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  • ืชืžื•ื ืช ื”ืกื•ืคืจ/ืชRon

ื‘ื™ื˜ืงื•ื™ืŸ: ืžืขืจื›ืช ืฉื™ืชื•ืคื™ืช ืœื›ืกืฃ ืืœืงื˜ืจื•ื ื™

ืžื” ื–ื” ื‘ื™ื˜ืงื•ื™ืŸ? BTC, ืื™ืš ื”ื•ื ืขื•ื‘ื“, ืžื” ื ืžืฆื ืžืื—ื•ืจื™ื• ื•ืœืžื” ืื ืฉื™ื ืงื•ื ื™ื ืื•ืชื•?

ืชืฉื•ื‘ื•ืช ืœื›ืœ ื”ืฉืืœื•ืช ืชืžืฆืื• ื‘ืžืืžืจ ื”ื‘ื.



ื‘ืงืฆืจื”, ื’ืจืกื” ืฉื™ืชื•ืคื™ืช ืœื—ืœื•ื˜ื™ืŸ ืฉืœ ื›ืกืฃ ืืœืงื˜ืจื•ื ื™ ืชืืคืฉืจ ืœืฉืœื•ื— ืชืฉืœื•ืžื™ื ืžืงื•ื•ื ื™ื

ื™ืฉื™ืจื•ืช ืžืฆื“ ืื—ื“ ืœืฉื ื™ ืžื‘ืœื™ ืœืขื‘ื•ืจ ื“ืจืš ืžื•ืกื“ ื›ืกืคื™. ื—ืชื™ืžื•ืช ื“ื™ื’ื™ื˜ืœื™ื•ืช ืžื”ื•ื•ืช ื—ืœืง

ืžื”ืคื™ืชืจื•ืŸ, ืื•ืœื ืขื™ืงืจ ื”ืชื•ืขืœืช ืชืื‘ื“ ืื ืฆื“ ืฉืœื™ืฉื™ ื ืืžืŸ ืขื“ื™ื™ืŸ ื“ืจื•ืฉ ื›ื“ื™ ืœืžื ื•ืข ื ื™ืฆื•ืœ

ื›ืคื•ืœ. ืื ื• ืžืฆื™ืขื™ื ืคื™ืชืจื•ืŸ ืœื‘ืขื™ื™ืช ื”ื ื™ืฆื•ืœ ื”ื›ืคื•ืœ ื”ืžืฉืชืžืฉ ื‘ืจืฉืช ืฉื™ืชื•ืคื™ืช. ื”ืจืฉืช ืžื™ื™ืฆืจืช

ื—ื•ืชืžื•ืช ื–ืžืŸ ืขื‘ื•ืจ ืคืขื•ืœื•ืช ืขืœ ื™ื“ื™ ื’ื™ื‘ื•ื‘ืŸ ืœืฉืจืฉืจืช ืžืชืžืฉื›ืช ืฉืœ ื”ื•ื›ื—ืช ืขื‘ื•ื“ื”, ื•ื‘ื›ืš

ืžื ื”ืœืช ืจื™ืฉื•ื ืฉืื™ื ื• ื ืชื•ืŸ ืœืฉื™ื ื•ื™ ืœืœื ืฉื—ื–ื•ืจ ื”ื•ื›ื—ืช ื”ืขื‘ื•ื“ื”. ื”ืฉืจืฉืจืช ื”ืืจื•ื›ื” ื‘ื™ื•ืชืจ

ืžืฉืžืฉืช ืœื ืจืง ื›ื”ื•ื›ื—ื” ืฉืœ ืกื“ืจ ื”ืื™ืจื•ืขื™ื ืฉื ืฆืคื•, ืืœื ื’ื ื”ื•ื›ื—ื” ืฉื”ื™ื ื”ื’ื™ืขื” ืžื”ืจื™ื›ื•ื–

