SqueakElib project

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SqueakElib project

Robert Withers
Good morning,

Here is a brief writeup of the SqueakElib project and its direction.

https://github.com/SqueakCryptographySquad/Cryptography-Common/wiki/SqueakElib.

All new squad members welcome.

Regards,
Robert

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Re: SqueakElib project

Ben Coman
This is interesting, "error correction through Reed Solomon encoding"
but its not clear how its used.  Maybe a sketch of the architecture
would be useful.
cheers -ben

On Fri, Dec 4, 2015 at 9:31 PM, Robert Withers
<[hidden email]> wrote:

> Good morning,
>
> Here is a brief writeup of the SqueakElib project and its direction.
>
> https://github.com/SqueakCryptographySquad/Cryptography-Common/wiki/SqueakElib.
>
> All new squad members welcome.
>
> Regards,
> Robert
>

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Re: SqueakElib project

Robert Withers
I could briefly explain and put creation of new SecureSession
architecture sketch on my medium stack. I have a few diagrams already
which I will add, but none of this new SecureSession design. This is
done so please check that page.

Reed Solomon encoding:
Using Reed-Solomon encoding for Forward Error Correction is used is
satellite communications. Other lossy communications probably uses this
or something similar. By interleaving RS encoded blocks, you quadruple
the contiguous bytes that can be corrupted and still recovered. My use
here will specify 4 interleaved blocks. So the encoding is really an RS
encoding of 4 blocks and then interleaving them.

Note that QR Codes are using RS encoding.

RS encoding uses a GaloisField, or a finite field. This is a system of
polynomials that are multiplied, divided, inversed and added to
transform the data into code (as in coded data). The Galois Field is
initialized with a primitive polynomial that sets the symbol size of
data, symbol size of code and the number of errors that is still
recoverable. Thus there are many different primitive polynomials as
there are uses of RS encoding. Note that the symbol size tends to be a
nibble. I use 3 different sized primitive polynomials, so I have
different sized blocks depending on the size of the payload to be
fragmented and encoded, in groups of 4 interleaved blocks.

The easiest RS encoding to look at has 9 data symbols, 15 code symbols
and can handle 3 symbol errors. Considering that these 15 symbols/block
will be interleaved with 3 other blocks, we are talking about 60
symbols, or 30 bytes coded. This is 18 bytes of data. As they are
interleaved with 3 errors per block permissible, that is 12 contiguous
bytes can be corrupted and the msg recovered.

The interleaving takes the first byte from each of 4 blocks, then the
second...

[byteA1, byteB1, byteC1, byteD1, byteA2, byteB2, ...]

I hope this helps! I'll add it to the project wiki.

Robert



On 12/05/2015 08:34 PM, Ben Coman wrote:

> This is interesting, "error correction through Reed Solomon encoding"
> but its not clear how its used.  Maybe a sketch of the architecture
> would be useful.
> cheers -ben
>
> On Fri, Dec 4, 2015 at 9:31 PM, Robert Withers
> <[hidden email]> wrote:
>> Good morning,
>>
>> Here is a brief writeup of the SqueakElib project and its direction.
>>
>> https://github.com/SqueakCryptographySquad/Cryptography-Common/wiki/SqueakElib.
>>
>> All new squad members welcome.
>>
>> Regards,
>> Robert
>>


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Re: SqueakElib project

Robert Withers


On 12/05/2015 09:30 PM, Robert Withers wrote:

> I could briefly explain and put creation of new SecureSession
> architecture sketch on my medium stack. I have a few diagrams already
> which I will add, but none of this new SecureSession design. This is
> done so please check that page.
>
> Reed Solomon encoding:
> Using Reed-Solomon encoding for Forward Error Correction is used is
> satellite communications. Other lossy communications probably uses
> this or something similar. By interleaving RS encoded blocks, you
> quadruple the contiguous bytes that can be corrupted and still
> recovered. My use here will specify 4 interleaved blocks. So the
> encoding is really an RS encoding of 4 blocks and then interleaving them.
>
> Note that QR Codes are using RS encoding.
>
> RS encoding uses a GaloisField, or a finite field. This is a system of
> polynomials that are multiplied, divided, inversed and added to
> transform the data into code (as in coded data). The Galois Field is
> initialized with a primitive polynomial that sets the symbol size of
> data, symbol size of code and the number of errors that is still
> recoverable. Thus there are many different primitive polynomials as
> there are uses of RS encoding. Note that the symbol size tends to be a
> nibble. I use 3 different sized primitive polynomials, so I have
> different sized blocks depending on the size of the payload to be
> fragmented and encoded, in groups of 4 interleaved blocks.
>
> The easiest RS encoding to look at has 9 data symbols, 15 code symbols
> and can handle 3 symbol errors. Considering that these 15
> symbols/block will be interleaved with 3 other blocks, we are talking
> about 60 symbols, or 30 bytes coded. This is 18 bytes of data. As they
> are interleaved with 3 errors per block permissible, that is 12
> contiguous bytes can be corrupted and the msg recovered.

