Elliptic curves are mathematical structures that can be used for cryptography. They are curves defined by cubic equations that form groups of points. Elliptic curve cryptography allows for shorter encryption keys compared to other methods, using fewer memory and processing resources while providing equivalent security.

1. Elliptic Curve Protocol

2. What are elliptic curves?
• An elliptic curve is a curve that's also
naturally a group.
• Elliptic curves appear in many diverse
areas of mathematics, ranging from
number theory to complex
analysis, and from cryptography to
mathematical physics.
• Ref: Joseph H. Silverman, Computational Number Theory and
• Applications to Cryptography
• University of Wyoming
• June 19 July 7, 2006

3. In simple words
• Elliptic curve is the set of points, that are
generated from the formula:
Y² = x³ + ax + b
Where 4a³ + 27 b² ≠ 0.
a&b Є K : 1. R : real Numbers
2. Q : Rational Numbers
3. C : Complex Numbers
4. Z /pZ : integer Modulres

4. What it looks like?

5. What it looks like?

6. What it looks like?

7. What it looks like?

8. Why Elliptic Curves…?
• Shorter encryption keys use fewer memory
and CPU resources.