17 new positions, 12 sold out, 48 added to, 146 trimmed.

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In a recent breakthrough, Chattopadhyay, Hatami, Lee, Lovett, Tal, and Viola (ECCC'26) established exponential correlation bounds for polynomials over $\mathbf{F}_2$ and, as a consequence, obtained a major improvement in PRG constructions for low-degree polynomials over the binary field. In particular, they obtained seed length $\widetilde{O}(d^2\log^2 n)$ for fooling degree-$d$ polynomials in $n$ variables with constant error. Our main contribution is to achieve the optimal dependence on the number of variables $n$, at the expense of a polynomial deterioration in the dependence on $d$. Specifically, we obtain seed length $O(d^4\log n)$, as well as a bound of $\widetilde{O}(d^3\log n)$. We also obtain nearly linear dependence on $\log(1/\varepsilon)$, improving the quadratic dependence in the Fourier-based PRG of Chattopadhyay et al. Finally, we show that a random walk on a $\lambda$-spectral expander fools degree-$d$ polynomials over $\mathbf{F}_2$ with error $O(d^2\lambda)$, provided that the labeling is balanced. The bound is independent of the walk length $n$. To prove this, we extend the Fourier-analytic approach of Cohen, Peri, and Ta-Shma (STOC '21), replacing level-wise bounds on the Fourier $L_1$ mass with bounds that account for cancellations among coefficients within each level.

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デュエルマスターズ 逆札篇 不明な不透明 メモッタ(ベリーレア) 燃えろ禁断！逆転のドギラゴン革命!!（DM26-RP2） | デュエマ 闇文明 クリーチャー デュエルマスターズ Amazon ようやく成長したジョー君に会えると思っていた読者の姿はお笑いだったぜ（prgs） www.corocoro.jp www.corocoro.jp 奇跡の勝太編オールスターズ！ ドルマゲドンWを禁断爆発させて...

We present two seed-recovery attacks on a family of local PRGs, which map an $n$-bit random seed to an $m$-bit pseudorandom string by applying $\XorMaj$ predicates. For PRGs with large locality, we extend the Group-and-Solve (GAS, Eurocrypt 26) framework to Guess-Filter-Solve (GFS). GFS first guesses that a set of seed bits are all $1$s and then filters for outputs whose inputs to $\Maj$ contain a sufficiently large subset of the guessed bits. Then high-bias noisy equations can be collected for the correct guess and solved by specific solvers. Compared with GAS, GFS collects substantially more noisy equations with high bias and hence outperforms GAS significantly, especially when the output is short. For example, for the challenge parameter $n=256$ and $m=2^{16}$ (STOC 16), the complexity for GFS is $2^{68.78}$ while it is $2^{157.91}$ for GAS. In addition, the asymptotic complexity of GFS is $2^{0.15n+o(n)}$. Independently, inspired by the Guess-and-Decode (GADec, TIT 22), we propose the Filter-Guess-Propagate (FGP) attack. Compared with GADec, FGP introduces two speed-up techniques at each iteration of Belief Propagation (BP): a filter scheme to reduce the number of equations and a dynamic-programming technique to update the log-likelihood ratios of variables efficiently. Together, these improvements enable FGP to perform fast BP and outperform GADec significantly. For $\XorMaj_{10,64}$ with $n=256$ and $m=2^{40}$ (Eurocrypt 24), the total complexity of FGP is $2^{52.66}$, whereas even a single BP iteration of GADec costs $2^{106.42}$. We further extend FGP to $\XorMod$ predicates and experimentally evaluate the resulting attack complexity. We also apply FGP to a ZKP protocol from Eurocrypt 25 and QuietOT from Asiacrypt 24, with only a small computational overhead. For the ZKP protocol, FGP leads to an attack on witness indistinguishability, while for QuietOT, it similarly yields an attack on OT receiver privacy.

We study cryptographic primitives that are both locally computable (i.e., in $\mathrm{NC}^0$) and exponentially secure. For pseudorandom generators (PRGs) and universal one-way hash functions (UOWHFs), we further require linear stretch and linear compression, respectively, which is essentially the best one can hope for in this setting. Such primitives simultaneously achieve an extreme level of security and efficiency: each output bit inspects only a constant number of input bits, while each input bit buys a constant amount of security and expansion/shrinkage, in an amortized sense. We refer to such primitives as \emph{bitwise optimal}. We prove that bitwise-optimal PRGs and UOWHFs can be obtained from \emph{any} exponentially secure one-way function (OWF) in $\mathrm{NC}^0$, thereby establishing an equivalence between these three primitives in the bitwise-optimal regime. Notably, an analogous equivalence is not known in the exponential-security regime for general, unrestricted cryptographic primitives without imposing an additional regularity condition. Our results combine the machinery of the author (Applebaum, FOCS'17) with new structural results on locally computable functions that may be of independent interest. We prove a sparsification theorem that reduces the output length of any exponentially secure local OWF to $O(n)$ while preserving exponential hardness, an input-locality reduction that bounds the number of outputs affected by each input bit, and a structural theorem showing that functions with bounded input locality are typically almost regular. Together, these ingredients remove the regularity assumption required by previous constructions and yield a non-black-box transformation from exponentially secure OWFs in $\mathrm{NC}^0$ to bitwise-optimal PRGs and UOWHFs. As an additional contribution, we prove a projection-based compression theorem for locally samplable sources.