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Post-quantum key exchange from the learning with errors problem — from the paper "Frodo: Take off the ring! Practical, Quantum-Secure Key Exchange from LWE", published in ACM CCS 2016,



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lwe-frodo is a C cryptographic library for post-quantum key exchange based on the learning with errors (LWE) problem. It is based on the following research paper:

  • Joppe Bos, Craig Costello, Léo Ducas, Ilya Mironov, Michael Naehrig, Valeria Nikolaenko, Ananth Raghunathan, Douglas Stebila. Frodo: Take off the ring! Practical, quantum-secure key exchange from LWE. In ACM Conference on Computer and Communications Security (CCS) 2016, ACM, October, 2016. DOI:10.1145/2976749.2978425, Eprint

You can download the PDF of the paper from the GitHub repository.

Python scripts for selecting parameters are available in the lwe-frodo/parameter-selection repository.


The software is plain C. Compilation has been tested using gcc on Ubuntu 16.04.1 and clang on Mac OS X 10.11.6. The software uses some routines from OpenSSL's libcrypto, so you will need to have OpenSSL installed.

To compile on Ubuntu:

sudo apt-get install make gcc libssl-dev

To compile on Mac OS X using brew:

You will need to have installed the Xcode developer tools, including the command-line programs and the brew package manager.

brew install openssl
make OPENSSL_DIR=/usr/local/opt/openssl

(You can also uncomment the appropriate line in the Makefile and then you only need to type make.)

You can also download and compile OpenSSL yourself following the instructions on the OpenSSL website. You will need to edit the Makefile to point to your copy of OpenSSL.


To run the basic test harness, type:


This will test various aspects of the library, including:

  • correctness of routines for packing / unpacking vectors in bit arrays
  • correctness and distribution of random sampling
  • correctness of key exchange

You can run the test harness in continuous mode by typing:

./test cont

This will run the test harness indefinitely (hit Ctrl-C to stop). Given that the probability of failure for the default parameters is 2-38.9, you should not see any failures unless you run it for several billion iterations.

You can get runtime benchmarking results by typing:

./test bench

In order to obtain accurate benchmarking results, you should disable hyperthreading (a.k.a. hardware multithreading) and TurboBoost. ./test bench will output instructions on how to do so.


The software includes 4 parameters sets, as described in the paper:

  • challenge — smaller parameters that should be reasonably accessible within the current cryptanalytic state-of-the-art
  • classical — provides 128-bit security against best-known classical attacks, but not against quantum attackers
  • recommended — provides ≥128 bits of security against best-known quantum attacks
  • paranoid — provides 128 bits of security against an algorithm reaching the complexity lower bound for sieving algorithms (see paper for details)

By default, the recommended parameters are used. This can be configured by editing lwe.h.


This software is licensed under the MIT License. For details, see LICENSE.txt.


JB and LD were supported in part by the Commission of the European Communities through the Horizon 2020 program under project number 645622 (PQCRYPTO). DS was supported in part by Australian Research Council (ARC) Discovery Project grant DP130104304 and a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant. The authors would like to thank Adam Langley, Eric Grosse, and Úlfar Erlingsson for their inputs. A large part of this work was done when VN was an intern with the Google Security and Privacy Research team.


Post-quantum key exchange from the learning with errors problem — from the paper "Frodo: Take off the ring! Practical, Quantum-Secure Key Exchange from LWE", published in ACM CCS 2016,








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