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https://github.com/jhumphry/SPARK_NORX

An Ada 2012 / SPARK 2014 project that implements the NORX authenticated encryption algorithm
https://github.com/jhumphry/SPARK_NORX

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An Ada 2012 / SPARK 2014 project that implements the NORX authenticated encryption algorithm

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# SPARK_NORX



## Introduction



This is an Ada 2012 / [SPARK 2014](http://spark-2014.org/) project that implements the

[NORX](https://norx.io/) Authenticated Encryption with Additional Data Algorithm, a third round

candidate in the [CAESAR](http://competitions.cr.yp.to/caesar.html) competition. NORX was designed

by Jean-Philippe Aumasson, Philipp Jovanovic and Samuel Neves.



The Ada code is written as a generic template, and each variant of NORX is generated from the same

code. There are some requirements of the Ada implementation (for example, `Storage_Element` must be

an 8-bit byte) and of the generic parameters (for example the rate, key size etc must all be

multiples of the word size).



This project targets version 3.0 of the specification for NORX32 and NORX64. The variants for

low-end systems are based on the separate paper 'NORX8 and NORX16: Authenticated Encryption for

Low-End Systems' by the same authors but with some modifications applied to maintain consistency

with the revisions made to the main specification.



This project is free software (using the ISC permissive licence) and is provided with no

warranties, as set out in the file `LICENSE`.



## Overview of the packages



The main generic package is `NORX` which implements the high-level API as set out in the NORX

specification. This consists of just two procedures, `AEADEnc` and `AEADDec`. The former procedure

takes in a key `K`, a 'nonce' `N`, an optional message header `A` (not encrypted), optional message

to be encrypted `M` and optional trailer `Z` (not encrypted) and returns the encrypted cipher-text

`C` and the authentication tag `T`. The latter procedure performs the decryption and returns the

decoded message and a Boolean that indicates whether the message was valid. If any of `A`, `M` or

`Z` parameters are not used, the constant `Null_Storage_Array` can be passed to the routines.



Packages `NORX6441` etc. are instantiations of this generic with the

parameters suggested by the NORX designers.



`NORX_Definitions` defines some constrained types used in the generic formal parameters and

`NORX_Load_Store` contains functions that convert between standard word sizes and `Storage_Array`

in Little-Endian format.



`NORX.Access_Internals` allows access to the lower-level API which allows you to follow the

internal state of the cipher as it processes some data. `NORX.Utils` contains useful helper

functions for printing out `Storage_Array` and `State` types.



## Examples



Three example programs are included. `norx_example` is a simple example of using the high-level API

and demonstrates successful encryption and decryption, and also unsuccessful decryption if the tag

is altered.



`norx_test_vectors` uses the lower-level API to print the trace of a sample encryption for each of

the suggested variants of NORX. These can be compared with the output from running `make debug` on

the reference C code provided by the NORX designers.



`norx_check_padding` checks that authenticated encryption and decryption works correctly when the

lengths of the header, message and trailer inputs vary. This is primarily to check for any bugs in

the implementation of the padding.



## Status of SPARK proof



As the code is written in SPARK, all of the standard instantiations of `NORX` can be proved free of

run-time exceptions for all but one type of check. Currently SPARK cannot prove the full

initialisation of output arrays where this is done one element at a time in a loop rather than in a

single array expression. SPARK will therefore report unproved checks of the form _'"C" might not be

initialised'_ for each procedure with an array output. Simply zeroing the output arrays at the

start of the procedures would resolve these unproved checks, but this would be inefficient and

would hide any real errors. Instead assertions of the form `C_Index = C'Last + 1` are proved at the

end of the procedures. These show that the whole array has been iterated over by the time the

procedure exits. `pragma Annotate` has been used to justify the output array initialisation for

these procedures.



However, SPARK GPL 2016, SPARK Discovery GPL 2017 and GNAT Community 2018 are able to prove the

absence of all other potential sources of run-time exceptions, which amount to 98% of the checks,

without manual intervention. It also proves that `AEADDec` will not return any decrypted data if

the tag verification failed. The GPL SPARK prover `gnatprove` shipped with GNAT Community 2018 from

[AdaCore](https://www.adacore.com/community) is primarily used for this project.



## Project files



Three project files for use with `GPRBuild` are provided. `spark_norx.gpr` builds the NORX code as

a static library. It takes two optional parameters:



- `mode` can be set to `debug` (the default) or `optimise`/`optimize`. This sets appropriate

compiler flags.



- `load_store` can be set to `explicit` (the default) or `le`. This setting controls how arrays of

bytes are converted into words. The `explicit` setting compiles functions that use bit shifts and

bit-wise operators to perform the conversions. The `explicit` setting should work everywhere. The

`le` setting uses unchecked type conversions. This may be faster but requires a Little-Endian

machine and an Ada compiler which uses compatible machine representation for the types.



`spark_norx_external.gpr` covers the same code, but does not trigger rebuilds of the library.

`spark_norx_examples.gpr` builds the example code.



## Using GNATprove for verification



To automatically verify the code (apart from array initialisation as discussed above), the GPS IDE

can be used. Alternatively the following commands can be used at the shell. The settings may need

to be varied depending on the speed of your machine.



- SPARK GPL 2016



    gnatprove -P spark_norx.gpr -U -j0 --level=0 --proof=progressive --warnings=continue

    

- SPARK Discovery GPL 2017



    gnatprove -P spark_norx.gpr -Xload_store=explicit -Xmode=debug -j0 --level=2



- GNAT Community 2018



    gnatprove -P spark_norx.gpr -j0 -Xload_store=explicit -Xmode=debug --level=0



Add `--report=all` if you want to see the checks that are proved as well.



For SPARK Discovery GPL 2017 the built-in SMT solver, Alt-Ergo, may not be able to prove all of the

VC. Add the alternative Z3 and/or CVC4 provers as explained in the SPARK user guide.



## Acknowledgements



Thanks to Philipp Jovanovic (NORX team), Claire Dross (AdaCore) and Yannick Moy (AdaCore) for

helpful comments and suggestions.