SVP challenge: a short vector in dimension 211 or higher
Difficulty 25: the record moved from 200 to 210 within ten months by sieving on GPUs, so dimension 211 is a matter of compute and engineering, not new ideas; far below lwe-quantum-hardness (79), which asks for asymptotic hardness. Application value 32: indirect, as calibration data for the attack-cost estimators behind ML-KEM and ML-DSA parameters. Leverage 24: feeds those estimators, but standard parameters sit far beyond any record.
The problem
Find a short vector in a random grid of 211 or more dimensions, beating the current public record.
- 1Random lattice in dimension d
- 2Sieve for a short vector
- 3Submit coefficients for checking
- 4Record sets the real attack price
The objects. Put linearly independent vectors as the columns of a matrix . The is every point where is a vector of whole numbers, a slanted grid in dimensions. The asks for the nonzero lattice point closest to the origin. A two-dimensional example shows why the basis matters: the columns and generate the ordinary integer grid, but the short vector only appears as . In hundreds of dimensions such hidden combinations are very hard to find.
Path to understanding
foundations → problemThe research entries this problem rests on, in the order to read them. Each links to its explainer.
- Start with
- Step 2
- Step 3
- Linear programmingAlgorithm
- Quantum algorithmsAlgorithm
- Step 4
- Step 5
- Lattice-based cryptography (LWE)Algorithm
- Step 6
State of the art
The Hall of Fame (October 2026) lists dimension 210, norm 3808, by Jintai Ding and Ziyu Zhao (January 2026, sieving); dimension 200, norm 3723, by Ziyu Zhao and Jintai Ding (March 2025); dimension 192, norm 3595, by Shi Bai, Yuanmi Chen, Jiangxia Ge, Yituo He, Xiangxue Li, Chao Sun and Yu Yu (September 2026); dimension 190, norm 3613, by Yao Sun and Shuai Chang (July 2024); dimension 188, norm 3582, by Leizhang Wang, Lin Wang, Baocang Wang, Geng Wang and Huiwen Jia (March 2025). All listed entries use sieving. Sieving cost grows exponentially in the dimension, so each step of ten dimensions multiplies the needed memory and time by a large factor.
Realistic applications
Records calibrate the cost models behind the security levels of lattice-based standards such as ML-KEM and ML-DSA. They do not break those schemes, whose parameters correspond to far larger dimensions.
What counts as solved
A submission accepted into the SVP challenge Hall of Fame in a dimension of at least 211, with the vector, the seed, the norm and a description of algorithm and hardware published.
How it gets verified
Bound / recordA numeric bound or record checked from a certificate or recomputation.
Quantity: the highest dimension for which a vector of norm below the challenge threshold has been found; record is dimension 210, norm 3808 (Ding and Zhao, January 2026). A claim is a vector in integer coordinates over the basis published at latticechallenge.org for seed 0 in dimension at least 211; checking is a matrix-vector product and a norm computation, plus the threshold comparison on the challenge page. Report algorithm (fplll, G6K or other), hardware and wall time; the Hall of Fame is the authority.
Claims under verification
+ add a claimNo claimed results on the Verification board for this problem yet.
Where the work is
Mostly large-memory, GPU-heavy sieving with careful engineering; algorithmic improvements help but the record chase is dominated by resources.
Bottlenecks
ranked by votes- #1ComputeMemory and time of sieving in dimension 211+
Sieving stores exponentially many vectors; each increase in dimension multiplies memory and time, so records need large GPU clusters.
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Connected problems
Progress
- Jan 1, 2026Dimension 210source
Ding and Zhao entered dimension 210, norm 3808, by sieving (submission date listed as 2026-01-1).