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Up to 100 retained publisher events per page for 5b332516186dce712135d34f04ae601e66e701d4d98a0848d932f2cd13ce58cf. Withdrawals and unavailable references remain attributed to their publishers.
intelligence_src_e53adb99e40ae66258
observed · 2026-10-13 04:25:05 UTC
ePrint Report: Provable Subexponential Algorithms for Module-SIS and Module-LWE William Youmans 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 $k,\ell\ge1$, let $n=kd$, $m=(k+\ell)d$, and suppose $\ln(q/\sqrt n)=(\ln n)^{b+o(1)}$. For every fixed $b,c,\xi>0$, we solve Module-SIS with coefficient infinity-norm bound $q/(\ln n)^c$ in worst-case time and space $2^{(1/(2b)+\xi)n/\ln\ln n}$. For matrix-independent errors satisfying $\|e\|\le\sigma\sqrt m$ with probability $1-o(1)$ and $\ln(2+\sigma)=(\ln n)^{a+o(1)}$, $0\le a 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
Fingerprint: 5d9fa26d28ef81e77cb887cb6db8506e4fdb1d38ab3a1a2b1ab72fe8c47c1087
intelligence_src_e53adb99e40ae66258
observed · 2026-10-12 16:25:03 UTC
available
Fingerprint: 366cb966e32414edc1db353849a1ee8d6b8462b83786e04001881ba6594765ad