Elliptic Curve Cryptography Video 2

Advance Cyber Security. Finding the coordinates of P_1+P_2 Point addition. Based on a Cubic curve with one real component

Category:

Science & Technology

Tags:

• Elliptic
• Curve
• Cryptography
• Adding
• P1
• P2

[TavarishReyes]

Mitch... Good luck in your studies, congratulations in advance for choosing ECC for your paper. I will be glad to know for final output results.

Cheers

IR

[Mitch0rs]

I am doing my master paper on encryption. We never had any classes about this type of encryption and i need to implement ECC in an FPGA. how would u connect ur endformula to encryption of data? what are the values of lamda and v?would P1 be ur data block and P2 ur key, where P1+P2 (y3 = lamda . x3 + v) would be ur encrypted data? im following with the mathmatics but not the link between the math and the implementation.

greetings Mitch

[TavarishReyes]

@Mitch0rs Hi Mitch... Take a look at NIST recommendation in regards how ECC implementation, here is a note;

NIST recommends fifteen elliptic curves. FIPS 186-3 has ten recommended finite fields:

Five prime fields for certain primes p of sizes 192, 224, 256, 384, and 521 bits. For each of the prime fields, one elliptic curve is recommended.

Five binary fields for m equal 163, 233, 283, 409, and 571. For each of the binary fields, one elliptic curve and one Koblitz curve was selected.

[TavarishReyes]

By the way

6 (Layer 6) is the coolest because it involves the applications "Secure Communications is one of the set" and in combination with the 7 layer model OSI reference model you can applied this to the TCP/IP stack. I hope this can give you an insight in regards your question. Cheers IR/>

[gohogsgo123]

Ok - I am with you on solving for P1 + P2. So how do we use this in conjunction with elliptic curve crytography?

[TavarishReyes]

@gohogsgo123 </ Good question mate, here is a personal approach, ECC is composed by 6 Layers,

1 Finite Field Arithmetic (Group Theory)

2 Elliptic Curve Arithmetic (Point Addition, Point Doubling)

3 Elliptic Curve Operation (Scalar Multiplication)

4 Elliptic Curve Primitives (**Key Generation, SecretKey{Signing}, PublicKey{Verifying}**)

5 Elliptic Curve Protocols (Diffie-Hellman, Authentication) some of this protocols are ranked as classified protocols by the NSA. (avoid 2 talk about that)

[Mitch0rs]

@TavarishReyes thx for the reply, i will take a look and see how much more questions i have tomorrow