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#include double AttackerSuccessProbability(double q, int z)

{

double p = 1.0 - q;

double lambda = z * (q / p);

double sum = 1.0;

int i, k;

for (k = 0; k <= z; k++)

{

double poisson = exp(-lambda);

for (i = 1; i <= k; i++)

poisson *= lambda / i;

sum -= poisson * (1 - pow(q / p, z - k));

}

return sum;

}

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z=1 P=0.2045873

z=2 P=0.0509779

z=3 P=0.0131722

z=4 P=0.0034552

z=5 P=0.0009137

z=6 P=0.0002428

z=7 P=0.0000647

z=8 P=0.0000173

z=9 P=0.0000046

z=10 P=0.0000012

µ±q=0.3ʱ

z=0 P=1.0000000

z=5 P=0.1773523

z=10 P=0.0416605

z=15 P=0.0101008

z=20 P=0.0024804

z=25 P=0.0006132

z=30 P=0.0001522

z=35 P=0.0000379

z=40 P=0.0000095

z=45 P=0.0000024

z=50 P=0.0000006

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W Dai£¨´÷ࣩ,a scheme for a group of untraceable digital pseudonyms to pay each other with money and to enforce contracts amongst themselves without outside help£¨Ò»ÖÖÄܹ»½èÖúµç×Ó¼ÙÃûÔÚȺÌåÄÚ²¿Ï໥֧¸¶²¢ÆÈʹ¸öÌå×ñÊØ¹æÔòÇÒ²»ÐèÒªÍâ½çЭÖúµÄµç×ÓÏÖ½ð»úÖÆ£©, ¡°B-money¡±, http://www.weidai.com/bmoney.txt, 1998?

H. Massias, X.S. Avila, and J.-J. Quisquater, ¡°Design of a secure timestamping service with minimal trust requirements,¡±£¨ÔÚ×îС»¯ÐÅÈεĻù´¡ÉÏÉè¼ÆÒ»ÖÖʱ¼ä´Á·þÎñÆ÷£© In 20th Symposium on Information Theory in the Benelux, May 1999.?

S. Haber, W.S. Stornetta, ¡°How to time-stamp a digital document,¡± £¨ÔõÑùΪµç×ÓÎļþÌí¼Óʱ¼ä´Á£©In Journal of Cryptology, vol 3, No.2, pages 99-111, 1991.?

D. Bayer, S. Haber, W.S. Stornetta, ¡°Improving the efficiency and reliability of digital time-stamping,¡±£¨ÌáÉýµç×Óʱ¼ä´ÁµÄЧÂʺͿɿ¿ÐÔ£© In Sequences II: Methods in Communication, Security and Computer Science, pages 329-334, 1993.?

S. Haber, W.S. Stornetta, ¡°Secure names for bit-strings,¡±£¨±ÈÌØ×Ö´®µÄ°²È«ÃüÃû£© In Proceedings of the 4th ACM Conference on Computer and Communications Security, pages 28-35, April 1997. on Computer and Communications Security, pages 28-35, April 1997.?

A. Back, ¡°Hashcash ¨C a denial of service counter-measure,¡±£¨¹þÏ£Ïֽ𡪡ª¾Ü¾ø·þÎñʽ¹¥»÷µÄ¿ËÖÆ·½·¨£©http://www.hashcash.org/papers/hashcash.pdf, 2002.?

R.C. Merkle, ¡°Protocols for public key cryptosystems,¡± £¨¹«Ô¿ÃÜÂëϵͳµÄЭÒ飩In Proc. 1980 Symposium on Security and Privacy, IEEE Computer Society, pages 122-133, April 1980.

S. Haber, W.S. Stornetta, ¡°Secure names for bit-strings,¡±£¨±ÈÌØ×Ö´®°²È«ÃüÃû£© In Proceedings of the 4th ACM Conference on Computer and Communications Security, pages 28-35, April 1997. on Computer and Communications Security, pages 28-35, April 1997.

H. Massias, X.S. Avila, and J.-J. Quisquater, ¡°Design of a secure timestamping service with minimal trust requirements,¡±£¨ÔÚ×îС»¯ÐÅÈεÄÌõ¼þÏÂÉè¼ÆÒ»ÖÖʱ¼ä´Á·þÎñÆ÷£© In 20th Symposium on Information Theory in the Benelux, May 1999.?

W. Feller, ¡°An introduction to probability theory and its applications,¡± £¨¸ÅÂÊѧÀíÂÛÓëÓ¦Óõ¼ÂÛ£©1957?

 

   
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