ื”ื’ื“ื•ืœ ื‘ื™ื•ืชืจ ืฉืœ ื›ื•ื— ื—ื™ืฉื•ื‘ื™. ื›ืœ ืขื•ื“ ืžืจื‘ื™ืช ื›ื•ื— ื”ื—ื™ืฉื•ื‘ ื ืฉืœื˜ ืขืœ ื™ื“ื™ ืฆืžืชื™ื ืฉืื™ื ื

ืžืฉืชืคื™ื ืคืขื•ืœื” ื›ื“ื™ ืœืชืงื•ืฃ ืืช ื”ืจืฉืช, ื”ื ื™ื™ืฆืจื• ืืช ื”ืฉืจืฉืจืช ื”ืืจื•ื›ื” ื‘ื™ื•ืชืจ ื•ื™ืขืœื• ื‘ืงืฆื‘

ืขืœ ืชื•ืงืคื™ื. ื”ืจืฉืช ืขืฆืžื” ื“ื•ืจืฉืช ืžื‘ื ื” ืžื–ืขืจื™. ื”ื•ื“ืขื•ืช ืžื•ืคืฆื•ืช ืขืœ ื‘ืกื™ืก ืžื™ื˜ื‘ ื”ืžืืžืฆื™ื,

ื•ืฆืžืชื™ื ื™ื›ื•ืœื™ื ืœืขื–ื•ื‘ ืืช ื”ืจืฉืช ื•ืœื”ืฆื˜ืจืฃ ืืœื™ื” ื›ืจืฆื•ื ื, ื•ืœืงื‘ืœ ืืช ืฉืจืฉืจืช ื”ื•ื›ื—ืช

ื”ืขื‘ื•ื“ื” ื”ืืจื•ื›ื” ื‘ื™ื•ืชืจ ื›ื”ื•ื›ื—ื” ืฉืœ ืžื” ืฉืงืจื” ื‘ื–ืžืŸ ื”ื™ืขื“ืจื•ืชื.


1. ืžื‘ื•ื ืœืงืจื™ืคื˜ื•

ืžืกื—ืจ ื‘ืื™ื ื˜ืจื ื˜ ื›ื™ื•ื ืžืกืชืžืš ื‘ืื•ืคืŸ ื›ืžืขื˜ ื‘ืœืขื“ื™ ืขืœ ืžื•ืกื“ื•ืช ื›ืกืคื™ื™ื ื”ืžืฉืžืฉื™ื ื›ืฆื“ ืฉืœื™ืฉื™ ื ืืžืŸ

ืœืขื™ื‘ื•ื“ ืชืฉืœื•ืžื™ื ืืœืงื˜ืจื•ื ื™ื™ื. ื”ืžืขืจื›ืช ืขื•ื‘ื“ืช ื‘ืื•ืคืŸ ืžืฉื‘ื™ืข ืจืฆื•ืŸ ืขื‘ื•ืจ ืจื•ื‘ ื”ืขืกืงืื•ืช, ืืš ืขื ื–ืืช,

ื”ื™ื ืขื“ื™ื™ืŸ ืกื•ื‘ืœืช ืžื”ื—ื•ืœืฉื•ืช ื”ื˜ื‘ื•ืขื•ืช ื‘ืžื•ื“ืœ ืžื‘ื•ืกืก ื”ืืžื•ืŸ. ืคืขื•ืœื•ืช ืฉื”ืŸ ืœื—ืœื•ื˜ื™ืŸ ื‘ืœืชื™-ื ื™ืชื ื•ืช

ืœื‘ื™ื˜ื•ืœ ืื™ื ืŸ ื‘ืืžืช ืืคืฉืจื™ื•ืช, ืžื›ื™ื•ื•ืŸ ืฉื”ืžื•ืกื“ ื”ื›ืกืคื™ ืื™ื ื• ื™ื›ื•ืœ ืœื”ื™ืžื ืข ืžื’ื™ืฉื•ืจ ืžื—ืœื•ืงื•ืช. ืขืœื•ืช

