE-rs, for 8-bit integers on a single thread, our refresh is 3.5 times faster than that of TFHE-rs, and 9.1 times faster with the comb bootstrap; multiplication is 6.5 times faster. In a residue number system, multiplication of integers modulo P̂ ≥ 2³² is 19 times faster than in TFHE-rs. The error bootstrap serves exclusively to refresh ciphertexts; evaluating any other function still requires programmable bootstrapping. Image showing part 2 of abstract.
November 9, 2026 at 2:03 AM
eprint.ing.bot
A New Approach to Reducing Modulus Requirements in Homomorphic Computation: Precision Allocation in CKKS (Zhaoyang Liang, Runkun Liu, Jingwei Fang, Dan Ding) ia.cr/2026/2562
Abstract. Fully homomorphic encryption (FHE) enables computation over encrypted data subject to the prescribed security and precision requirements (allowable deviations from ideal results). Among all FHE schemes, CKKS is a representative scheme for approximate arithmetic, allowing the same operation on multiple values packed into a single RLWE ciphertext. Reducing ciphertext modulus Q for given output precision requirements under RLWE security constraints is a central challenge in homomorphic computation. However, despite advances in plaintext and ciphertext representations, algorithmic optimizations, and modulus management, the budget in most existing approaches remains dependent on the highest required precision and cannot reduce the baseline modulus cost to overcome encryption noise. In this work, we make average rather than maximum precision requirements govern the modulus budget and achieve savings in the baseline cost. Under decryption correctness constraints, we make these possible by allocating arbitrary output precision among independent values and quantify the modulus savings arising from differences in their precision requirements. As a bonus, our construction preserves the standard CKKS ciphertext format, which helps maintain compatibility with existing optimizations. And the construction inherits the IND-CPA security of CKKS without additional cryptographic assumptions. In a repeated squaring experiment, we use 67% fewer initial modulus bits and one quarter of the ring dimension of standard CKKS, while meeting the same precision and security requirements. Image showing part 2 of abstract.
November 9, 2026 at 1:55 AM
mathoc-bot.bsky.social
Jes\'us Camacho: Calmness Modulus of Parameterized Convex Constraint Systems: Exact Closed-Form Formulas via Second-Order Admissibility https://arxiv.org/abs/2611.06224 https://arxiv.org/pdf/2611.06224 https://arxiv.org/html/2611.06224
November 5, 2026 at 6:49 AM
optb0t.bsky.social
📚 New Arxiv Paper

Title: Calmness Modulus of Parameterized Convex Constraint Systems: Exact Closed-Form Formulas via Second-Order Admissibility
Authors: Jes\'us Camacho

Read more: https://arxiv.org/abs/2611.06224
November 5, 2026 at 8:02 AM
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Jambon: Asynchronous Universally Composable Threshold FHE with Low Communication (Jung Hee Cheon, Kevin Choi, Changmin Lee, JeongHwan Lee, Junho Lim, Duc Anh Luong) ia.cr/2026/2290
Abstract. Threshold fully homomorphic encryption distributes decryption authority among multiple parties, but achieving strong security can significantly increase the required ciphertext modulus and the size of each decryption response. Existing parameter analyses typically focus on threshold decryption alone. In particular, the recent work of Kim et al. (KLL$^+$26) analyzes correctness and strong simulation security of partial decryption without covering distributed key generation (DKG). When the parties generate the keys themselves, the DKG and partial-decryption protocols must satisfy their respective correctness and security requirements. We revisit correctness and simulation-security requirements for threshold decryption when it is composed with DKG. We then introduce Jambon, which applies deterministic rounding to partial decryptions to further reduce the modulus used for decryption responses. The composed security bound accounts separately for setup and decryption errors. We prove exact recovery for BFV and extend the approach to CKKS under an additional condition. Under the stated temporary-HE assumptions and resource hybrids, we establish universally composable security with strong threshold privacy against static malicious corruption in the random-oracle model. We prove security for the DKG and its composition with verifiable partial decryption. Under the stated algebraic and statistical parameters, Jambon’s numerical decryption responses are at least 60% smaller than the native responses of the updated KLL$^+$26 strong-security construction at every threshold considered for 256, 512, and 1024 parties. This comparison uses the specified sufficient bounds and excludes proof and setup traffic. Image showing part 2 of abstract.
