By Stefania Cavallar, Bruce Dodson, Arjen K. Lenstra, Walter Lioen, Peter L. Montgomery (auth.), Bart Preneel (eds.)
This ebook constitutes the refereed lawsuits of the overseas convention at the conception and alertness of Cryptographic innovations, EUROCRYPT 2000, held in Bruges, Belgium, in may perhaps 2000. The 39 revised complete papers provided have been rigorously chosen from a complete of a hundred and fifty submissions in the course of a hugely aggressive reviewing strategy. The booklet is split in topical sections of factoring and discrete logarithm, electronic signatures, deepest details retrieval, key administration protocols, threshold cryptography, public-key encryption, quantum cryptography, multi-party computation and data thought, zero-knowledge, symmetric cryptography, Boolean features and undefined, balloting schemes, and circulate ciphers and block ciphers.
Read or Download Advances in Cryptology — EUROCRYPT 2000: International Conference on the Theory and Application of Cryptographic Techniques Bruges, Belgium, May 14–18, 2000 Proceedings PDF
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Additional info for Advances in Cryptology — EUROCRYPT 2000: International Conference on the Theory and Application of Cryptographic Techniques Bruges, Belgium, May 14–18, 2000 Proceedings
The size of the Jacobian is around 1041 . Such a curve is not breakable by a parallel collision 30 Pierrick Gaudry search based on the birthday paradox (variants of Rho); indeed even using the automorphism, we should compute about 263 operations in the Jacobian. We give the same indications as for the previous curve. ) 717. 5 (720) total time for collecting the relations 797 073 sec = 9 days time for writing relations on the basis 12 057 sec time for preprocessing the matrix 880 sec size of the matrix 162 873 × 162 874 total time for Lanczos 1 038 534 sec = 12 days 6 Conclusion We have proposed an algorithm for the hyperelliptic discrete log problem, which is simpler to implement and to analyze than the previous ones.
The bottom consists of a single wafer of GaAs, containing one ‘cell’ for each diﬀerent p. Each cell contains an LED, a photodetector, an A register representing the value of p, for each r corresponding to that p a B register initially loaded with a representation of r, and wiring. The top of the cylinder contains a summing photodetector that measures the total light intensity emitted by the bottom LED’s and a clocking LED that distributes the clock signal by ﬂashing at a ﬁxed clock rate. As clock signal j is received by a cell’s photodetector, the values of the B registers are decremented by one, if a resulting value represents zero the cell’s LED ﬂashes with intensity proportional to log(p), and the A register is copied to the B register representing zero.
We assume that the genus grows with and is always large enough. More precisely, if we have log , we can let vary the smoothness bound S (instead of have it ﬁxed to one), and √ we obtain a subexponential algorithm with expected running time qg [1/2 2]. This result is part of a work with Andreas Enge, where a general framework for this kind of attack is given . Acknowledgements I am most indebted to Fran¸cois Morain for many fruitful discussions and comments. I would like to thank Emmanuel Thom´e, particularly for his help for linear algebra.