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Does randomization make a big difference in the output of the BKZ algorithm?

We all know that block Korkine-Zolotarev (BKZ) algorithm is essentially a deterministic lattice reduction algorithm. However, in the actual implementation, the BKZ algorithm contains some ...
constantine's user avatar
1 vote
0 answers
244 views

Sentinel ("trick") values for lattice attack on DSA with biased k (MSB)

I'm studying lattice attack using this sage script. There are 2 options in script: LSB and MSB. The most interesting option for me is MSB. It recovers private key with less then 100 signatures ...
Igor Matyuh's user avatar
3 votes
2 answers
541 views

Distribution of the Difference of Uniformly Random Elements

In the search to decision reduction of 'On Ideal Lattices and Learning with Errors over Rings', the authors implicitly use the fact that the difference of distinct, uniformly random elements of a (...
a196884's user avatar
  • 381
9 votes
1 answer
2k views

Discrete Gaussian Sampling role in Lattice-Based Crypto?

I'm reading up on how post-quantum cryptography works, and stumbled upon the notion of discrete Gaussian sampling. However, I can't understand where it fits in the greater picture - currently it feels ...
Daniel B's user avatar
  • 357
3 votes
1 answer
98 views

Why is a bit biased when generated from random $v \in Z_q$ for odd q?

I am not understanding the following from "Lattice Cryptography for the Internet" by C. Peikert (pages 10, 11): When $q$ is odd, while it is possible to use the above methods to agree on a bit ...
Node.JS's user avatar
  • 322
6 votes
2 answers
781 views

Randomness re-use in LWE encryption scheme

Let me describe the scheme first, it is the scheme proposed by O. Regev when he introduced the LWE assumption. $sk = \textbf{s} \in \mathbf{Z}_q^n$ $pk = \textbf{A}\textbf{s}+\textbf{e}$ where $\...
Florian Bourse's user avatar