#11565: RSA Cryptosystem
-------------------------------------+-------------------------------------
Reporter: ajeeshr | Owner: mvngu
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.6
Component: cryptography | Resolution:
Keywords: RSA, crypto, | Merged in:
public key encryption | Reviewers:
Authors: Peter Story, | Work issues:
Ajeesh Ravindran | Commit:
Report Upstream: N/A | 3c8e43ae07f14dbc6c42f42c5e91cfee5b3f2e45
Branch: | Stopgaps:
u/peter.story/rsa_cryptosystem |
Dependencies: |
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Comment (by peter.story):
@vdelecroix, thanks for bringing the `__init__` and `__eq__` methods to my
attention. I copied the implementations from ajeeshr, who had copied them
from `BlumGoldwasser`, the other `PublicKeyCryptosystem`. The reason
`BlumGoldwasser` implements them is to override the
`PublicKeyCryptosystem` implementations, which is necessary because
`BlumGoldwasser` doesn't initialize its superclass properly (it may be
helpful to read the code for the Cryptosystem class's `__init__` and
`__eq__`, which can be found on lines 104-212 in cryptosystem.py).
I modified `__eq__` to fix the issue you identified. Now, the method just
compares the class of the two objects being compared. This is a change
that should also be made to `BlumGoldwasser`.
However, `__init__` will be trickier to fix properly. According to the
`Cryptosystem` class, which `RSACryptosystem` inherits through
`PublicKeyCryptosystem`, I should be passing the following arguments to my
superclass's `__init__` method: `plaintext_space, ciphertext_space,
key_space, block_length=1, period=None`. Without fixing this, inherited
methods like the following will fail:
{{{
sage: rc = RSACryptosystem()
sage: rc.key_space()
AttributeError: 'RSACryptosystem' object has no attribute '_key_space'
}}}
The following values seem to make the most sense to me, but I'm not
certain:
* plaintext_space = group of all integers
* ciphertext_space = group of all integers
* key_space: I have no idea how to specify this one as a group.
Ideally, I would give plaintext_space and ciphertext_space as integers mod
n, instead of the group of all integers. However, this would require
giving the RSACryptosystem class state, recording public and private keys
internally. This would have the effect of making it more opaque, since
users wouldn't need to explicitly pass keys to encrypt and decrypt. Thus,
I think it makes sense to keep plaintext_space and ciphertext_space as the
groups of all integers. Comments on this would be appreciated.
Side note: `__init__` will also need to be fixed in `BlumGoldwasser`:
{{{
sage: from sage.crypto.public_key.blum_goldwasser import BlumGoldwasser
sage: bs = BlumGoldwasser()
sage: bs.key_space()
AttributeError: 'BlumGoldwasser' object has no attribute '_key_space'
}}}
Also, as suggested by kcrisman, I corrected several formatting issues with
the documentation. Thanks to vdelecroix, I removed unnecessary
redeclarations of variables in my tests, except where redeclaring improved
readability.
--
Ticket URL: <http://trac.sagemath.org/ticket/11565#comment:23>
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