Cryptography and elliptic curvesCurves on elliptic ruled surfaces?Elliptic Curves and cryptography. Recommended ReadingElliptic curves over the complex numbers: everything “well known”? Elliptic Curves and Torsion PointsElliptic Curves over Rings?Isogeny classes and elliptic curves over finite fieldsModular polynomials for elliptic curves point countingFinding cyclic subgroups of points on elliptic curves for isogeny based cryptographyIs hyperelliptic cryptography “practical”?Largest rank assumed by infinitely many elliptic curves
Cryptography and elliptic curves
Curves on elliptic ruled surfaces?Elliptic Curves and cryptography. Recommended ReadingElliptic curves over the complex numbers: everything “well known”? Elliptic Curves and Torsion PointsElliptic Curves over Rings?Isogeny classes and elliptic curves over finite fieldsModular polynomials for elliptic curves point countingFinding cyclic subgroups of points on elliptic curves for isogeny based cryptographyIs hyperelliptic cryptography “practical”?Largest rank assumed by infinitely many elliptic curves
$begingroup$
Cryptography sometimes uses elliptic curves over finite fields. Does cryptography also use elliptic curves over $mathbbQ$ or rational points on them?
nt.number-theory elliptic-curves cryptography
edited May 9 at 11:20
Matt F.
7,29211947
asked May 9 at 10:44
elliptic curveelliptic curve
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Cryptography sometimes uses elliptic curves over finite fields. Does cryptography also use elliptic curves over $mathbbQ$ or rational points on them?
nt.number-theory elliptic-curves cryptography
edited May 9 at 11:20
Matt F.
7,29211947
asked May 9 at 10:44
elliptic curveelliptic curve
1154
New contributor
elliptic curve is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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I'm not sure why this question was closed. Maybe not specific enough? Maybe the question could be phrased as "Could you point me to some literature on the use of elliptic curves over $mathbb Q$ in cryptography?" But it seems a legitimate question. I'm going to vote to reopen. If you feel it should be closed, please provide a reason.
$endgroup$
– Joe Silverman
May 9 at 12:19
add a comment |
$begingroup$
Cryptography sometimes uses elliptic curves over finite fields. Does cryptography also use elliptic curves over $mathbbQ$ or rational points on them?
nt.number-theory elliptic-curves cryptography
edited May 9 at 11:20
Matt F.
7,29211947
asked May 9 at 10:44
elliptic curveelliptic curve
1154
New contributor
elliptic curve is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Cryptography sometimes uses elliptic curves over finite fields. Does cryptography also use elliptic curves over $mathbbQ$ or rational points on them?
nt.number-theory elliptic-curves cryptography
nt.number-theory elliptic-curves cryptography
edited May 9 at 11:20
Matt F.
7,29211947
asked May 9 at 10:44
elliptic curveelliptic curve
1154
New contributor
elliptic curve is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited May 9 at 11:20
Matt F.
7,29211947
asked May 9 at 10:44
elliptic curveelliptic curve
1154
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elliptic curve is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited May 9 at 11:20
Matt F.
7,29211947
edited May 9 at 11:20
Matt F.
7,29211947
edited May 9 at 11:20
Matt F.
7,29211947
7,29211947
asked May 9 at 10:44
elliptic curveelliptic curve
1154
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elliptic curve is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked May 9 at 10:44
elliptic curveelliptic curve
1154
asked May 9 at 10:44
elliptic curveelliptic curve
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1154
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elliptic curve is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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13
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I'm not sure why this question was closed. Maybe not specific enough? Maybe the question could be phrased as "Could you point me to some literature on the use of elliptic curves over $mathbb Q$ in cryptography?" But it seems a legitimate question. I'm going to vote to reopen. If you feel it should be closed, please provide a reason.
