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# Elliptic Curve Cryptography (ECC) - Science topic

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Questions related to Elliptic Curve Cryptography (ECC)

I need the difference between Schnorr and ECC in a little bit detail, theoretical and practical. What is the difference in both of the properties like execution time, key sizes, and message sizes?

In ECDH, when two person wants to share private key, they first select a point G on elliptic curve and after that, each of them pick a random integer a and b, respectively, and multiply with G. After the multiplication each of them shares aG and bG with each other and after that, they multiply again using their keys a(bG) and b(aG), respectively, and creates a shared key between themselves. However, if one person wants to communicate with a group of person (more than 2) using a shared key utilizing ECDH, how he can use this method? because each of the person may choose different integer while establishing the key.

How to employ ECDH in key exchange with a group of people?

I am trying to implement an experiment to verify the performance of some public key algorithms, in an attempt to evaluate the importance of Elliptic Curve Cryptography (ECC) over other public key crypto-system..

I study these terms in

1- Elliptic Curve Cryptography (ECC)

2- Discrete Logarithmic Problem (DLP)

3- Diffie-Hellman Technique

But I don't know the procedure for a protocol that could verifiably protect in the random oracle model against the hardness assumptions of the aforesaid 3 techniques.

With the invention of quantum computers, the existing cryptosystems may be broken in the future. This has attracted a new crytosystem known as Quantum Cryptography (QC). What are the advantages of QC over ECC? What are the disadvantages compared to ECC?

Please, which is more computationally efficient, Modular exponentiation or Elliptic curve scalar multiplication (ECSM)?

If A1,...,An be users in a network , and they want to use El-Gamal cryptosystem for their cryptography . I want to know what amount of memory used for the job better for every one of A1 , ... , An. for example n=2^10 . In fact in this example how many initial points is better to use ??

For example If I use about 100 initial point in my program and If keys sizes are 512 bits , 2*100*2^10*512 bits memory need for every users . 2^20*100 bits = 12.5 MB !!! Is it colophon & reasonable ?

Thank you all .

In imaginary quadratic fields we have:

* ELL(O_K) : = {elliptic curves E/C with End(E) ∼= O_K}/{isomorphism over C}

∼= {lattices L with End(L) ∼= OK}/{homothety}∼=ideal class group CL(K)

* #CL(K)=#ELL(O_K)

this notation at the papper :A SUMMARY OF THE CM THEORY OF ELLIPTIC CURVES

JAYCE GETZ

I try to search one paper between 2014-2016 talk about encrypt the data in cloud computing using ECDH + ANN. Thanks

How are eigen values and eigen vectors connected with elliptic curve cryptography?

Dear all,

I'd like to know how many joules a scalar multiplication in the ECDLP of ECC is needed?

Best regards

It could be thought this question as a different approach if it is compared with research recently.

I have a new method, so the comparison among methods play a crucial role in improving this method.

I want to determine the number of points on E in terms of æ and ß. For example:

For Koblitz curves one can compute this cardinality using a Lucas sequence but I am working in Elliptic curves over F_{2

^{n}} (not necessary Koblitz curves) given by the equation Y^{2}+ XY = X^{3}+ æX^{2}+ ß where æ and ß are elements in F_{2^{n}} and Tr(æ) = 1.Up to date, multiplication algorithm are considering two-operation multiplication. For multiple-operation multiplication, it is not discussed in the liternature. The existing subquadratic algorithm such as karatsuba algorithm, cook-took algorithm, and winograd FFT, are discussed on two-operation multiplication. multiple-operation multiplications have achieved fast algorithm for computing inversion, exponentiation, and even for point addition, due to these applications is performed by succesive multiplication.

I want to know about process of encryption and decryption of a database by using elliptic curve cryptography.

I want to know the possible attacks over ECC-based cryptographic algorithms and the weakness that allows such attacks.

I need to know if there is such that relation in the case of real quadratic fields.

Mainly at the doubling of point at Yp=0.

If we consider O(point at infinity) as (0,0) then it must hold P+O=P.

Suppose we take P(3,10) + O(0,0) and perform additive property of ECC then point comes is (3,13) rather than (3,10). What to do in this case?