Introduction Our contributions Conclusion

Eric Brier1

Description

Niveau: Supérieur
Introduction Our contributions Conclusion Efficient Indifferentiable Hashing into Ordinary Elliptic Curves Eric Brier1 Jean-Sebastien Coron2 Thomas Icart2 David Madore3 Hugues Randriam3 Mehdi Tibouchi2,4 1Ingenico 2Universite du Luxembourg 3TELECOM-ParisTech 4Ecole normale superieure CRYPTO, 2010-08-16

• ordinary elliptic


• efficient indifferentiable


• curve over


• hashing into


• deterministic hashing


• introduction elliptic curves


• elliptic curve

Sujets

• Ingenico

Informations

• Publié par: chaeh
• Nombre de lectures: 11
• Langue: English

Extrait

Introduction

Efficient

Our contributions

Indifferentiable Elliptic

E ´ ricBrier 1 David Madore 3

Hashing Curves

Jean-S´ebastienCoron 2 Hugues Randriam 3

1 Ingenico

2 uLexe´udsrtiinevUrgmbou

3 TELECOM-ParisTech

´ 4 nelocEureieerp´sulemaor

into

Ordinary

Thomas Icart 2 Mehdi Tibouchi 2,4

CRYPTO, 2010-08-16

Conclusion

Introduction

Introduction Elliptic curves Hashing to elliptic curves Deterministic hashing

Our contributions Admissible encodings A general construction An efficient construction Side contributions

Conclusion

Our contributions

Outline

Conclusion

Introduction

Introduction Elliptic curves Hashing to elliptic curves Deterministic hashing

Our contributions Admissible encodings A general construction An efficient construction Side contributions

Conclusion

Our contributions

Outline

Conclusion

Introduction

• •

•

•

Our contributions

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

Conclusion

(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. Also come with rich structures such as pairings.

Introduction

• •

•

•

Our contributions

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

Conclusion

(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 k elliptic curve groups of order≈2 2 , keys of length≈2k. Also come with rich structures such as pairings.

Introduction

• •

•

•

Our contributions

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

Conclusion

(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. Also come with rich structures such as pairings.

Introduction

• •

•

•

Our contributions

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

Conclusion

(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. Also come with rich structures such as pairings.

Introduction

Introduction Elliptic curves Hashing to elliptic curves Deterministic hashing

Our contributions Admissible encodings A general construction An efficient construction Side contributions

Conclusion

Our contributions

Outline

Conclusion