$endgroup$
– Joe Silverman
May 9 at 12:19
add a comment |
13
$begingroup$
I'm not sure why this question was closed. Maybe not specific enough? Maybe the question could be phrased as "Could you point me to some literature on the use of elliptic curves over $mathbb Q$ in cryptography?" But it seems a legitimate question. I'm going to vote to reopen. If you feel it should be closed, please provide a reason.
$endgroup$
– Joe Silverman
May 9 at 12:19
13
13
$begingroup$
I'm not sure why this question was closed. Maybe not specific enough? Maybe the question could be phrased as "Could you point me to some literature on the use of elliptic curves over $mathbb Q$ in cryptography?" But it seems a legitimate question. I'm going to vote to reopen. If you feel it should be closed, please provide a reason.
$endgroup$
– Joe Silverman
May 9 at 12:19
$begingroup$
I'm not sure why this question was closed. Maybe not specific enough? Maybe the question could be phrased as "Could you point me to some literature on the use of elliptic curves over $mathbb Q$ in cryptography?" But it seems a legitimate question. I'm going to vote to reopen. If you feel it should be closed, please provide a reason.
$endgroup$
– Joe Silverman
May 9 at 12:19
add a comment |
1 Answer
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Not directly, as far as I know, since explicitly computing large multiples of points in $E(mathbb Q)$ is infeasible. However, people have considered lifting points from $E(mathbb F_p)$ to $E(mathbb Q)$ or to the $p$-adics $E(mathbb Q_p)$ in order to devise algorithms to solve the discrete log problem in $E(mathbb F_p)$ (although, unsuccessfully so far). Here are a few papers to get you started:
- Elliptic curve discrete logarithms and the index calculus. Advances in cryptology—ASIACRYPT'98 (Beijing), 110–125, Lecture Notes in Comput. Sci., 1514, Springer, Berlin, 1998
- The xedni calculus and the elliptic curve discrete logarithm problem. Des. Codes Cryptogr. 20 (2000), no. 1, 5–40; Analysis of the xedni calculus attack. Des. Codes Cryptogr. 20 (2000), no. 1, 41–64.
- Lifting and elliptic curve discrete logarithms, Selected Areas of
Cryptography (SAC 2008), Lecture Notes in Computer Science 5381,
Springer-Verlag, Berlin, 2009, 82--102.
answered May 9 at 11:45
Joe SilvermanJoe Silverman
31.7k189161
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1 Answer
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$begingroup$
Not directly, as far as I know, since explicitly computing large multiples of points in $E(mathbb Q)$ is infeasible. However, people have considered lifting points from $E(mathbb F_p)$ to $E(mathbb Q)$ or to the $p$-adics $E(mathbb Q_p)$ in order to devise algorithms to solve the discrete log problem in $E(mathbb F_p)$ (although, unsuccessfully so far). Here are a few papers to get you started:
- Elliptic curve discrete logarithms and the index calculus. Advances in cryptology—ASIACRYPT'98 (Beijing), 110–125, Lecture Notes in Comput. Sci., 1514, Springer, Berlin, 1998
- The xedni calculus and the elliptic curve discrete logarithm problem. Des. Codes Cryptogr. 20 (2000), no. 1, 5–40; Analysis of the xedni calculus attack. Des. Codes Cryptogr. 20 (2000), no. 1, 41–64.
- Lifting and elliptic curve discrete logarithms, Selected Areas of
Cryptography (SAC 2008), Lecture Notes in Computer Science 5381,
Springer-Verlag, Berlin, 2009, 82--102.
answered May 9 at 11:45
Joe SilvermanJoe Silverman
31.7k189161
$endgroup$
add a comment |
$begingroup$
Not directly, as far as I know, since explicitly computing large multiples of points in $E(mathbb Q)$ is infeasible. However, people have considered lifting points from $E(mathbb F_p)$ to $E(mathbb Q)$ or to the $p$-adics $E(mathbb Q_p)$ in order to devise algorithms to solve the discrete log problem in $E(mathbb F_p)$ (although, unsuccessfully so far). Here are a few papers to get you started:
- Elliptic curve discrete logarithms and the index calculus. Advances in cryptology—ASIACRYPT'98 (Beijing), 110–125, Lecture Notes in Comput. Sci., 1514, Springer, Berlin, 1998
- The xedni calculus and the elliptic curve discrete logarithm problem. Des. Codes Cryptogr. 20 (2000), no. 1, 5–40; Analysis of the xedni calculus attack. Des. Codes Cryptogr. 20 (2000), no. 1, 41–64.
