I need to implement cryptographic operations starting with the curve NISTP256. I have been told to implement it using Montgomery method. I read a pfd from http://saluc.engr.uconn.edu/refs/sidechannel/okeya00elliptic.pdf. It states that the order of the curve must be divisible by 4. But the curve's order is not a multiple of 4.

So does that mean the curve cannot be implemented using Montgomery method or is there any other ways to implement it?

  • $\begingroup$ Probably your instructor (?) didn't mean the Montgomery Ladder (point multiplication algorithm) but the Montgomery method(s) for large integer arithmetic. See the HAC for reference. $\endgroup$ – SEJPM Nov 30 '15 at 14:02
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    $\begingroup$ The Montgomery ladder does exist for any group. What is not doable is to work with P-256 in Montgomery coordinates, since as @abejoe correctly points out, Montgomery curves are necessarily of order divisible by 4. $\endgroup$ – Samuel Neves Nov 30 '15 at 14:22
  • $\begingroup$ @SamuelNeves Thank you for your information. Hence I conclude that P-256 curves cannot be implemented using Montgomery method. $\endgroup$ – abejoe Dec 7 '15 at 10:03

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