ื”ื’ื™ืฉื•ืจ ืžืขืœื” ืืช ืขืœื•ื™ื•ืช ื”ืคืขื•ืœื”, ืžื” ืฉืžื’ื‘ื™ืœ ืืช ื”ื’ื•ื“ืœ ื”ืžืขืฉื™ ื”ืžื–ืขืจื™ ืœืขืกืงื” ื•ืžื•ื ืข ืืช ื”ืืคืฉืจื•ืช

ืœืขืกืงืื•ืช ืื’ื‘ื™ื•ืช ืงื˜ื ื•ืช, ื•ื™ืฉ ืขืœื•ืช ืจื—ื‘ื” ื™ื•ืชืจ ื‘ืื•ื‘ื“ืŸ ื”ื™ื›ื•ืœืช ืœื‘ืฆืข ืชืฉืœื•ืžื™ื ื‘ืœืชื™-ื ื™ืชื ื™ื ืœื‘ื™ื˜ื•ืœ

ืขื‘ื•ืจ ืฉื™ืจื•ืชื™ื ื‘ืœืชื™-ื ื™ืชื ื™ื ืœื‘ื™ื˜ื•ืœ. ื”ืืคืฉืจื•ืช ืœื‘ื™ื˜ื•ืœ ืžืจื—ื™ื‘ื” ืืช ื”ืฆื•ืจืš ื‘ืืžื•ืŸ. ืกื•ื—ืจื™ื ื—ื™ื™ื‘ื™ื

ืœื”ื™ื–ื”ืจ ืžืœืงื•ื—ื•ืชื™ื”ื, ื•ืœื”ื˜ืจื™ื— ืื•ืชื ืœืกืคืง ื™ื•ืชืจ ืžื™ื“ืข ืžืืฉืจ ื”ื™ื” ื ื—ื•ืฅ ืื—ืจืช. ื”ื ืžืฉืœื™ืžื™ื ื‘ืœื™ืช

ื‘ืจื™ืจื” ืขื ืื—ื•ื– ืžืกื•ื™ื ืฉืœ ื”ื•ื ืื”, ื”ื ืชืคืฉ ื›ื‘ืœืชื™-ื ืžื ืข. ื ื™ืชืŸ ืœื”ื™ืžื ืข ืžื”ืขืœื•ื™ื•ืช ื”ืืœื• ื•ืžื—ื•ืกืจ

ื”ื•ื•ื“ืื•ืช ื‘ืชืฉืœื•ืžื™ื ืขืœ ื™ื“ื™ ืฉื™ืžื•ืฉ ื‘ืžื˜ื‘ืข ื’ืฉืžื™, ืืš ืื™ืŸ ื‘ื ืžืฆื ืžื ื’ื ื•ืŸ ืœื‘ืฆืข ืชืฉืœื•ืžื™ื ืขืœ ื’ื‘ื™ ืขืจื•ืฅ

ืชืงืฉื•ืจืช ืœืœื ืฆื“ ื ืืžืŸ.

ื ื—ื•ืฆื” ืžืขืจื›ืช ืชืฉืœื•ืžื™ื ืืœืงื˜ืจื•ื ื™ื™ื ื”ืžื‘ื•ืกืกืช ืขืœ ื”ื•ื›ื—ื” ืงืจื™ืคื˜ื•ื’ืจืคื™ืช ื‘ืžืงื•ื ืืžื•ืŸ,

ื”ืžืืคืฉืจืช ืœื›ืœ ืฉื ื™ ืฆื“ื“ื™ื ื”ื—ืคืฆื™ื ื‘ื“ื‘ืจ ืœื‘ืฆืข ืคืขื•ืœื” ื–ื” ืขื ื–ื” ื‘ืื•ืคืŸ ื™ืฉื™ืจ ืœืœื ืฆื•ืจืš ื‘ืฆื“ ืฉืœื™ืฉื™

