#19531: Add conversion from fields to binary-like strings
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Reporter: tgagne | Owner:
Type: | Status: new
enhancement | Milestone: sage-6.10
Priority: major | Keywords: finite field, hex strings,
Component: finite | binary strings
rings | Authors:
Merged in: | Report Upstream: N/A
Reviewers: | Branch:
Work issues: | Dependencies:
Commit: |
Stopgaps: |
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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`.
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Ticket URL: <http://trac.sagemath.org/ticket/19531>
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