I need to make a correction to what I've said, that is 3 symbol errors
per coded block, or 3 nibbles. So the contiguous space that can be
recovered is 6 bytes coded, out of 30 bytes. Higher degree primitive
polynomials have different sizes for data, code, errors and so a larger
encoding with 4-block interleaving may result in hundreds of contiguous
bytes being resilient. I do think it is in the neighborhood of 10-20% of
the coded message is recoverable, generally.

Robert

>
> The interleaving takes the first byte from each of 4 blocks, then the
> second...
>
> [byteA1, byteB1, byteC1, byteD1, byteA2, byteB2, ...]
>
> I hope this helps! I'll add it to the project wiki.
>
> Robert
>
>
>
> On 12/05/2015 08:34 PM, Ben Coman wrote:
>> This is interesting, "error correction through Reed Solomon encoding"
>> but its not clear how its used.  Maybe a sketch of the architecture
>> would be useful.
>> cheers -ben
>>
>> On Fri, Dec 4, 2015 at 9:31 PM, Robert Withers
>> <[hidden email]> wrote:
>>> Good morning,
>>>
>>> Here is a brief writeup of the SqueakElib project and its direction.
>>>
>>> https://github.com/SqueakCryptographySquad/Cryptography-Common/wiki/SqueakElib.
>>>
>>>
>>> All new squad members welcome.
>>>
>>> Regards,
>>> Robert
>>>
>


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Re: SqueakElib project

Robert Withers
In reply to this post by Ben Coman
Please ask for any details or clarifications you would like added to this diagram of the SecureSession protocol stack. Ty, Robert.



On 12/05/2015 08:34 PM, Ben Coman wrote:
This is interesting, "error correction through Reed Solomon encoding"
but its not clear how its used.  Maybe a sketch of the architecture
would be useful.
cheers -ben

On Fri, Dec 4, 2015 at 9:31 PM, Robert Withers
[hidden email] wrote:
Good morning,

Here is a brief writeup of the SqueakElib project and its direction.

https://github.com/SqueakCryptographySquad/Cryptography-Common/wiki/SqueakElib.

All new squad members welcome.

Regards,
Robert


    


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Re: SqueakElib project

Ben Coman
Which layer does the Reed Solomon encoding?
cheers -ben

On Sun, Dec 6, 2015 at 7:24 PM, Robert Withers <[hidden email]> wrote:
Please ask for any details or clarifications you would like added to this diagram of the SecureSession protocol stack. Ty, Robert.


On 12/05/2015 08:34 PM, Ben Coman wrote:
This is interesting, "error correction through Reed Solomon encoding"
but its not clear how its used.  Maybe a sketch of the architecture
would be useful.
cheers -ben

On Fri, Dec 4, 2015 at 9:31 PM, Robert Withers
[hidden email] wrote:
Good morning,

Here is a brief writeup of the SqueakElib project and its direction.

https://github.com/SqueakCryptographySquad/Cryptography-Common/wiki/SqueakElib.

All new squad members welcome.

Regards,
Robert


    







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Re: SqueakElib project

Robert Withers
That is the FEC for Forward Error Correction.

Robert

On 12/06/2015 07:18 AM, Ben Coman wrote:
Which layer does the Reed Solomon encoding?
cheers -ben

On Sun, Dec 6, 2015 at 7:24 PM, Robert Withers <[hidden email]> wrote:
Please ask for any details or clarifications you would like added to this diagram of the SecureSession protocol stack. Ty, Robert.


On 12/05/2015 08:34 PM, Ben Coman wrote:
This is interesting, "error correction through Reed Solomon encoding"
but its not clear how its used.  Maybe a sketch of the architecture
would be useful.
cheers -ben

On Fri, Dec 4, 2015 at 9:31 PM, Robert Withers
[hidden email] wrote:
Good morning,

Here is a brief writeup of the SqueakElib project and its direction.

https://github.com/SqueakCryptographySquad/Cryptography-Common/wiki/SqueakElib.

All new squad members welcome.

Regards,
Robert