ื ืืžืŸ. ืคืขื•ืœื•ืช ืฉืžื‘ื—ื™ื ื” ื—ื™ืฉื•ื‘ื™ืช ืื™ืŸ ื–ื” ืžืขืฉื™ ืœื”ืคื•ืš ืื•ืชืŸ ื™ื’ื ื• ืขืœ ืžื•ื›ืจื™ื ืžืคื ื™ ื”ื•ื ืื”, ื•ื ื™ืชืŸ ื‘ืงืœื•ืช

ืœืžืžืฉ ืžื ื’ื ื•ื ื™ ื”ืฉืœืฉื” ืฉื’ืจืชื™ื™ื ื‘ื›ื“ื™ ืœื”ื’ืŸ ืขืœ ืงื•ื ื™ื. ื‘ืžืืžืจ ื–ื”, ืื ื• ืžืฆื™ืขื™ื ืคื™ืชืจื•ืŸ ืœื‘ืขื™ื™ืช ื”ื ื™ืฆื•ืœ

ื”ื›ืคื•ืœ ื”ืžืฉืชืžืฉ ื‘ืฉืจืช ื—ื•ืชืžื•ืช-ื–ืžืŸ ืฉื™ืชื•ืคื™ ืžื‘ื•ื–ืจ ื‘ืฉื‘ื™ืœ ืœื™ืฆื•ืจ ื”ื•ื›ื—ื” ื—ื™ืฉื•ื‘ื™ืช ืฉืœ ื”ืกื“ืจ

ื”ื›ืจื•ื ื•ืœื•ื’ื™ ืฉืœ ืคืขื•ืœื•ืช. ื”ืžืขืจื›ืช ื‘ื˜ื•ื—ื” ื›ืœ ืขื•ื“ ื”ืฆืžืชื™ื ื”ื™ืฉืจื™ื ืฉื•ืœื˜ื™ื ื™ื—ื“ ื‘ื™ื•ืชืจ ืขื•ืฆืžืช ื—ื™ืฉื•ื‘

ืžื›ืœ ืงื‘ื•ืฆืช ืฆืžืชื™ื ืชื•ืงืคื™ื ื”ืžืฉืชืคื™ื ืคืขื•ืœื”.


2. ืคืขื•ืœื•ืช

ืื ื• ืžื’ื“ื™ืจื™ื ืžื˜ื‘ืข ืืœืงื˜ืจื•ื ื™ ื›ืฉืจืฉืจืช ืฉืœ ื—ืชื™ืžื•ืช ื“ื™ื’ื™ื˜ืœื™ื•ืช. ื›ืœ ื‘ืขืœื™ื ืžืขื‘ื™ืจ ืืช ื”ืžื˜ื‘ืข ืœื‘ื

ื”ืงื•ื“ืžืช ื•ื”ืžืคืชื— ื”ืฆื™ื‘ื•ืจื™ ืฉืœ (transaction) ืฉืœ ื”ืคืขื•ืœื” (Hash) ืื—ืจื™ื• ืขืœ ื™ื“ื™ ื—ืชื™ืžืช ื’ื™ื‘ื•ื‘

ื”ื‘ืขืœื™ื ื”ื‘ืื™ื, ื•ื”ื•ืกืคืช ืืœื• ืœืกื•ืฃ ื”ืžื˜ื‘ืข. ืžืงื‘ืœ ืชืฉืœื•ื ื™ื›ื•ืœ ืœืืžืช ืืช ื”ื—ืชื™ืžื•ืช ื‘ื›ื“ื™ ืœื•ื•ื“ื ืืช

ืฉืจืฉืจืช ื”ื‘ืขืœื•ืช

ื”ื‘ืขื™ื” ื”ื™ื ื›ืžื•ื‘ืŸ ืฉืžืงื‘ืœ ื”ืชืฉืœื•ื ืื™ื ื• ื™ื›ื•ืœ ืœื•ื“ื ืฉืืฃ ืื—ื“ ืžื”ื‘ืขืœื™ื ืœื ืฉื™ืœื ื‘ืืžืฆืขื•ืช ื”ืžื˜ื‘ืข