- Lifting and elliptic curve discrete logarithms, Selected Areas of
Cryptography (SAC 2008), Lecture Notes in Computer Science 5381,
Springer-Verlag, Berlin, 2009, 82--102.
answered May 9 at 11:45
Joe SilvermanJoe Silverman
31.7k189161
$endgroup$
add a comment |
$begingroup$
Not directly, as far as I know, since explicitly computing large multiples of points in $E(mathbb Q)$ is infeasible. However, people have considered lifting points from $E(mathbb F_p)$ to $E(mathbb Q)$ or to the $p$-adics $E(mathbb Q_p)$ in order to devise algorithms to solve the discrete log problem in $E(mathbb F_p)$ (although, unsuccessfully so far). Here are a few papers to get you started:
- Elliptic curve discrete logarithms and the index calculus. Advances in cryptology—ASIACRYPT'98 (Beijing), 110–125, Lecture Notes in Comput. Sci., 1514, Springer, Berlin, 1998
- The xedni calculus and the elliptic curve discrete logarithm problem. Des. Codes Cryptogr. 20 (2000), no. 1, 5–40; Analysis of the xedni calculus attack. Des. Codes Cryptogr. 20 (2000), no. 1, 41–64.
- Lifting and elliptic curve discrete logarithms, Selected Areas of
Cryptography (SAC 2008), Lecture Notes in Computer Science 5381,
Springer-Verlag, Berlin, 2009, 82--102.
answered May 9 at 11:45
Joe SilvermanJoe Silverman
31.7k189161
$endgroup$
Not directly, as far as I know, since explicitly computing large multiples of points in $E(mathbb Q)$ is infeasible. However, people have considered lifting points from $E(mathbb F_p)$ to $E(mathbb Q)$ or to the $p$-adics $E(mathbb Q_p)$ in order to devise algorithms to solve the discrete log problem in $E(mathbb F_p)$ (although, unsuccessfully so far). Here are a few papers to get you started:
- Elliptic curve discrete logarithms and the index calculus. Advances in cryptology—ASIACRYPT'98 (Beijing), 110–125, Lecture Notes in Comput. Sci., 1514, Springer, Berlin, 1998
- The xedni calculus and the elliptic curve discrete logarithm problem. Des. Codes Cryptogr. 20 (2000), no. 1, 5–40; Analysis of the xedni calculus attack. Des. Codes Cryptogr. 20 (2000), no. 1, 41–64.
- Lifting and elliptic curve discrete logarithms, Selected Areas of
Cryptography (SAC 2008), Lecture Notes in Computer Science 5381,
Springer-Verlag, Berlin, 2009, 82--102.
answered May 9 at 11:45
Joe SilvermanJoe Silverman
31.7k189161
edited May 9 at 12:21
answered May 9 at 11:45
Joe SilvermanJoe Silverman
31.7k189161
answered May 9 at 11:45
Joe SilvermanJoe Silverman
31.7k189161
answered May 9 at 11:45
Joe SilvermanJoe Silverman
31.7k189161
31.7k189161
add a comment |
add a comment |
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I'm not sure why this question was closed. Maybe not specific enough? Maybe the question could be phrased as "Could you point me to some literature on the use of elliptic curves over $mathbb Q$ in cryptography?" But it seems a legitimate question. I'm going to vote to reopen. If you feel it should be closed, please provide a reason.
$endgroup$
– Joe Silverman
May 9 at 12:19