Sign in

Huck Bennett

@huckbennett.bsky.social
709 followers 232 following 180 posts

Faculty at the University of Colorado. Interested in theoretical computer science, and especially lattices. Also: mountains, running, music. home.cs.colorado.edu/~hbennett

PostsRepliesMedia
Reposted by Huck Bennett
Joshua Grochow @joshuagrochow.bsky.social · 14h
U Colorado Boulder Computer Science is hiring in #Quantum Computation, including: - Quantum CS Theory - Applications of QC to important or emerging areas Details: jobs.colorado.edu/jobs/JobDeta... Pls help spread the word, and reach out to me if you have questions. #🧮 #AcademicSky #TCSSky
jobs.colorado.edu
Tenure-Track Faculty in Quantum Computation
1118
Huck Bennett @huckbennett.bsky.social · 29/09/2026
Is reading and understanding a paper the same as writing a paper? What about rewriting a paper in my own words? Now, what if I pay my (hypothetical) human friend Eliza $200 a month to write papers for me with the understanding that I'll put my name on them but add in an Eliza statement? 2/2
110
Huck Bennett @huckbennett.bsky.social · 29/09/2026
I really appreciate the report from the Simons Institute's AI + TCS working group (simons.berkeley.edu/ai-tcs-worki...), even though I don't agree with all of its recommendations. The central thing that I'm wary about is 3.1/3a as a blanket policy. 1/2
161
Huck Bennett @huckbennett.bsky.social · 29/09/2026
Incompetence and/or malpractice. As with any powerful and dangerous tool, "Whoops! How did that happen? We didn't expect that." is not acceptable. (The OpenAI equivocating that Jeremy got on Twitter is not at all convincing.)
120
Huck Bennett @huckbennett.bsky.social · 28/09/2026
Definitely!
010
Huck Bennett @huckbennett.bsky.social · 22/09/2026
I wouldn't deride the mathematicians too much. I imagine that most of them are doing their best to try to address a very difficult situation.
100
Huck Bennett @huckbennett.bsky.social · 22/09/2026
Wow does the post title bury the lede! I particularly like the pictured comment.
35715
Huck Bennett @huckbennett.bsky.social · 21/09/2026
Congratulations to PNW running/mountain friend Jess (and her esteemed pacer Colin) on outright winning the Mountain Lakes 100-mile race in Oregon! She was 50 minutes ahead of #2 (also a woman) and ~78 ahead of the first man. Fun fact: 100% of my volcano summits have been with Colin and Jess!
2026 Mountain Lakes 100 Race Results
050
Reposted by Huck Bennett
Clément Canonne @ccanonne.github.io · 19/09/2026
Good question! There is a range of nuanced opinions on this, from "No" to "Are you kidding? No."
2331
Reposted by Huck Bennett
Lance Fortnow @lance.fortnow.com · 17/09/2026
STOC call for papers is out. Deadline is November 2. acm-stoc.org/stoc202... New rules for the AI era: limited submissions, public posting and a required video. Is it a coincidence that the camera-ready deadline is April Fools Day?
0125
Huck Bennett @huckbennett.bsky.social · 14/09/2026
I realized that I used @ccanonne.github.io 's apt phrase "bad actors" subconsciously: bsky.app/profile/ccan...
000
Huck Bennett @huckbennett.bsky.social · 14/09/2026
I might addend the last bit to "proving what they can before bad actors try to scoop them with AI."
120
Huck Bennett @huckbennett.bsky.social · 14/09/2026
💯. What a sad place we've ended up in. A year or two ago, we'd just be celebrating the results and the authors.
2161
Reposted by Huck Bennett
Maria Leonor Pacheco @mlpacheco.bsky.social · 10/09/2026
Come join us in Boulder! Feel free to get in touch if you have any questions. jobs.colorado.edu/jobs/JobDeta...
jobs.colorado.edu
Tenure-Track Faculty in Artificial Intelligence
095
Reposted by Huck Bennett
Terence Tao @teorth.bsky.social · 11/09/2026
A group of 25 Fields Medalists, including myself, have made a joint declaration on Math and AI: mathandai.org . We welcome additional signatories. See also this article in the Economist announcing the declaration: www.economist.com/science-and-...
mathandai.org
Declaration — Math and AI
Read the declaration and add your name.
