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In Charm Crypto, I want to compute the XOR of two pairing elements belonging to group GT. However, it seems that XOR operation is not supported but only multiplication(mul) and division(div) operations are supported for pairing element of group GT.

I want to compute the XOR for the same because of the algorithm which I am trying to implement. Below is basically what my algorithm will do in simple sense.

>>> from charm.toolbox.pairinggroup import PairingGroup, GT
>>> group = PairingGroup('SS512')
>>> val1 = group.random(GT)
>>> val2 = group.random(GT)
>>> val = val1 ^ val2
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unsupported operand type(s) for ^: 'pairing.Element' and 'pairing.Element'
>>>

The val1 and val2 are two pairing elements and I want to compute the XOR operation between them.

Can someone please guide me in this regard? What is the solution for this problem?

ashizz
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  • [Line 79](https://github.com/JHUISI/charm/blob/dev/charm/toolbox/pairinggroup.py#L79), it returns a tuple, if you know python you can handle the x-or, however, there is no guarantee that the result will be a point. – kelalaka Oct 16 '21 at 19:25

1 Answers1

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XOR is not an operation that pairing groups are designed to do. You'll likely need to XOR the X coordinates of the two points and hope that the result is still a valid X coordinate from which you can derive the Y coordinate and get a point. You'll have a hard time doing this in Charm.

You should move on to another library and write a custom implementation.

kinshukdua
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