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# 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.<ref name="ref_dda76e85">[https://www.degruyter.com/view/journals/jmc/14/1/article-p25.xml?language=en Quasi-subfield Polynomials and the Elliptic Curve Discrete Logarithm Problem]</ref>
 
# 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.<ref name="ref_dda76e85">[https://www.degruyter.com/view/journals/jmc/14/1/article-p25.xml?language=en Quasi-subfield Polynomials and the Elliptic Curve Discrete Logarithm Problem]</ref>
 
# 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.<ref name="ref_dda76e85" />
 
# 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.<ref name="ref_dda76e85" />
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===소스===
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<references />
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== 노트 ==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q864003 Q864003]
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===말뭉치===
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# In this paper, we propose a new algorithm to solve another form of elliptic curve discrete logarithm problem with auxiliary inputs.<ref name="ref_1ae93405">[https://www.hindawi.com/journals/mpe/2016/5361695/ Research on Attacking a Special Elliptic Curve Discrete Logarithm Problem]</ref>
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# The computational problem is called elliptic curve discrete logarithm problem (ECDLP).<ref name="ref_1ae93405" />
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# This is called as Elliptic Curve Discrete Logarithm Problem.<ref name="ref_b7cf54d9">[https://sefiks.com/2018/02/28/attacking-elliptic-curve-discrete-logarithm-problem/ Solving Elliptic Curve Discrete Logarithm Problem]</ref>
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# Even though, this approach reduces the complexity dramatically, elliptic curve cryptography is still too powerful and elliptic curve discrete logarithm problem is still hard.<ref name="ref_b7cf54d9" />
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# This problem is called Elliptic Curve Discrete Logarithm Problem – or ECDLP for short.<ref name="ref_a4f4bf0b">[https://trustica.cz/en/2018/05/10/elliptic-curves-discrete-logarithm-problem/ Elliptic curves: discrete logarithm problem]</ref>
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# Along this line, we show that the elliptic curve discrete logarithm problem can be reduced to three partial lifting problems.<ref name="ref_8c292407">[https://dl.acm.org/citation.cfm?id=3118843 Partial Lifting and the Elliptic Curve Discrete Logarithm Problem]</ref>
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# 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.<ref name="ref_8c292407" />
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# Computing the private key from the public key in this kind of cryptosystem is called the elliptic curve discrete logarithm function.<ref name="ref_c7c89683">[https://blog.cloudflare.com/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/ A (Relatively Easy To Understand) Primer on Elliptic Curve Cryptography]</ref>
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# The elliptic curve discrete logarithm is the hard problem underpinning elliptic curve cryptography.<ref name="ref_c7c89683" />
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# We study the elliptic curve discrete logarithm problem over finite extension fields.<ref name="ref_89142ddf">[https://www.cambridge.org/core/journals/compositio-mathematica/article/on-the-discrete-logarithm-problem-in-elliptic-curves/59B877810708C90F6287972486A5BF0C On the discrete logarithm problem in elliptic curves]</ref>
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# We continue our study on the elliptic curve discrete logarithm problem over finite extension fields.<ref name="ref_b73936ad">[https://projecteuclid.org/euclid.ant/1513730029 Diem : On the discrete logarithm problem in elliptic curves II]</ref>
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# The security of several elliptic curve cryptosystems is based on the difficulty to compute the discrete logarithm problem.<ref name="ref_27c298e5">[https://infoscience.epfl.ch/record/52470?ln=en Computation of the discrete logarithm on elliptic curves of trace one]</ref>
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# 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.<ref name="ref_27c298e5" />
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# As an aside, Semaev’s choice of title “New algorithm for the discrete logarithm problem on elliptic curves” seems exaggerated.<ref name="ref_19a743ad">[https://ellipticnews.wordpress.com/2015/04/13/elliptic-curve-discrete-logarithm-problem-in-characteristic-two/ Elliptic curve discrete logarithm problem in characteristic two]</ref>
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# The MOV attack reduces an elliptic curve discrete logarithm to a logarithm over a finite field using the Weil pairing.<ref name="ref_dafb79a1">[https://fse.studenttheses.ub.rug.nl/22732/ The Discrete Logarithm Problem on Supersingular Elliptic Curves]</ref>
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# The discrete logarithm problem in a finite field can be solved efficiently using Index Calculus.<ref name="ref_dafb79a1" />
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# 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.<ref name="ref_8888652c">[http://lnu.diva-portal.org/smash/record.jsf?pid=diva2:1326270 On Pollard's rho method for solving the elliptic curve discrete logarithm problem]</ref>
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# 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.<ref name="ref_2465ecf2">[http://www.ipam.ucla.edu/abstract/?tid=6673&pcode=SCWS1 The height function and the elliptic curve discrete logarithm problem]</ref>
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# rho() : the discrete logarithm operation, using Pollard's rho algorithm.<ref name="ref_13740851">[https://github.com/zhangyuesai/elliptic-curve zhangyuesai/elliptic-curve: Pollard's rho algorithm for discrete logarithms on elliptic curves.]</ref>
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# 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.<ref name="ref_273c5d08">[http://www.academia.edu/Documents/in/Elliptic_Curve_Discrete_Logarithm_Problem_ECDLP_ Elliptic Curve Discrete Logarithm Problem (ECDLP) Research Papers]</ref>
 
