Elliptic Curves

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The use of elliptic curves for public-key cryptography was first suggested in 1985. After resisting decades of attacks, they started to see widespread use from around 2005, providing several benefits over previous public-key cryptosystems such as RSA.

Smaller EC keys offer greater strength, with a 256-bit EC key having the same security level as a 3072-bit RSA key. Furthermore, several operations using those keys (including signing) can be more efficient both time- and memory-wise. Finally, since ECC is more complex than RSA, it has the welcome effect of encouraging developers to make use of trusted libraries rather than rolling their own.

This course is aimed to give you an intuition for the trapdoor function behind ECC; dip your toes into the mathematical structure underlying it; and have you breaking popular schemes like ECDSA.

4299 Players Solving
618 Players Completed
620 Points to Earn


Elliptic Curves - Background Background Reading 5
Elliptic Curves - Starter Point Negation 10
Elliptic Curves - Starter Point Addition 30
Elliptic Curves - Starter Scalar Multiplication 35
Elliptic Curves - Starter Curves and Logs 40
Elliptic Curves - Starter Efficient Exchange 50
Elliptic Curves - Side Channels Montgomery's Ladder 40
Elliptic Curves - Parameter Choice Smooth Criminal 60
Elliptic Curves - Signatures Curveball 100
Elliptic Curves - Signatures ProSign 3 100
Elliptic Curves - Parameter Choice Moving Problems 150

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