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ECC multiplication over GF(p) is clearly one-way.

How about ECC over real number?

Is ECC division over real number also practically impossible?

zzinny
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  • I don't believe ECC would even work over real numbers. – forest Jul 25 '19 at 02:41
  • @forest Could you explain more about that in detail? – zzinny Jul 25 '19 at 02:58
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    Arithmetic over real numbers is not efficiently computable (if it is computable at all). Also, floating-point numbers do not form a field. – fkraiem Jul 25 '19 at 03:55
  • Well, it is of course possible to canonically encode a real number to binary, and then use an integer representation of that number to perform a calculation. Of course, it depends on your requirements if this is useful at all as the real number would loose its original meaning within the cryptosystem. – Maarten Bodewes Jul 25 '19 at 09:49
  • I think the last part of the answer of fgrieu should answer your question on one-wayness / security. Feel free to post a more specific followup question if anything is unclear on that. Note that we have to decide on a particular scheme before we can answer if it is one-way or not. Without pinpointing a particular scheme - as there doesn't seem to be a commonly used one - the question cannot be answered. – Maarten Bodewes Jul 25 '19 at 09:54

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