November 9, 2026 at 1:24 AM
mooooooo.qaf.men.ap.brid.gy
unknown-loverz OST: Modulus Theme

https://music.youtube.com/watch?v=ZfWSOs5YbQ8
November 2, 2026 at 4:46 PM
mooooooo.qaf.men.ap.brid.gy
checking the modulus while me and the devil plays no such thing as a coincidence
November 2, 2026 at 4:46 PM
mathpr-bot.bsky.social
Rainer Buckdahn, Paolo Di Tella, Juan Li: Degenerate McKean--Vlasov SDE with Yamada--Osgood Coefficients and Arbitrary Modulus of Continuity in Wasserstein Distance https://arxiv.org/abs/2611.05091 https://arxiv.org/pdf/2611.05091 https://arxiv.org/html/2611.05091
November 4, 2026 at 6:50 AM
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When Elliptic-Curve Semiprimality Certificates Reveal Factors (Giuseppe Vitto) ia.cr/2026/2620
Abstract. Public certificates of semiprimality could support cryptographic modulus generation by proving that an integer has exactly two prime factors without revealing them. Their usefulness in this setting depends on whether the certificate preserves the difficulty of factoring. Motivated by the examples of Reble and Broadhurst, we formalize semiprimality certificates by adapting the Goldwasser-Kilian primality criterion. For certificates with a prime point order, our semiprimality theorem uses public data (N, S, E, P) comprising a composite nonsquare integer N, an elliptic curve E over ℤ/Nℤ, a certified prime S > (N^(1/6) + 1)², and a point P ∈ E(ℤ/Nℤ) of order S modulo every prime divisor of N. Hasse’s bound forces each prime divisor above N^(1/3), proving that N has exactly two prime factors. For such semiprimality certificates constructed using complex multiplication (CM), we show that a norm-lattice reconstruction factors N from (N, S, D) alone in expected polynomial time when the Frobenius at every prime divisor lies in a known imaginary quadratic field of fundamental discriminant D or has trace zero, and gcd (S, 2DN) = 1. Applying this reconstruction and complementary public-point and quadratic-twist attacks, we factor Reble’s 1084-digit and Broadhurst’s 5061-digit moduli. These attacks also defeat proposed repairs based on hidden cofactors, withheld CM maps, or private isogeny descent within a known field under the stated hypotheses. We leave open whether one can efficiently produce a public Goldwasser-Kilian-based certificate for a fixed modulus, using its privately known factors, while preserving its factoring difficulty relative to the General Number Field Sieve. Image showing part 2 of abstract.
November 9, 2026 at 2:01 AM
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Information Loss Is All You Need: TC⁰ Pseudorandomness from Worst-Case Lattices (Chen Qian) ia.cr/2026/2752
Abstract. Pseudorandomness plays a central role in algorithms, complexity theory, and cryptography. We ask whether deterministic information loss alone can yield post-quantum pseudorandomness with TC⁰ evaluation. Learning with errors (LWE) hides linear measurements with random noise. Learning with rounding (LWR) replaces noise with deterministic rounding, but a standard polynomial-modulus hardness reduction requires parameters tailored to a predetermined sample bound. Decisional Diffie–Hellman offers a noiseless algebraic route to pseudorandomness, but its standard instantiations are vulnerable to quantum algorithms. We show that deterministic rounding achieves this under quantum worst-case lattice hardness, with fixed polynomial parameters and no predetermined sample bound. We introduce the learning with algebraic rounding (LAR) assumption, which applies an explicit integer rounding map to blocks of secret-dependent linear measurements and encodes the result in a lattice quotient. For one fixed family with polynomially bounded modulus and dimensions, its deterministic labels on exactly uniform, secret-independent public matrices are computationally indistinguishable from independent uniform labels for every polynomial number of classical random examples. Our classical reduction from Gaussian LWE, combined with the quantum worst-case reduction to LWE, bases LAR on GapSVP and SIVP over general lattices at approximation factor Õ(q), where q is the modulus. To prove this, we develop a source-independent affine transport framework that may be of independent interest. Using public affine maps sampled independently of the hidden errors, it transports the Gaussian error law close to uniform on the rounding map’s zero-label fiber while preserving exactly uniform public matrices. For every fixed inverse-polynomial accuracy, we give a polynomial-time sampler for the same public parameter family. This yields the first post-quantum weak pseudorandom function with joint key-and-input evaluation in TC⁰, secure against uniform quantum polynomial-time distinguishers given any polynomial number of classical uniform random examples. We also establish the hardness of learning polynomial-size two-hidden-layer ReLU networks from noiseless uniform random examples, even for quantum polynomial-time improper learners. Image showing part 2 of abstract. Image showing part 3 of abstract.
