What do you mean by discrete logarithm?
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.
How do you do discrete logs?
Finding a discrete logarithm can be very easy. For example, say G = Z/mZ and g = 1. More specifically, say m = 100 and t = 17. Then logg t = 17 (or more precisely 17 mod 100).
Why are discrete logs 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.
What is discrete logarithm and when can we define it for a set of numbers?
If is an arbitrary integer relatively prime to and is a primitive root of , then there exists among the numbers 0, 1, 2., , where is the totient function, exactly one number such that. The number is then called the discrete logarithm of with respect to the base modulo and is denoted.
How is discrete logarithm evaluated for a number?
of k by evaluating the discrete logarithm k = loga r, and then compute m ≡ t · b−k (mod p), or she could compute Bob’s value of d by evaluating d = loga b and then compute m the same way Bob does.
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.
Are logarithms discrete or continuous?
Therefore, logarithms are part of discrete and continuous mathematics as they help in modeling different situations of discrete and continuous mathematical problems. Logarithms are not just a tool for finding the logarithmic function; they are used in many different contexts to model and solve problems in mathematics.
What is discrete log in polynomial time?
Can the discrete logarithm be computed in polynomial time on a classical computer? (more unsolved problems in computer science) The discrete logarithm problem is considered to be computationally intractable. That is, no efficient classical algorithm is known for computing discrete logarithms in general.
Which is better ECC or RSA?
The foremost benefit of ECC is that it’s simply stronger than RSA for key sizes in use today. The typical ECC key size of 256 bits is equivalent to a 3072-bit RSA key and 10,000 times stronger than a 2048-bit RSA key! To stay ahead of an attacker’s computing power, RSA keys must get longer.
Which one is better RSA or ECC?
ECC is more secure than RSA and is in its adaptive phase. Its usage is expected to scale up in the near future. RSA requires much bigger key lengths to implement encryption. ECC requires much shorter key lengths compared to RSA.
What is the difference between ECC and RSA?
The primary difference between RSA vs ECC certificates is in the encryption strength. Elliptic Curve Cryptography (ECC) provides an equivalent level of encryption strength as RSA (Rivest-Shamir-Adleman) algorithm with a shorter key length.