# Hardness of approximating the shortest vector problem in lattices

@article{Khot2004HardnessOA, title={Hardness of approximating the shortest vector problem in lattices}, author={S. Khot}, journal={45th Annual IEEE Symposium on Foundations of Computer Science}, year={2004}, pages={126-135} }

Let p > 1 be any fixed real. We show that assuming NP /spl nsube/ RP, it is hard to approximate the shortest vector problem (SVP) in l/sub p/ norm within an arbitrarily large constant factor. Under the stronger assumption NP /spl nsube/ RTIME(2/sup poly(log n)/), we show that the problem is hard to approximate within factor 2/sup log n1/2 - /spl epsi// where n is the dimension of the lattice and /spl epsi/> 0 is an arbitrarily small constant. This greatly improves all previous results in l/sub… CONTINUE READING

202 Citations

Tensor-based hardness of the shortest vector problem to within almost polynomial factors

- Computer Science, Mathematics
- 2007

- 89
- PDF

The complexity of the covering radius problem on lattices and codes

- Mathematics, Computer Science
- 2004

- 19
- PDF

Worst-case to average-case reductions based on Gaussian measures

- Mathematics, Computer Science
- 2004

- 324
- PDF

Worst-Case to Average-Case Reductions Based on Gaussian Measures

- Computer Science, Mathematics
- 2007

- 523
- PDF

Lattices that admit logarithmic worst-case to average-case connection factors

- Mathematics, Computer Science
- 2007

- 72
- PDF

Hardness of the covering radius problem on lattices

- Mathematics, Computer Science
- 2006

- 25
- Highly Influenced
- PDF

Inapproximability Results for the Weight Problems of Subgroup Permutation Codes

- Mathematics, Computer Science
- 2012

#### References

##### Publications referenced by this paper.

SHOWING 1-4 OF 4 REFERENCES

Factoring polynomials with rational coefficients

- Computer Science, Mathematics
- 1982

- 3,637
- Highly Influential
- PDF

Applications of a new transference theorem to Ajtai's connection factor

- Mathematics, Computer Science
- 1999

- 17
- Highly Influential