November 9, 2026 at 2:16 AM
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Efficient Implementations of Small-Modulus Lattice KEM Components (Ying Liu, Yu Zhang, Xianhui Lu) ia.cr/2026/2692
Abstract. Small moduli support compact polynomial representations in lattice-based key encapsulation mechanisms (KEMs), including BAT (TCHES 2022) and END (ASIACRYPT 2026, to appear). However, compact encodings can be costly to convert, and uniform generation must account for both coefficient-extraction cost and random-bit demand. Incomplete number-theoretic transforms also leave residual polynomial products. To address these costs, we exploit the structure of moduli 257 and 769 to improve encoding, uniform public polynomial generation, and polynomial multiplication. At q = 257, we introduce zero-selector encoding: zero payload bytes locate ambiguous coefficients, and selector bits resolve their values. We analyze selector capacity, overflow, and key-generation retries. For n = 1024, a 1033-byte configuration has overflow probability at most 2⁻¹²⁸ under independent uniform coefficients. Checked AVX2 decoding takes 213 cycles, compared with 2203 cycles for BAT’s 1040-byte format. At q = 769, we lower conversion costs using an existing compact radix format at the same encoded length as BAT. We specialize rejection sampling to simplify coefficient extraction at q = 257 and reduce random-bit demand at q = 769. At (q, n) = (769, 1024), expected candidate-bit demand decreases by 24.39% relative to direct 10-bit rejection. Four-polynomial generation uses 7.14-13.21% fewer AVX2 cycles. For residual multiplication, proven range bounds justify omitting strict input-centering corrections, while register scheduling reduces stack accesses. We integrate the public-key codecs and multiplication components into BAT and END. Across the tested C and AVX2 implementations, encapsulation costs decrease by 39.93 − 55.25% in BAT and 41.36 − 48.84% in END. The corresponding decapsulation reductions are 5.42 − 8.55% in BAT and, for END, 23.99 − 45.89% in C and 6.98 − 8.04% in AVX2. END AVX2 gains mainly come from the public key codec. These results quantify the effect of modulus-specific optimizations on complete component and KEM costs. Image showing part 2 of abstract.
November 9, 2026 at 2:10 AM
bigearthdata.ai
1 cell dysfunction and tumor immunosuppression
->Nature | More on "Tumor stiffness and immune dysfunction" at BigEarthData.ai
1 cell dysfunction and tumor immunosuppression
(a) Quantification of tumor tissue stiffness from patients with pancreatic cancer (n = 20, ≥ 2,000 data points per sample). Samples with top 5 (high-stiffness group) and bottom 5 (low-stiffness group) Young’s modulus were subjected to scRNA-seq analysis. (b) Uniform manifold approximation and projection (UMAP) plots showing 67,782 cells of 35 subtypes (left), and non-malignant cell distribution in two groups (right). (c) Expression of marker genes across cell types in human scRNA-seq data. (d) Bar plot showing the fractions of cells with significant changes between the two groups. (e) Statistics of Th1 cell cluster in public human pancreatic cancer scRNA-seq data. Two groups were defined based on the expression of stiffness signature (n = 21 high-stiffness, n = 22 low-stiffness). (f) Pearson correlation between stiffness signature score and Th1 signature score in pancreatic cancer patients from TCGA database. For box plots in (a and e), the centerlines indicate the median; the top and bottom hinges indicate the 25th and 75th percentiles; the whiskers represent 1.5× the interquartile range; and the lines in the upper and lower of the whiskers indicate the maxima and minima. P values were calculated by Fisher’s exact test in (d) and two-sided Wilcoxon rank-sum test in...
