What level of crypto security?

The security level for Elliptic Curve Cryptography is determined by the cardinality of the group rational points. The group order has to be known to generate secure elliptic curves. In other words: we need to pick a curve of known order.

Two main approaches to do this are:

1. Random approach

a. Pick random paramaters a and b

b. Use point counting algorithm for finding the group order

2. Complex multiplication approach

a. Define the group order candidates

b. Determine a and b using complex multiplication

I’m still digesting this dissertation about algorithm for determining cardinality to limit the complexity (whatever that means 😉 )

Will add more details on this, very soon!

[Sources: Harald Baier dissertation and Intan’s notes]

Some progress on the research

So far I divide my (dissertation) research into two main “streams” : crypto and math.

Here’s the current activities and the progress on each stream :

1. Crypto

a. Developing code in C for implementing ECC. Still working on the basics of number theory.

b. Defining metrics (cost, flexibility, security, performance, interoperability, accountability). I have met Dr. Budi Rahardjo for discussing about security metrics, and he pointed out that periodicity, randomness and avalanche effects might be the properties for measuring security.

c. Discussion about cryptosystems. I met Budi Sulis, who’s doing chaos cryptography for his doctoral research, and we discussed about chaos cryptography and elliptic curve cryptography and compared both cryptosystem.

2. Math (algebra)

a. Catching up on learning those algebra thingies

b. Doing some research on cryptosystem based on imaginary quadratic order with Intan from Math Dept.

Now about problem definition. I have already identify several problems for each layer on the picture

1. Field arithmetic implementation: optimal hw/sw combination (partitioning), interoperable and reconfigurable hardware architecture, VLSI design

2. Curve arithmetic implementation: generating and optimizing secure elliptic curve

3. Mathematical framework: theorem provers, formalize mathematics

4. Protocols and standards: (not yet)

5. Not yet categorized: attack on ecc (Pollard Rho, side channel)

Well, that’s what I have right now, but I will still revise this posting for more minor updates 🙂