How do you find a discrete log on a calculator?

How do you find a discrete log on a calculator?

Example: Find the number n such that 7n ≡ 23 (mod 43241). Type 7 in the Base input box, 23 in the Power input box and 43241 in the Mod input box. Then press the button named “Discrete logarithm”. The result is 3360 + 3930 k.

Which algorithm is based on discrete logarithm?

While there is no publicly known algorithm for solving the discrete logarithm problem in general, the first three steps of the number field sieve algorithm only depend on the group G, not on the specific elements of G whose finite log is desired.

What is the use of discrete logarithm?

The term “discrete logarithm” is most commonly used in cryptography, although the term “generalized multiplicative order” is sometimes used as well (Schneier 1996, p. 501). In number theory, the term “index” is generally used instead (Gauss 1801; Nagell 1951, p.

Why is the discrete log problem hard?

For the discrete algorithm problem, you normally would not write the whole group (or even its multiplication table of size n2) as the input, but only some key parameters which allow calculating the group law, as well as the element of which you want to get the logarithm.

Does RSA use discrete log?

RSA labs makes a similar statement: The discrete logarithm problem bears the same relation to these systems as factoring does to the RSA system: the security of these systems rests on the assumption that discrete logarithms are difficult to compute.

What is elliptic curve discrete logarithm?

The elliptic curve discrete logarithm problem (ECDLP) is the following computational problem: Given points P, Q ∈ E(Fq) to find an integer a, if it exists, such that Q = aP. We focus on the case of elliptic curves, but occasionally this involves mention of higher genus curves and their divisor class groups.

What is discrete algorithm?

Discrete logarithms are logarithms defined with regard to multiplicative cyclic groups. The discrete logarithm problem is defined as: given a group G, a generator g of the group and an element h of G, to find the discrete logarithm to the base g of h in the group G. Discrete logarithm problem is not always hard.

What do you mean by discrete logarithm problem?

Discrete logarithms are logarithms defined with regard to multiplicative cyclic groups. The discrete logarithm to the base g of h in the group G is defined to be x . For example, if the group is Z5*, and the generator is 2, then the discrete logarithm of 1 is 4 because 24 ≡ 1 mod 5.

Is discrete log NP hard difficult?

NP…which is the most difficult open problem in theoretical computer science. Avi Wigderson has shown that there is no “natural proof” (in the sense of [RR]) that the DLP requires circuits of greater than half-exponential size.

How hard is discrete logarithm problem?

The discrete logarithm to the base g of h in the group G is defined to be x . For example, if the group is Z5*, and the generator is 2, then the discrete logarithm of 1 is 4 because 24 ≡ 1 mod 5. Discrete logarithm problem is not always hard. The hardness of finding discrete logarithms depends on the groups.

Why is RSA hard?

The RSA Assumption is that the RSA Problem is hard to solve when the modulus n is sufficiently large and randomly generated, and the plain- text M (and hence the ciphertext C) is a random integer between 0 and n − 1. The randomness of the plaintext M over the range [0,n−1] is important in the assumption.

Which elliptic curve should I use?

As you can see, the most popular (preferred) elliptic curve is NIST P-256, followed by X25519.

How hard is finding the discrete logarithm?

How hard is finding the discrete logarithm? The discrete logarithm is the same as finding b in ab = c mod N, given a, c, and N. I wonder what complexity groups (e.g. for classical and quantum computers) this is in, and what approaches (i.e. algorithms) are the best for accomplishing this task.

Which is an example of discrete logarithm in alpertron?

Example: Find the number n such that 7 n ≡ 23 (mod 43241). Type 7 in the Base input box, 23 in the Power input box and 43241 in the Mod input box. Then press the button named “Discrete logarithm”. The result is 3360 + 3930 k. As a check you can compute 7 3360 ≡ 23 (mod 43241) and 7 3930 ≡ 1 (mod 43241).

How to get rid of binary exponentiation in discrete logarithm?

A possible improvement is to get rid of binary exponentiation or log (b) factor in the second phase of the algorithm. This can be done by keeping a variable that multiplies by ‘a’ each time as ‘an’. Let’s see the program to understand more.

How are discrete logarithms defined in cyclic groups?

Discrete logarithms are logarithms defined with regard to multiplicative cyclic groups. If G is a multiplicative cyclic group and g is a generator of G, then from the definition of cyclic groups, we know every element h in G can be written as gx for some x. The discrete logarithm to the base g of h in the group G is defined to be x .