www.nature.com
November 9, 2026 at 1:19 PM
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Provable Subexponential Algorithms for Module-SIS and Module-LWE (William Youmans) ia.cr/2026/2420
Abstract. Ducas, Engelberts and Loyer (CRYPTO 2025) turned Wagner’s generalized birthday algorithm into a provable subexponential-time Gaussian sampler for unstructured short integer solutions. Recent preprints of Han, Gao and Hu, and of Chen, Jiang, Wang and Zhang, obtain low-sample decision learning-with-errors algorithms from this framework. We extend it to module matrices over power-of-two cyclotomic rings, for every residue degree of the prime modulus. For fixed module ranks k, ℓ ≥ 1, let n = kd, m = (k + ℓ)d, and suppose $\ln(q/\sqrt n)=(\ln n)^{b+o(1)}$. For every fixed b, c, ξ > 0, we solve Module-SIS with coefficient infinity-norm bound q/(ln n)^(c) in worst-case time and space 2^((1/(2b) + ξ)n/ln ln n). For matrix-independent errors satisfying $\|e\|\le\sigma\sqrt m$ with probability 1 − o(1) and ln (2 + σ) = (ln n)^(a + o(1)), 0 ≤ a < b, decision and search Module-LWE take 2^((1/(2(b − a)) + ξ)n/ln ln n). Success is 1 − o(1) using only the given k + ℓ ring samples; error coordinates need not be independent. The structural ingredient is a Chinese-remainder-support uncertainty bound: the loss of randomness of sparse dual labels is compensated by an arithmetic lower bound on their length. Scalar row perturbations give search over the base field, and small integer shears remove a singular-block loss. Projection, the Han–Gao–Hu martingale analysis, and a finite enumeration sampler give a common algorithmic framework. We also prove sample-preserving scalar search-LWE and narrow Module-LWE algorithms. In particular, for polynomial prime q = n^(κ + o(1)), κ > 1/2, one ring sample and growing rank suffice for decision and search in time and space 2^((1/2 + ξ)n/ln ln n) when the sample supplies (1 + o(1))n/ln ln n scalar responses. Here “narrow” restricts both secret and error. Separate heuristic estimates in the model of Ducas, Engelberts and Loyer suggest that Wagner-style attacks do not reach the NIST security targets of ML-KEM and ML-DSA. Image showing part 2 of abstract.
November 9, 2026 at 1:39 AM
meenakshi-rawat.bsky.social
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November 6, 2026 at 4:19 AM
eprint.ing.bot
BOLT-FHE: An Efficient Unified Framework for GPU-based TFHE Bootstrapping via On-Chip Local Tiling Strategies (Yanren Chen, Fangyu Zheng, Guang Fan, Jiankuo Dong, Wenxu Tang, Tian Zhou, Jingqiang Lin, Jiwu Jing) ia.cr/2026/2356
Abstract. Bootstrapping is the main performance bottleneck in bitwise Fully Homomorphic Encryption (FHE), and practical acceleration requires careful orchestration of the blind rotation and external product chain under GPU resource constraints. This paper presents BOLT-FHE, a GPU bootstrapping framework that emphasizes block-local execution, on-chip tiling, and a unified MegaKernel supporting both gadget decomposition and modulus raising, with optional support for a recently proposed technique (Bergerat et al, CHES 2025) based on the common mask assumption (CM packing). Our design keeps the accumulator update chain within a single thread block and fuses NTT/INTT, external products, and accumulator updates using a fixed execution template. Two compile-time parameters—WPP (warps per polynomial) and IPT (items per thread)—control multi-warp cooperation and per-thread register footprint, enabling consistent kernel structure across different parameter sets. On an NVIDIA RTX 4090, BOLT-FHE reaches 40,166 bootstrappings per second at 128-bit security, demonstrating high-throughput TFHE bootstrapping on a commodity GPU. Compared to the state-of-the-art GPU implementation VeloFHE (Shen et al, CHES 2025), BOLT-FHE achieves 1.85×–2.92× speedups with gadget decomposition. In particular, for modulus raising, BOLT-FHE improves by 2.38×–2.42× without CM packing, and by 3.17×–3.31× under the best packing configuration, reflecting the combined benefits of fused arithmetic, more regular memory access, and amortization enabled by CM packing. Overall, BOLT-FHE shows that a portable, fused-kernel organization with explicit on-chip budgeting can substantially improve TFHE bootstrapping throughput while remaining compatible with both noise management paths. Image showing part 2 of abstract.