422055930
Huck Bennett @huckbennett.bsky.social · 04/09/2026
Since there's no triple heart/triple celebrate reaction: ❤️❤️❤️🎉🎉🎉
010
Huck Bennett @huckbennett.bsky.social · 31/08/2026
I found Venkat's letter (written in his role as Director of the Simons Institute) on TCS and AI insightful: simons.berkeley.edu/news/letter-.... In particular, "Informed by the results of a widely circulated survey, the Simons Institute will convene a working group next month..."
simons.berkeley.edu
010
Reposted by Huck Bennett
Gülce @gkardesd.bsky.social · 29/08/2026
New on the low-depth complexity of Group Isomorphism: the first nontrivial circuit lower bounds and quasipoly-size depth-2 1/2 upper bounds -- departing from the generator-enumerator approach underlying prior low-depth work: instead we use composition series, group extensions, & short presentations.
arxiv.org
Group Isomorphism and the Polylogarithmic-Time Hierarchy: Depth-2$\frac{1}{2}$ Circuits and Lower Bounds
In this paper, we investigate the low-depth circuit complexity of Group Isomorphism in the multiplication (Cayley) table model. We prove the first circuit lower bounds for Group Isomorphism: namely, w...
2196
Huck Bennett @huckbennett.bsky.social · 26/08/2026
Presumably the Australian one involves everyone taking a selfie with a koala individually (cf. the 2014 G20 summit) followed by everyone hopping around like a kangaroo in unison.
020
Huck Bennett @huckbennett.bsky.social · 22/08/2026
It was ironic to land in Canada's capital as an American shortly after Carney's speech (www.nytimes.com/2026/08/22/w...), but so far so good! Ottawa is beautiful.
nytimes.com
Carney Slams U.S.-Canada Trade Proposal and Vows Retaliation
Prime Minister Mark Carney gave a powerful speech to Canadians on Saturday morning, hours after ordering negotiators to suspend U.S. trade talks despite President Trump’s punishing tariffs.
010
Huck Bennett @huckbennett.bsky.social · 22/08/2026
I'm in Ottawa, ON, Canada to give a couple of talks at the Selected Areas in Cryptography (SAC) summer school on Monday: sacworkshop.org/SAC26/schedu.... The first is about lattice basics, LWE, and LWE optimizations. The second is on the lattice-isomorphism problem and related cryptography.
sacworkshop.org
Schedule - Selected Areas in Cryptography (SAC) 2026
August 24–28, 2026 at the University of Ottawa. SAC is Canada's research conference on cryptography, held annually since 1994.
161
Reposted by Huck Bennett
karthikcs.bsky.social @karthikcs.bsky.social · 22/08/2026
Video playlists from the recently concluded DIMACS workshops: • Algebraic Techniques in FGC (July 20–22): www.youtube.com/playlist?lis... • FGC of String Problems (July 23–25): www.youtube.com/playlist?lis... • FGC of Graph Problems (July 27–31): www.youtube.com/playlist?lis...
083
Huck Bennett @huckbennett.bsky.social · 21/08/2026
I never realized that Kurt Vonnegut was writing about graph theory!
040
Huck Bennett @huckbennett.bsky.social · 17/08/2026
Additionally, Santiago just finished his master's at Cornell and will start a Ph.D. in crypto at Northeastern this fall, and Karthik (kgajulapalli.org) just finished his Ph.D. at Georgetown and will start as faculty at the University of Central Florida this fall. 14/14
kgajulapalli.org
Karthik Gajulapalli
000
Huck Bennett @huckbennett.bsky.social · 17/08/2026
A particular shout-out to the awesome junior researchers on these papers, who include all four of my Ph.D. students---Evelyn (www.evelynw.xyz), Peter (kirotas.github.io), Bryant, and Matthew (www.matthewfoxphysics.com). These are Peter and Bryant's first papers! 13/
kirotas.github.io
110
Huck Bennett @huckbennett.bsky.social · 17/08/2026
LCE is essentially the D = 1 case of code distortion. We give algorithms and show hardness, and study concepts like successive minima of codes and the 0 -> 0 "norm" on subspaces. This work adapts a number of ideas from analogous work on lattices (arxiv.org/abs/1605.03613). 12/
arxiv.org
On the Lattice Distortion Problem
We introduce and study the \emph{Lattice Distortion Problem} (LDP). LDP asks how "similar" two lattices are. I.e., what is the minimal distortion of a linear bijection between the two lattices? LDP ge...
