I will just scribble notes here about what I got from the regular discussion today:
- Is it relevant to observe the input and output class groups? Which condition regarding to this correslation should be considered as “secure”?
- How many class numbers will be needed to be consedered as “secure”? How does the number affects the security? Any research on that?
- Generating curve, then choose the generator, or vice versa? Observe the effect of applying different generators
- Is it possible (if possible, is it necessary?) to apply some feedback to the system?
- Find the most convenient way to convert plaintext to point in ECC
- Find out more about cryptanalysis on ECC
- Getting ready for quals! QUALS!!!
I’m now building some simple codes for converting plain text character to a point on an elliptic curve.
Here’s how I’m gonna do it, based on Mike Rosing’s hints:
- Take the data, and treat it as an x value
- If x value fit on the curve, then find y. Each x value has two y values associated with it.
- If x value does not fit on the curve, add extra bits to the data (but make sure not to mess with the raw data)
- Check again
- Repeat until the combination of the raw data and extra bits does fit on the curve.
To get the x value back, just mask off the extra bits to recover the raw data.
Going to give a presentation at the Math Dept. tomorrow. Talking about cryptography and ECC and ECDLP. Will avoid explaining about those math equations, otherwise the students will eat me alive, hi hi hi
Wish me luck 
After spending hours googling and reading some pdf and presentation files, I still cannot find the correlation between the term “diffusion” with ECC.
For now I do really think that the term “diffusion” is only for symmetric-key system.
Will find out more about it later. Hmmm….
To make sure that your cryptosystem is secure, then you have to do cryptanalysis.
The known attacks for ECC are:
* The Pohlig-Hellman algorithm (which reduces the problem to subgroups of prime order)
* Shanks’ baby-step-giant-step method
* Pollard’s methods, the rho method and the kangaroo method, both of which have parallel versions due to van Oorschot and Wiener
* The Menezes-Okamoto-Vanstone (MOV) attack using the Weil pairing
* The Frey-Rueck attack using the Tate pairing
* The attacks on anomalous elliptic curves (i.e., elliptic curves over F_p which have p points) due to Semaev, Satoh-Araki and Smart
* Weil descent (for some special finite fields)
* Algebro-geometric attack
Next step will be to choose which attacks to be used for measuring the level of security of ECC.
Diffusion means many bits of the plaintext (possibly all) affect each bit of the ciphertext.
Confusion means there is a low statistical bias of bits in the ciphertext.
Question: the diffusion behaviour for ECC in encryption process?
What is the relationship of randomness with ECC? Which part of ECC has property of randomness?
1. From the discussion with Intan:
- Updating the topics of our research (while still looking for any similar works on these topics)
- She gave my premises and hypothesis document some revisions
- Agreed to add a member to our research proposal (three heads are better than two )
2. From the discussion with Dr. Budi Rahardjo, Budi Sulis and Primus:
- Why singular and supersingular elliptic curves are avoided?
- What is the connection between ECC and randomness?
- (My) hypothesis #2 is trivial
. How to prove that? What’s the strategy?
- How do you define a curve based of the known order?
- Budi Sulis let me to keep this book that I had been looking for! Thanks!
Well, after wandering around trying to find a topic that suit both me and Intan, we then agreed that we will keep doing our research and support each other.
More about it here.
It’s the time to be aware, and respond to THIS!!!
Let’s go into action!
