#19531: Add conversion from fields to binary-like strings
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Reporter: tgagne | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.10
Component: finite rings | Resolution:
Keywords: finite field, hex strings, | Merged in:
binary strings | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Old description:
> There should be the ability to convert binary and hex strings into
> elements from the fields `GF(2^n)` and `GF(2^(4n))` and vice versa.
>
> - A field `GF(2^(4n))` should accept length `n` hex strings of the form
> `0xfff...` and produce the corresponding field element.
> - A field `GF(2^n)` should accept length `n` binary strings of the form
> `0b111...` and produce the corresponding field element.
> - Matrix spaces and vector spaces over these fields should accept strings
> of similar form and should break up the strings accordingly to produce a
> matrix or vector.
> - Elements of the field `GF(2^(4n))` should be able to convert themselves
> into length `n` hex strings of the form `0xfff...`.
> - Elements of the field `GF(2^n)` should be able to convert themselves
> into length `n` binary strings of the form `0b111...`.
> - Matrices and vectors over these finite fields should be able to combine
> the individual hex/binary strings for each of its elements into a single
> long string.
>
> One of the ultimate goals for adding this is to use it for conversion in
> cryptographic modules which involve finite fields, such as `mq.SR`.
New description:
There should be the ability to convert binary and hex strings into
elements from the fields `GF(2^n)` and `GF(2^(4n))` and vice versa.
- A field `GF(2^(4n))` should accept length `n` hex strings of the form
`0xfff...` and produce the corresponding field element.
- A field `GF(2^n)` should accept length `n` binary strings of the form
`0b111...` and produce the corresponding field element.
- Elements of the field `GF(2^(4n))` should be able to convert themselves
into length `n` hex strings of the form `0xfff...`.
- Elements of the field `GF(2^n)` should be able to convert themselves
into length `n` binary strings of the form `0b111...`.
One of the ultimate goals for adding this is to use it for conversion in
cryptographic modules which involve finite fields, such as `mq.SR`.
--
Comment (by tgagne):
Replying to [comment:3 jdemeyer]:
> Please create a new ticket for the vector and matrix case, let's just
deal with the fields here.
A ticket for that's been created at #19578.
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Ticket URL: <http://trac.sagemath.org/ticket/19531#comment:10>
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