===소스===
 
===소스===
 
  <references />
 
  <references />

2020년 12월 21일 (월) 18:39 판

노트

위키데이터

말뭉치

  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]

소스

  1. ↑ 1.0 1.1 1.2 1.3 Discrete Logarithm Problem
  2. ↑ 2.0 2.1 2.2 Discrete logarithm
  3. ↑ 3.0 3.1 Discrete Logarithms - an overview
  4. ↑ The discrete logarithm problem (video)
  5. ↑ Solving the discrete logarithm problem for a weak group
  6. ↑ On the discrete logarithm problem in elliptic curves
  7. ↑ Diem : On the discrete logarithm problem in elliptic curves II
  8. ↑ Towards Zero Knowledge Proof — 0x01 — The Discrete Logarithm problem: A constructive approach
  9. ↑ 9.0 9.1 Quasi-subfield Polynomials and the Elliptic Curve Discrete Logarithm Problem

노트

위키데이터

말뭉치

  1. In this paper, we propose a new algorithm to solve another form of elliptic curve discrete logarithm problem with auxiliary inputs.[1]
  2. The computational problem is called elliptic curve discrete logarithm problem (ECDLP).[1]
  3. This is called as Elliptic Curve Discrete Logarithm Problem.[2]
  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.[2]
  5. This problem is called Elliptic Curve Discrete Logarithm Problem – or ECDLP for short.[3]
  6. Along this line, we show that the elliptic curve discrete logarithm problem can be reduced to three partial lifting problems.[4]
  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.[4]
  8. Computing the private key from the public key in this kind of cryptosystem is called the elliptic curve discrete logarithm function.[5]
  9. The elliptic curve discrete logarithm is the hard problem underpinning elliptic curve cryptography.[5]
  10. We study the elliptic curve discrete logarithm problem over finite extension fields.[6]
  11. We continue our study on the elliptic curve discrete logarithm problem over finite extension fields.[7]
  12. The security of several elliptic curve cryptosystems is based on the difficulty to compute the discrete logarithm problem.[8]
  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.[8]
  14. As an aside, Semaev’s choice of title “New algorithm for the discrete logarithm problem on elliptic curves” seems exaggerated.[9]
  15. The MOV attack reduces an elliptic curve discrete logarithm to a logarithm over a finite field using the Weil pairing.[10]
  16. The discrete logarithm problem in a finite field can be solved efficiently using Index Calculus.[10]
  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.[11]
  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.[12]
  19. rho() : the discrete logarithm operation, using Pollard's rho algorithm.[13]
  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.[14]

소스

  1. ↑ 1.0 1.1 Research on Attacking a Special Elliptic Curve Discrete Logarithm Problem
  2. ↑ 2.0 2.1 Solving Elliptic Curve Discrete Logarithm Problem
  3. ↑ Elliptic curves: discrete logarithm problem
  4. ↑ 4.0 4.1 Partial Lifting and the Elliptic Curve Discrete Logarithm Problem
  5. ↑ 5.0 5.1 A (Relatively Easy To Understand) Primer on Elliptic Curve Cryptography
  6. ↑ On the discrete logarithm problem in elliptic curves
  7. ↑ Diem : On the discrete logarithm problem in elliptic curves II
  8. ↑ 8.0 8.1 Computation of the discrete logarithm on elliptic curves of trace one
  9. ↑ Elliptic curve discrete logarithm problem in characteristic two
  10. ↑ 10.0 10.1 The Discrete Logarithm Problem on Supersingular Elliptic Curves
  11. ↑ On Pollard's rho method for solving the elliptic curve discrete logarithm problem
  12. ↑ The height function and the elliptic curve discrete logarithm problem
  13. ↑ zhangyuesai/elliptic-curve: Pollard's rho algorithm for discrete logarithms on elliptic curves.
  14. ↑ Elliptic Curve Discrete Logarithm Problem (ECDLP) Research Papers
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