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  1. The discrete logarithm to the base g of h in the group G is defined to be x .[1]
  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.[1]
  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.[1]
  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.[1]
  5. Other base-10 logarithms in the real numbers are not instances of the discrete logarithm problem, because they involve non-integer exponents.[2]
  6. Can the discrete logarithm be computed in polynomial time on a classical computer?[2]
  7. The discrete logarithm problem is considered to be computationally intractable.[2]
  8. In designing public-key cryptosystems, two problems dominate the designs: the integer factorization problem and the discrete logarithm problem.[3]
  9. In the next part of the chapter, we will take a look at the discrete logarithm problem and discuss its application to cryptography.[3]
  10. This is called the discrete logarithm problem.[4]
  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.[5]
  12. We study the elliptic curve discrete logarithm problem over finite extension fields.[6]
  13. We continue our study on the elliptic curve discrete logarithm problem over finite extension fields.[7]
  14. Crypto-schemes where the Discrete Logarithm problem is hard are known as ElGamal crypto-schemes.[8]
  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.[9]
  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.[9]

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  • [{'LOWER': 'discrete'}, {'LEMMA': 'logarithm'}]