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david committed Mar 25, 2016
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# Ways to generate a non-prime DH modulus to create a NOBUS backdoor

This `README` documents the different methods researched and implemented in [backdoor_generator.sage](backdoor_generator.sage) to generate backdoored DH parameters.
* [backdoor_generator.sage](backdoor_generator.sage) is a script to generate the backdoored DH parameters.

* [dhparams_exporter.py](dhparams_exporter.py): a script to export your backdoored parameters to *go* code or an *ASN.1 DER* encoded file (for anything OpenSSL).
* [dhparams_exporter.py](dhparams_exporter.py) is a script to export your backdoored parameters to *go* code (the attack in [/attack](/attack) is coded in go) or to an *ASN.1 DER* encoded file (for anything OpenSSL).

* [backdoor_generator_tests.sage](backdoor_generator_tests.sage) is a script that tests the attacks.

Expand All @@ -13,4 +13,4 @@ The obvious way of building a backdoor is to ease the discrete logarithm problem
* SNFS (depends on the modulus as well)
* Pohlig-Hellman (`O(sqrt(q))` with `q` largest factor of the order)

In order to make the backdoor NOBUS we use a composite modulus, there are two methods here: hide in the composite modulus a small subgroup generated by a specific generator, or hide in the composite modulus a smooth order that we can use with Pohlig-Hellman. These methods are documented in `/whitepaper.tex` as for now (work in progress paper), or you can look at the code in `backdoor_generator.sage`.
In order to make the backdoor NOBUS we use a composite modulus, there are two methods here: hide in the composite modulus a small subgroup generated by a specific generator (CM-HSS), or hide in the composite modulus a smooth order that we can use with Pohlig-Hellman (CM-HSO). These methods are documented in [backdoor_generator.sage](backdoor_generator.sage) and are detailed in `/whitepaper.tex` (work in progress paper).

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