https://github.com/haochenuw/galoisrlwe

MSR (Microsoft Research) internship project.
https://github.com/haochenuw/galoisrlwe

Last synced: about 21 hours ago
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MSR (Microsoft Research) internship project.

• Host: GitHub
• URL: https://github.com/haochenuw/galoisrlwe
• Owner: haochenuw
• Created: 2015-07-29T00:07:04.000Z (over 9 years ago)
• Default Branch: master
• Last Pushed: 2015-12-06T01:28:52.000Z (almost 9 years ago)
• Last Synced: 2023-06-03T19:50:16.610Z (over 1 year ago)
• Language: TeX
• Homepage:
• Size: 12 MB
• Stars: 6
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# GaloisRLWE

These code assists a search for vulnerable Galois RLWE instances.

#### SubgroupModm.sage

- a class, instances of which represent subgroups H of G = (Z/mZ)^*. The input to the constructor is m and a list of generators for H.

- Computes the set H.

- Computes a set of coset representatives for the quotient group G/H.

- Given an integer a such that gcd(a,m) = 1, computes the order of a in G/H.

- Computes the discriminant of the field QQ(zeta_m)^H, using Hasse's formula (note: slow).

- Depends on: None.

#### MyLatticeSampler.sage

- Modifies the current implementation of discrete Gaussian lattice sampler in sage (bug fixes + optimization).

- Can sample from a discrete Gaussian on a lattice in R^n, given as the span of the columns of a n-by-n matrix.

- Can perform Babai's nearest plane algorithm.

- Preprocessing: we do a LLL/BKZ reduction on the input, to optimize the above two functions.

- Depends on: None.

#### SubCyCSampler.sage

- Provides a class representing a RLWE instance from a subfield of the m-th cyclotomic field, where m is odd and square free.

- Can generate RLWE samples.

- Can compute primes of a given degree.

- Compute the canonical normal integral basis of O_K, and its embedding matrix (real and complex).

- Can compute the numerical discriminant of the ring of integers O_K.

- Given a prime q, can compute the image of the canonical basis modulo a prime ideal above q.

- Depends on: SubgroupModm.sage, MyLatticeSampler.sage, misc.sage

#### misc.sage

- Chi-square test for samples in some finite field.

- Small field chi-square test.

- Generate uniform samples in finite fields.

- Some other miscellaneous functions.

- Depends on: SubgroupModm.sage

#### DirectCycSampler.sage

- Samples from arbitrary cyclotomic fields, using power basis and PLWE sampling (discrete Gaussian over ZZ on each coefficients).

- Depends on: None.