Introduction Our Proof Conclusion

Description

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

Subjects

• Documents
• Education
• Fouqué
• École normale
• Elliptic curve

Informations

• Published by: pefav
• Reads: 13
• Language: English

Exrait

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)∈F 2 such that:

y 2 =x 3 +ax+b

C

(witha,b∈Ffixed 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 order≈2 2k , keys of length≈2k. 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)∈F 2 such that:

y 2 =x 3 +ax+b

C

(witha,b∈Ffixed 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 order≈2 2k , keys of length≈2k 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)∈F 2 such that:

y 2 =x 3 +ax+b

C

(witha,b∈Ffixed 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 order≈2 2k , keys of length≈2k 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)∈F 2 such that:

y 2 =x 3 +ax+b

C

(witha,b∈Ffixed 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 order≈2 2k , keys of length≈2k. Also come with rich structures such as pairings.

onclusion