November 9, 2026 at 1:32 AM
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Rotate Once, Read Many Times: on the Output Noise of Multi-Value Bootstrapping (Philippe Chartier, Michel Koskas, Mohammed Lemou) ia.cr/2026/2332
Abstract. In FHEW/TFHE, a programmable bootstrap evaluates an arbitrary function of the encrypted message, encoded as the of a blind rotation. We work in a prime-power cyclotomic ring whose prime is the plaintext modulus p (a that leaves the ring degree free as a security parameter) and compare the (SVM), one rotation per function, with the (MVM), one rotation shared by all. Factoring the test polynomial as v_(f)^(*) = 𝔅_(f)^(*) ⋅ 𝔴, the function carried by the dual module and the rotated factor by the torus, lets a single hypothesis (a centered accumulator error of covariance G) cover both modes: the two variances are values of one G-form, and their ratio is the exact amplification. The f-independent factorizations are then parametrized by a non-zero ring element, the cofactor, and by the integer lift of the table: at a random lift the cofactor is chosen by a shortest-vector problem for an explicit quadratic form, then the lift by a closest-vector problem of rank p − 1. In the spherical model that form is a trace norm and two designs compete: the canonical cofactor, of noise cost p(p + 1)/6, and the pivot, which reads the integer table itself at noise cost 2p, at a random lift; the optimized lift then favours the canonical cofactor on the generic tables. Under the other natural covariance, the block Laplacian, it is optimal for every p. Both cofactors are measured, in the key-noise regime, on a complete implementation, publicly available. Image showing part 2 of abstract.
November 9, 2026 at 1:29 AM
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A Subexponential Algorithm for Binary LWE with Sublinear Samples (Zhili Chen, Kaijie Jiang, Anyu Wang, Chuanqi Zhang) ia.cr/2026/2289
Abstract. We study Binary LWE with polynomial modulus in the regime of a linear number of samples. Prior work of Kirchner and Fouque and of Herold, Kirshanova, and May (CRYPTO ’15, DCC ’18) gives an algorithm running in time exp (O(n/log log n)) using O(nlog n) samples, leaving open whether the same complexity can be achieved with only m = Θ(n) samples. We resolve this problem by showing that the same complexity is achievable with even a sublinear number of samples. Fix any constant a > 1/2, let q = n^(a + o(1)) be an odd prime, and let m = ⌈n/log log n⌉. We give a randomized algorithm that distinguishes (A, A^(⊤)s + e) ∈ ℤ_(q)^(n × m) × ℤ_(q)^(m) from a uniformly random pair, for every fixed secret–error pair satisfying ∥s∥₂² + ∥e∥₂² = O(m + n). Its expected running time and space are exp (O(n/log log n)). A crucial component is a new instantiation of the auxiliary superlattices in the Gaussian–Wagner framework of Ducas, Engelberts, and Loyer (CRYPTO ’25). These superlattices have sufficiently small smoothing parameters even when the approximation parameter for the entire output list is subexponentially small, while still admitting exact shifted discrete Gaussian sampling within the claimed running time. A Euclidean dual-minimum argument simultaneously controls the smoothing parameters of all projected relevant lattices. Combining the resulting short vectors with an Aharonov–Regev Fourier distinguisher yields the claimed sublinear sample LWE algorithm. Image showing part 2 of abstract.
November 9, 2026 at 1:24 AM