100
Huck Bennett @huckbennett.bsky.social · 17/08/2026
Paper #4: "The Code Distortion Problem," arxiv.org/abs/2607.26261, at APPROX 26, with Matthew Fox and Bryant Morrell. We generalize Linear Code Equivalence (LCE; an important problem in crypto) to ask what the minimum *distortion* D of a linear map between two codes is. 11/
arxiv.org
100
Huck Bennett @huckbennett.bsky.social · 17/08/2026
This improves quantitatively on the prior work of Haviv and Regev (ieeexplore.ieee.org/document/166...). It heavily uses work of Manurangsi on the hardness of the Linear Discrepancy Problem (arxiv.org/abs/2107.01235), and unifies the problems. It also shows hardness of LinDisc in l_p norms. 10/
ieeexplore.ieee.org
100
Huck Bennett @huckbennett.bsky.social · 17/08/2026
In particular, it is (and remains) a beautiful open question to show that CRP in the l_2 norm is Pi_2-hard to approximate to within a small constant. We made some progress in this direction by showing NP-hardness for CRP in explicit finite l_p norms for the first time. 9/
ieeexplore.ieee.org
100
Huck Bennett @huckbennett.bsky.social · 17/08/2026
Paper #3: "Hardness of the Binary Covering Radius Problem in Large ℓ_p Norms," arxiv.org/abs/2603.03219, at APPROX 26, with Peter Ly. The Covering Radius Problem (CRP) is one of the most fundamental lattice problems, but its complexity is not well understood compared to others. 8/
arxiv.org
Hardness of the Binary Covering Radius Problem in Large $\ell_p$ Norms
We study the hardness of the $γ$-approximate decisional Covering Radius Problem on lattices in the $\ell_p$ norm ($γ$-$\text{GapCRP}_p$). Specifically, we prove that there is an explicit function $γ(p...
110
Huck Bennett @huckbennett.bsky.social · 17/08/2026
As a bonus, in an appendix we give a careful write-up of a folklore very flexible/good compressed sensing scheme (works over any ring, has nearly optimal parameters and running time, measurement matrix is binary). See my previous comment on this too: bsky.app/profile/huck.... 7/
100
Huck Bennett @huckbennett.bsky.social · 17/08/2026
We also match the fastest known randomized algorithms for OSMM (arxiv.org/abs/2309.06317). Our algorithms use a reduction to compressed sensing and in the randomized case, MM verification (so that a strong derandomization of Freivalds' algorithm would derandomize our OSMM alg). 6/
arxiv.org
The Time Complexity of Fully Sparse Matrix Multiplication
What is the time complexity of matrix multiplication of sparse integer matrices with $m_{in}$ nonzeros in the input and $m_{out}$ nonzeros in the output? This paper provides improved upper bounds for ...
110
Huck Bennett @huckbennett.bsky.social · 17/08/2026
Paper #2: "Output-Sparse Matrix Multiplication Using Compressed Sensing," arxiv.org/abs/2508.10250, at RANDOM 26, with Karthik Gajulapalli, Alexander Golovnev, and Evelyn Warton. We give the fastest known deterministic algorithm for output-sparse MM (i.e., MM where the product matrix is sparse). 5/
arxiv.org
Output-Sparse Matrix Multiplication Using Compressed Sensing
We give two algorithms for output-sparse matrix multiplication (OSMM), the problem of multiplying two $n \times n$ matrices $A, B$ when their product $AB$ is promised to have at most $O(n^δ)$ many non...
100
Huck Bennett @huckbennett.bsky.social · 17/08/2026
These primitives are Fully Homomorphic Encryption (computing on encrypted data) and Identity Based Encryption (PKE where a party's name or email address serves as the public key). The proofs port ideas from LWE crypto to LIP crypto. (The recent attack on HAWK does not affect this work.) 4/
100
Huck Bennett @huckbennett.bsky.social · 17/08/2026
Works from a couple of years ago (eprint.iacr.org/2021/1332, eprint.iacr.org/2021/1548) showed how to get basic crypto (KEMs/PKE, signatures) from the assumption that a variant of LIP is hard. We show how to construct more advanced primitives from a similar assumption. 3/
eprint.iacr.org
On the Lattice Isomorphism Problem, Quadratic Forms, Remarkable Lattices, and Cryptography
A natural and recurring idea in the knapsack/lattice cryptography literature is to start from a lattice with remarkable decoding capability as your private key, and hide it somehow to make a public ke...
100
Huck Bennett @huckbennett.bsky.social · 17/08/2026
Paper #1: "Advanced cryptography from lattice isomorphism—new constructions of IBE and FHE", eprint.iacr.org/2026/465, at CRYPTO 26, with Santiago Lai and @noahsd.bsky.social. The Lattice Isomorphism Problem is to determine, given two lattices as input, whether one is a rotation of the other. 2/
eprint.iacr.org
Advanced cryptography from lattice isomorphism—new constructions of IBE and FHE
We show how to translate some of the more advanced techniques used in LWE-based cryptography to the setting of lattice-isomorphism-based cryptography, which was recently introduced by Ducas and van Wo...
100
Huck Bennett @huckbennett.bsky.social · 17/08/2026
Here's a thread about four papers of mine that are being presented at conferences this week. I won't be at any of them due to the start of classes at CU, but my awesome students and collaborators will! (And, no, none of these papers used AI except for typo checking in one case.) 1/
181
Huck Bennett @huckbennett.bsky.social · 14/08/2026
Congratulations!
