What is discrete algorithm in cryptography?

For example, a popular choice of groups for discrete logarithm based crypto-systems is Zp* where p is a prime number. However, if p−1 is a product of small primes, then the Pohlig–Hellman algorithm can solve the discrete logarithm problem in this group very efficiently.

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.

Why is discrete logarithm problem hard?

However, in general the discrete logarithm problem is still considered to be hard. In particular, this is the case for the multiplicative group of finite fields with medium to large characteristic and for the additive group of a general elliptic curve.

How do you solve a discrete logarithm?

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).

Is discrete log NP hard difficult?

The subset of NP to which all problems in NP can be reduced, i.e. the subset of NP that is NP-hard. All problems which are in NP but neither in P nor in NPC.

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 the importance of discrete logarithms?

Aside from the intrinsic interest that the problem of computing discrete logarithms has, it is of considerable importance in cryptography. An efficient algorithm for discrete logarithms would make several authentication and key-exchange systems insecure.

Does RSA use factorization?

The reason factorization remains a challenging prob- lem is the size of numbers that are used in crypto-systems such as RSA. Currently the largest number that has been factored is 768 bits (232 decimal digits). RSA keys are generally at least 1024 bits long (309 dec- imal digits).

Whats is RSA?

Responsible service of alcohol (known as RSA) training is a form of education provided to servers and sellers of alcohol to prevent intoxication, drunk driving and underage drinking.

Who broke RSA?

Researchers crack the world’s toughest encryption by listening to the tiny sounds made by your computer’s CPU. Security researchers have successfully broken one of the most secure encryption algorithms, 4096-bit RSA, by listening — yes, with a microphone — to a computer as it decrypts some encrypted data.

Is RSA based on discrete log?

How much is an RSA?

Here are the costs to complete your RSA, including our discounts: Queensland, Western Australia, South Australia, ACT, TAS, Northern Territory: $24 online. Victoria: $50 to $150 online only during Covid 19 Pandemic. New South Wales: $125 online and $150 in classroom.