I'm new to cryptography and the associated level of maths. I'm practising past papers for an exam and found the question:

Show that the condition 4a^3 + 27b^2 ≠ 0 mod p is fulfilled for the elliptic curve y^2 ≡ x^2 + 2x + 2 mod 17.

Surely elliptic curves usually follow the format y^2 ≡ x^3 + ax + b mod p?

The x^2 has thrown me on this - can anyone clarify if this looks like a typo?

Many thanks, Paul

  • $\begingroup$ Surely the definition of an elliptic curve has been given in class. What is it? $\endgroup$ – fkraiem May 15 '18 at 11:57
  • $\begingroup$ Yes, it was given as: y^2 ≡ x^3 + ax + b mod p $\endgroup$ – Paul May 15 '18 at 12:00
  • $\begingroup$ You guessed it, what's in the question does not match your definition. My bets are on a typo. $\endgroup$ – fgrieu May 15 '18 at 12:25
  • $\begingroup$ Yes, I thought that might be the case, but as my mathematical ability is very basic, I did not want to presume anything. Thanks @fgrieu $\endgroup$ – Paul May 15 '18 at 12:33
  • $\begingroup$ In fact, the question cannot possibly be correct as stated (even if a different curve model had been introduced in class): That curve has genus $0$, hence is (by definition) certainly not an elliptic curve. $\endgroup$ – yyyyyyy May 15 '18 at 15:11

It would appear that this is a typo in the question on the past exam paper, and it should read y^2 ≡ x^3 + 2x + 2 mod 17

| improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.