020
Reposted by Huck Bennett
Sasho Nikolov @thesasho.bsky.social · 10/08/2026
Nikhil Bansal and I wrote a book-length survey of algorithmic and geometric methods in discrepancy theory, and a draft of it is online arxiv.org/abs/2608.00140. This book has been years in the making, and I’m excited to share it. More 👇
arxiv.org
Discrepancy Theory: An Algorithmic and Geometric Perspective
Combinatorial discrepancy theory is a subject with roots in combinatorics, geometry, and number theory, and with numerous applications to mathematics and computer science. At its core, discrepancy the...
1327
Huck Bennett @huckbennett.bsky.social · 04/08/2026
Congratulations to Venkat! We recently used the explicit expander construction from GUV (the CCC paper) to get a compressed sensing scheme, which is the key to our MM algorithms in arxiv.org/abs/2508.10250. (Thanks to @eigx.bsky.social for the pointer to GUV!)
arxiv.org
Output-Sparse Matrix Multiplication Using Compressed Sensing
We give two algorithms for output-sparse matrix multiplication (OSMM), the problem of multiplying two $n \times n$ matrices $A, B$ when their product $AB$ is promised to have at most $O(n^δ)$ many non...
060
Huck Bennett @huckbennett.bsky.social · 03/08/2026
Ha, wow. I mean, now I'm waiting for c = 1/2 - eps. (I'd of course love to show that myself, but this is moving very fast now.) I wonder if the very non-tight exponent in the original paper was because it somehow made the proof easier to formalize in Lean, or if it was for some other reason.
110
Huck Bennett @huckbennett.bsky.social · 03/08/2026
Oops: The paper shows hardness with γ = n^c in the ell_2 norm for c = 1/400, not c = 1/200. It gets c = 1/(200p) in the ell_p norm. As Chris pointed out, this is not at all tight though: bsky.app/profile/chri....
110
Huck Bennett @huckbennett.bsky.social · 02/08/2026
Was this the most important big-AI company LLM result about lattices this week? Theoretically, yes. Practically, no. Also, Claude found a faster exponential-time algorithm for a key recovery attack on the submitted-to-NIST signature scheme HAWK. See Chris's thread: bsky.app/profile/chri.... 5/5
140
Huck Bennett @huckbennett.bsky.social · 02/08/2026
Alas, not all approx factors γ are the same: γ-CVP for γ = n^{1/2} is in coNP, and so it likely isn't NP-hard. Still, the new result with γ = n^{1/200} comes close to the n^{1/2} barrier for the first time. Previously no poly hardness was known, and now it's a matter of pinning down the exponent. 4/
252
Huck Bennett @huckbennett.bsky.social · 02/08/2026
If you assume that γ-SVP and γ-CVP have similar complexity (which is often true) and treat all polynomial approx factors γ as about the same, this new result might suggest that we're close to basing (public-key) cryptography just on NP-hardness. That would be amazing. 3/
121
Huck Bennett @huckbennett.bsky.social · 02/08/2026
First, why is this interesting? Here's an image from eccc.weizmann.ac.il/report/2022/... about the related problem SVP with varying approx factors. The middle regime says that if γ-SVP is hard for a large enough polynomial gamma (say, γ~=n^2) then lattice-based cryptography is *provably* secure. 2/
122
Huck Bennett @huckbennett.bsky.social · 02/08/2026
Yes, the result itself is very interesting (more on this below). From a skim, I agree with Noah that the paper is not well-written. Am I happy to see LLMs invade TCS? No, it's terrible. Is this the most impactful LLM result about lattices this week? Unclear. 1/
1276
Reposted by Huck Bennett
Huck Bennett @huckbennett.bsky.social · 24/07/2026
I enjoyed reading that Yu Deng almost became a professional Go player. Go is a fantastic game, which I used to play quite a lot. Here's a picture of playing Go and chess simultaneously with my Go BFF John (www.chungenliu.com; now a full professor of sociology!) when he visited Boulder recently. 3/3
Playing Go and chess simultaneously.
151
Huck Bennett @huckbennett.bsky.social · 24/07/2026
But with 74% less brain damage!
000
Huck Bennett @huckbennett.bsky.social · 24/07/2026
I enjoyed reading that Yu Deng almost became a professional Go player. Go is a fantastic game, which I used to play quite a lot. Here's a picture of playing Go and chess simultaneously with my Go BFF John (www.chungenliu.com; now a full professor of sociology!) when he visited Boulder recently. 3/3
Playing Go and chess simultaneously.
151