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노트

위키데이터

• ID : Q864003

말뭉치

1. The discrete logarithm to the base g of h in the group G is defined to be x .
2. 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.
3. That's why we always want p to be a safe prime when using Z p * as the basis of discrete logarithm based crypto-systems.
4. This guarantees that p-1 = 2q has a large prime factor so that the Pohlig–Hellman algorithm cannot solve the discrete logarithm problem easily.
5. Other base-10 logarithms in the real numbers are not instances of the discrete logarithm problem, because they involve non-integer exponents.
6. Can the discrete logarithm be computed in polynomial time on a classical computer?
7. The discrete logarithm problem is considered to be computationally intractable.
8. In designing public-key cryptosystems, two problems dominate the designs: the integer factorization problem and the discrete logarithm problem.
9. In the next part of the chapter, we will take a look at the discrete logarithm problem and discuss its application to cryptography.
10. This is called the discrete logarithm problem.
11. I was reading an answer about an attack on a weak group for the discrete logarithm problem and wanted to formalize and verify that the attack was correct.
12. We study the elliptic curve discrete logarithm problem over finite extension fields.
13. We continue our study on the elliptic curve discrete logarithm problem over finite extension fields.
14. Crypto-schemes where the Discrete Logarithm problem is hard are known as ElGamal crypto-schemes.
15. The hardness of the discrete logarithm problem (DLP) in cyclic groups has been one of the key mathematical problems underlying many public key cryptosystems in use today.
16. Apart from the above mentioned links to efficient attacks on the elliptic curve discrete logarithm problem, this problem is an interesting mathematical problem in its own right.

노트

위키데이터

• ID : Q864003

말뭉치

1. In this paper, we propose a new algorithm to solve another form of elliptic curve discrete logarithm problem with auxiliary inputs.
2. The computational problem is called elliptic curve discrete logarithm problem (ECDLP).
3. This is called as Elliptic Curve Discrete Logarithm Problem.
4. Even though, this approach reduces the complexity dramatically, elliptic curve cryptography is still too powerful and elliptic curve discrete logarithm problem is still hard.
5. This problem is called Elliptic Curve Discrete Logarithm Problem – or ECDLP for short.
6. Along this line, we show that the elliptic curve discrete logarithm problem can be reduced to three partial lifting problems.
7. Should the elliptic curve discrete logarithm problem admit no subexponential time attack, then our results suggest that gaining partial information about lifting would be at least as hard.
8. Computing the private key from the public key in this kind of cryptosystem is called the elliptic curve discrete logarithm function.
9. The elliptic curve discrete logarithm is the hard problem underpinning elliptic curve cryptography.
10. We study the elliptic curve discrete logarithm problem over finite extension fields.
11. We continue our study on the elliptic curve discrete logarithm problem over finite extension fields.
12. The security of several elliptic curve cryptosystems is based on the difficulty to compute the discrete logarithm problem.
13. The motivation of using elliptic curves in cryptography is that there is no known sub-exponential algorithm which solves the Elliptic Curve Discrete Logarithm Problem (ECDLP) in general.
14. As an aside, Semaev’s choice of title “New algorithm for the discrete logarithm problem on elliptic curves” seems exaggerated.
15. The MOV attack reduces an elliptic curve discrete logarithm to a logarithm over a finite field using the Weil pairing.
16. The discrete logarithm problem in a finite field can be solved efficiently using Index Calculus.
17. Cryptosystems based on elliptic curves are in wide-spread use, they are considered secure because of the difficulty to solve the elliptic curve discrete logarithm problem.
18. From the inception of elliptic curve cryptography it has been suggested that the height function on elliptic curves provides a barrier to solving the elliptic curve discrete logarithm problem.
19. rho() : the discrete logarithm operation, using Pollard's rho algorithm.
20. This paper introduces a new proxy signcryption scheme based on the Discrete Logarithm Problem (DLP) with a reduced computational complexity compared to other schemes in literature.