79 Pages
English
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Introduction Our Proof Conclusion

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79 Pages
English

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Introduction Our Proof Conclusion Estimating the Size of the Image of Deterministic Hash Functions to Elliptic Curves Pierre-Alain Fouque Mehdi Tibouchi Ecole normale superieure Latincrypt, 2010-08-09

  • ecole normale

  • proof conclusion

  • curve over

  • deterministic hashing

  • order ≈

  • introduction elliptic curves

  • density theorem

  • elliptic curve


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IntroductionOurrPoof
Estimating the Size of the Image of Deterministic Hash Functions to Elliptic Curves
Pierre-Alain Fouque Mehdi Tibouchi
´ Ecolenormalesup´erieure
Latincrypt, 2010-08-09
Conclusion
Introudction
Introduction Elliptic curves Hashing to elliptic curves Deterministic hashing Icart’s conjecture
Our Proof Overview Galois groups Chebotarev density theorem Generalizations
Conclusion
OurrPofo
Outline
oCcnulisno
Introudtcoin
Introduction Elliptic curves Hashing to elliptic curves Deterministic hashing Icart’s conjecture
Our Proof Overview Galois groups Chebotarev density theorem Generalizations
Conclusion
OurProfo
Outline
oCcnulisno
nItroductionOurProfo
Elliptic curve cryptography
Ffinite field of characteristic>3 (for simplicity’s sake). Recall that an elliptic curve overFis the set of points (x,y)F2 such that:
y2=x3+ax+b
C
(witha,bFfixed parameters), together with a point at infinity. This set of points forms an abelian group where the Discrete Logarithm Problem and Diffie-Hellman-type problems are believed to be hard (no attack better than the generic ones).  forInteresting for cryptography:kbits of security, one can use elliptic curve groups of order22k, keys of length2k. Also come with rich structures such as pairings.
onclusion
IntroudctionOurProfo
Elliptic curve cryptography
Ffinite field of characteristic>3 (for simplicity’s sake). Recall that an elliptic curve overFis the set of points (x,y)F2 such that:
y2=x3+ax+b
C
(witha,bFfixed parameters), together with a point at infinity. This set of points forms an abelian group where the Discrete Logarithm Problem and Diffie-Hellman-type problems are believed to be hard (no attack better than the generic ones). Interesting for cryptography: forkbits of security, one can use elliptic curve groups of order22k, keys of length2k come. Also with rich structures such as pairings.
onclusion
nIrtoductionuOrrPoof
Elliptic curve cryptography
Ffinite field of characteristic>3 (for simplicity’s sake). Recall that an elliptic curve overFis the set of points (x,y)F2 such that:
y2=x3+ax+b
C
(witha,bFfixed parameters), together with a point at infinity. This set of points forms an abelian group where the Discrete Logarithm Problem and Diffie-Hellman-type problems are believed to be hard (no attack better than the generic ones). Interesting for cryptography: forkbits of security, one can use elliptic curve groups of order22k, keys of length2k come. Also with rich structures such as pairings.
onclusion
nIrtoudtcoinOurrPoof
Elliptic curve cryptography
Ffinite field of characteristic>3 (for simplicity’s sake). Recall that an elliptic curve overFis the set of points (x,y)F2 such that:
y2=x3+ax+b
C
(witha,bFfixed parameters), together with a point at infinity. This set of points forms an abelian group where the Discrete Logarithm Problem and Diffie-Hellman-type problems are believed to be hard (no attack better than the generic ones).  forInteresting for cryptography:kbits of security, one can use elliptic curve groups of order22k, keys of length2k. Also come with rich structures such as pairings.
onclusion