ECC: A lightweight means to secure transaction in insecure world

Introduction

Laymen explanation

If you have ever paid for anything (purchase etc) online (via internet), you must be puzzled about safety and security. Will someone else know about my personal info? Will someone make a fake transaction and you need to pay? You might be relaxed since many people surrounding are doing online transaction.

Now, your curious mind will ask many questions. How your safety and security is ensured? This article will help your to understand Elliptic curve cryptography role in this.

Technical explanation

As the wireless industry explodes, it faces a growing need for security. Applications in sectors of the economy such as healthcare, financial services, and government depend on the underlying security already available in the wired computing environment. Both for secure (authenticated, private) Web transactions and for secure (signed, encrypted) messaging, a full and efficient public key infrastructure is needed.

Three basic choices for public key systems are available for these applications:

• RSA

• Diffie-Hellman (DH) or Digital Signature Algorithm (DSA) modulo a prime p

• Elliptic Curve Diffie-Hellman (ECDH) or Elliptic Curve Digital Signature Algorithm (ECDSA)

The primary benefit promised by ECC is a smaller key size, reducing storage and transmission requirements, i.e. that an elliptic curve group could provide the same level of security afforded by an RSA-based system with a large modulus and correspondingly larger key.

Intuitive mathematics

One of the most important basis of security in cryptography is giving hackers no choice other than brute force approach of attack. It means that the crypto system should be designed in such a way that no shortcut is possible to attack. Unsolved mathematical problems are loved due to this. RSA, ECC, Diffie-hallman all relies on such unsolved mathematical problems.

Also, Design must consider other requirements like secrets should not be guessable. Due to this, randomness is highly important in ECC.

Now, The way we can play with numbers in real life (add/subtract), ECC should also allow it. Due to this, it is important that ECC curve must satisfy mathematical group property.

Example ECC curves

For current cryptographic purposes, an elliptic curve is a plane curve over a finite field (rather than the real numbers) which consists of the points satisfying the equation

along with a distinguished point at infinity, denoted ∞. (The coordinates here are to be chosen from a fixed finite field of characteristic not equal to 2 or 3, or the curve equation will be somewhat more complicated.)

This set together with the group operation of elliptic curves is an Abelian group, with the point at infinity as identity element.

Security body like NIST provides elliptic curve parameters.

Reference

https://en.wikipedia.org/wiki/Elliptic_curve_cryptography

http://www.msr-waypoint.com/en-us/um/people/klauter/ieeefinal.pdf

http://crypto.stackexchange.com/questions/10263/should-we-trust-the-nist-recommended-ecc-parameters

https://www.linkedin.com/pulse/ecc-lightweight-means-secure-transaction-insecure-world-deepak-kumar/?trackingId=ZFi1TtcqSUqX9aK7NMQeOA%3D%3D