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Is Elliptic Curve Discrete Logarithm Problem NP-Hard or NP-Complete

Groups where discrete logarithm is hardWhy must the order of basepoint of elliptic curve be prime?Discrete Logarithm Problem with Base 2Topics in elliptic curves over finite fieldsComparison of discrete logarithms.Prove that an algorithm that solves Basis Problem for $E[m]$ can be used to solve the ECDLP (Elliptic Curve Discrete Logarithm Problem)How do you compute order of points in elliptic curve?Isomorphisms to Additive Group of Integers to Solve ECDLPIs elliptic curve suitable for using in ECDLP?Research in the Discrete Logarithm Problem

1

$begingroup$

I have trouble classifying Elliptic Curve Discrete Logarithm Problem as NP-Hard or NP-Complete. Where does ECDLP belong? Any brief comprehensive answer is encouraged. Thanks.

elliptic-curves cryptography np-complete discrete-logarithms

share|cite|improve this question

edited Mar 13 at 22:56

Henno Brandsma

113k348122

asked Mar 13 at 7:15

EliyahEliyah

1287

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I don't think anyone knows....
  $endgroup$
  – Lord Shark the Unknown
  Mar 13 at 7:19
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @LordSharktheUnknown Why, please enlighten me?
  $endgroup$
  – Eliyah
  Mar 13 at 7:27
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  It's unknown. You'll be famous if you can prove it to be NP hard or NP complete...
  $endgroup$
  – Henno Brandsma
  Mar 13 at 16:46
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Why is it unknown? Why is it not NP-Hard?
  $endgroup$
  – Eliyah
  Mar 14 at 2:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Because there is no proof that it is or is not. There are many open problems in this area. Cryptography is based on ignorance.
  $endgroup$
  – Henno Brandsma
  Mar 15 at 18:19
  
  

  
  
  
  

add a comment | 

1

$begingroup$

I have trouble classifying Elliptic Curve Discrete Logarithm Problem as NP-Hard or NP-Complete. Where does ECDLP belong? Any brief comprehensive answer is encouraged. Thanks.

elliptic-curves cryptography np-complete discrete-logarithms

share|cite|improve this question

edited Mar 13 at 22:56

Henno Brandsma

113k348122

asked Mar 13 at 7:15

EliyahEliyah

1287

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I don't think anyone knows....
  $endgroup$
  – Lord Shark the Unknown
  Mar 13 at 7:19
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @LordSharktheUnknown Why, please enlighten me?
  $endgroup$
  – Eliyah
  Mar 13 at 7:27
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  It's unknown. You'll be famous if you can prove it to be NP hard or NP complete...
  $endgroup$
  – Henno Brandsma
  Mar 13 at 16:46
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Why is it unknown? Why is it not NP-Hard?
  $endgroup$
  – Eliyah
  Mar 14 at 2:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Because there is no proof that it is or is not. There are many open problems in this area. Cryptography is based on ignorance.
  $endgroup$
  – Henno Brandsma
  Mar 15 at 18:19
  
  

  
  
  
  

add a comment | 

$begingroup$

I have trouble classifying Elliptic Curve Discrete Logarithm Problem as NP-Hard or NP-Complete. Where does ECDLP belong? Any brief comprehensive answer is encouraged. Thanks.

elliptic-curves cryptography np-complete discrete-logarithms

share|cite|improve this question

edited Mar 13 at 22:56

Henno Brandsma

113k348122

asked Mar 13 at 7:15

EliyahEliyah

1287

$endgroup$

share|cite|improve this question

edited Mar 13 at 22:56

Henno Brandsma

113k348122

asked Mar 13 at 7:15

EliyahEliyah

1287

share|cite|improve this question

edited Mar 13 at 22:56

Henno Brandsma

113k348122

asked Mar 13 at 7:15

EliyahEliyah

1287

edited Mar 13 at 22:56

Henno Brandsma

113k348122

edited Mar 13 at 22:56

Henno Brandsma

113k348122

asked Mar 13 at 7:15

EliyahEliyah

1287

asked Mar 13 at 7:15

EliyahEliyah

1287