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Okay, so letamp;#39;s look at an important area of cryptography and that is related to pairing-based cryptography and as weamp;#39;ll find this is an area thatamp;#39;s used within a whole lot of privacy observing methods and within public-key encryption So, first, weamp;#39;ll start off with the basics of elliptic curves. Elliptic curves are used extensively in our security industry. Elliptic curve cryptography (ECC) is at the core of methods such as the ECDH (Elliptic Curve Diffie-Hellman) and ECDSA (Elliptic Curve Digital Signature Algorithm) and EdDSA. This is a key exchange method (KEM) and these are digital signature methods. So how does elliptic curve cryptography actually work? Well, we start off with an equation such as this and we created within a finite field so that we have a prime number of p. So, for example, with Curve 25519 this is 2 to the power of 255 minus 19. So we use a prime number and this equation here and we end up with a series of
