The efficiency and security of a real quadratic field based key exchange protocol

Michael J. Jacobson; Renate Scheidler; Hugh C. Williams

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Jacobson, Michael J., Scheidler, Renate and Williams, Hugh C.. "The efficiency and security of a real quadratic field based key exchange protocol". Public-Key Cryptography and Computational Number Theory: Proceedings of the International Conference organized by the Stefan Banach International Mathematical Center Warsaw, Poland, September 11-15, 2000, edited by Kazimierz Alster, Jerzy Urbanowicz and Hugh C. Williams, Berlin, New York: De Gruyter, 2001, pp. 89-112. https://doi.org/10.1515/9783110881035.89

Jacobson, M., Scheidler, R. & Williams, H. (2001). The efficiency and security of a real quadratic field based key exchange protocol. In K. Alster, J. Urbanowicz & H. Williams (Ed.), Public-Key Cryptography and Computational Number Theory: Proceedings of the International Conference organized by the Stefan Banach International Mathematical Center Warsaw, Poland, September 11-15, 2000 (pp. 89-112). Berlin, New York: De Gruyter. https://doi.org/10.1515/9783110881035.89

Jacobson, M., Scheidler, R. and Williams, H. 2001. The efficiency and security of a real quadratic field based key exchange protocol. In: Alster, K., Urbanowicz, J. and Williams, H. ed. Public-Key Cryptography and Computational Number Theory: Proceedings of the International Conference organized by the Stefan Banach International Mathematical Center Warsaw, Poland, September 11-15, 2000. Berlin, New York: De Gruyter, pp. 89-112. https://doi.org/10.1515/9783110881035.89

Jacobson, Michael J., Scheidler, Renate and Williams, Hugh C.. "The efficiency and security of a real quadratic field based key exchange protocol" In Public-Key Cryptography and Computational Number Theory: Proceedings of the International Conference organized by the Stefan Banach International Mathematical Center Warsaw, Poland, September 11-15, 2000 edited by Kazimierz Alster, Jerzy Urbanowicz and Hugh C. Williams, 89-112. Berlin, New York: De Gruyter, 2001. https://doi.org/10.1515/9783110881035.89

Jacobson M, Scheidler R, Williams H. The efficiency and security of a real quadratic field based key exchange protocol. In: Alster K, Urbanowicz J, Williams H (ed.) Public-Key Cryptography and Computational Number Theory: Proceedings of the International Conference organized by the Stefan Banach International Mathematical Center Warsaw, Poland, September 11-15, 2000. Berlin, New York: De Gruyter; 2001. p.89-112. https://doi.org/10.1515/9783110881035.89

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Chapters in this book

I-VI I
Preface VII
Mathematics, cryptology, and technology IX
Table of contents XI
A survey on IQ cryptography 1
Algebraic groups and discrete logarithm 17
Fermat numbers, Wieferich and Wilson primes: computations and generalizations 29
How to distinguish hyperelliptic curves in even characteristic 49
Limitations of constructive Weil descent 59
On the security of a public-key cryptosystem 71
Optimizations for NTRU 77
The efficiency and security of a real quadratic field based key exchange protocol 89
Extending the binary gcd algorithms 113
Stochastic kleptography detection 137
An overview of the XTR public key system 151
A survey of IND-CCA secure public-key encryption schemes relative to factoring 181
Efficient point multiplication for elliptic curves over special optimal extension fields 197
Error-correcting codes and cryptography 209
Secret public key schemes 221
Index form surfaces and construction of elliptic curves over large finite fields 239
On the size of solutions of the inequality φ(ax + b) < φ(ax) 249
Security of DL-encryption and signatures against generic attacks—a survey 257
Square-root algorithms for the discrete logarithm problem (a survey) 283
Height functions on elliptic curves 303
List of participants 323
List of contributors 329

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https://doi.org/10.1515/9783110881035.89

Chapters in this book

I-VI I
Preface VII
Mathematics, cryptology, and technology IX
Table of contents XI
A survey on IQ cryptography 1
Algebraic groups and discrete logarithm 17
Fermat numbers, Wieferich and Wilson primes: computations and generalizations 29
How to distinguish hyperelliptic curves in even characteristic 49
Limitations of constructive Weil descent 59
On the security of a public-key cryptosystem 71
Optimizations for NTRU 77
The efficiency and security of a real quadratic field based key exchange protocol 89
Extending the binary gcd algorithms 113
Stochastic kleptography detection 137
An overview of the XTR public key system 151
A survey of IND-CCA secure public-key encryption schemes relative to factoring 181
Efficient point multiplication for elliptic curves over special optimal extension fields 197
Error-correcting codes and cryptography 209
Secret public key schemes 221
Index form surfaces and construction of elliptic curves over large finite fields 239
On the size of solutions of the inequality φ(ax + b) < φ(ax) 249
Security of DL-encryption and signatures against generic attacks—a survey 257
Square-root algorithms for the discrete logarithm problem (a survey) 283
Height functions on elliptic curves 303
List of participants 323
List of contributors 329

The efficiency and security of a real quadratic field based key exchange protocol

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