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What is the discrete logarithm problem on the elliptic curve?

Formally, the elliptic curve discrete logarithm problem (ECDLP) is the problem of finding an integer value e within the bounds of 1 and the number of points on the elliptic curve (which ~= the order of the finite cyclic group), such that the scalar multiplication of a primitive element G with e, i.e. eG, produces

What are the weaknesses of ECC?

The main disadvantage of ECC is that it isnt easy to securely implement. Compared to RSA, which is much simpler on both the verification and encryption sides, ECC is a steeper learning curve and a bit slower for accumulating actionable results.

What are the weakness of elliptic curves?

If your curve has as many points as your field has elements then the ECDLP can be broken easily. The number of points is dictated by A and B. Other weak curves are the supersingular ones where you can use Index-Calculus for breaking ECDLP.

Can elliptic curve cryptography be broken?

Quantum computing attack Shors algorithm can be used to break elliptic curve cryptography by computing discrete logarithms on a hypothetical quantum computer. The latest quantum resource estimates for breaking a curve with a 256-bit modulus (128-bit security level) are 2330 qubits and 126 billion Toffoli gates.

What is the difficulty of the discrete logarithm problem?

So while the DLP is generally considered a hard problem, its difficulty really depends not on the order of the group (or its structure), but on how the group is explicitly rep- resented. Every group of prime order p is isomorphic to Z/pZ; computing the discrete logarithm amounts to computing this isomorphism.

What is the ECDLP explained?

The ECDLP is a special case of the discrete logarithm problem in which the cyclic group G is represented by the group of points on an elliptic curve. It is of cryptographic interest because its apparent intractability is the basis for the security of elliptic curve cryptography.

What are the disadvantages of ECDSA?

A drawback of ECDSA is that it is complex to implement, whereas RSA is more easily set-up in comparison. The simplicity of RSA is often a draw to organizations, as it offer less roadblocks in its set-up.

Why is ECC hard to break?

ECC is considered more secure than RSA, because RSA is based on factoring large numbers, a problem that computers have solved. In contrast, elliptic curve cryptography is based on the discrete logarithm problem, which is much harder to solve.

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