ืคื™ืชืจื•ืŸ ื ืคื•ืฅ ื”ื•ื ืœื”ื›ื ื™ืก ืกืžื›ื•ืช ืžืจื›ื–ื™ืช ื”ื–ื•ื›ื” ืœืืžื•ืŸ, .(double-spend , ืคืขืžื™ื™ื (ื ื™ืฆื•ืœ ื›ืคื•ืœ

ืžื˜ื‘ืขื”, ืฉื‘ื•ื“ืงืช ื›ืœ ืคืขื•ืœื” ื›ื ื’ื“ ื ื™ืฆื•ืœ ื›ืคื•ืœ. ืœืื—ืจ ื›ืœ ืคืขื•ืœื”, ื”ืžื˜ื‘ืข ื—ื™ื™ื‘ ืœื—ื–ื•ืจ ืืœ ื”ืžื˜ื‘ืขื” ื›ื“ื™

ืœื”ื ืคื™ืง ืžื˜ื‘ืข ื—ื“ืฉ, ื•ืจืง ืขืœ ืžื˜ื‘ืขื•ืช ืฉื”ื•ื ืคืงื• ื™ืฉื™ืจื•ืช ืžื”ืžื˜ื‘ืขื” ืกื•ืžื›ื™ื ืฉืœื ืขื‘ืจื• ื ื™ืฆื•ืœ ื›ืคื•ืœ.

ื”ื‘ืขื™ื” ื‘ืคื™ืชืจื•ืŸ ื–ื” ื”ื•ื ืฉื”ื’ื•ืจืœ ืฉืœ ื”ืžืขืจื›ืช ื”ื›ืกืคื™ืช ื‘ื›ืœืœื•ืชื” ืชืœื•ื™ ื‘ื—ื‘ืจื” ื”ืžืคืขื™ืœื” ืืช ื”ืžื˜ื‘ืขื”,

ื”ื™ื•ืช ื•ื›ืœ ืคืขื•ืœื” ื—ื™ื™ื‘ืช ืœืขื‘ื•ืจ ื“ืจื›ื, ื‘ื“ื™ื•ืง ื›ืžื• ื‘ื‘ื ืง.

ืื ื• ื–ืงื•ืงื™ื ืœื“ืจืš ื‘ื” ืžืงื‘ืœ ื”ืชืฉืœื•ื ื™ื•ื›ืœ ืœื“ืขืช ืฉื”ื‘ืขืœื™ื ื”ืงื•ื“ืžื™ื ืœื ื—ืชื ืขืœ ืืฃ ืคืขื•ืœื”

ืžื•ืงื“ืžืช ื™ื•ืชืจ. ืœืฆืจื›ื™ื ืฉืœื ื•, ื”ืคืขื•ืœื” ื”ืžื•ืงื“ืžืช ื‘ื™ื•ืชืจ ื”ื™ื ื”ืงื•ื‘ืขืช, ื›ืš ืฉืื™ื ื ื• ื“ื•ืื’ื™ื ืžื ืกื™ื•ื ื•ืช

ืžืื•ื—ืจื™ื ื™ื•ืชืจ ืœื ื™ืฆื•ืœ ื›ืคื•ืœ. ื”ื“ืจืš ื”ื™ื—ื™ื“ื” ืœืืฉืจ ืืช ื”ืขื“ืจ ืคืขื•ืœื” ื”ื™ื ืœื”ื™ื•ืช ืžื•ื“ืข ืœื›ืœ ื”ืคืขื•ืœื•ืช.

ื‘ืžื•ื“ืœ ืžื‘ื•ืกืก ื”ืžื˜ื‘ืขื”, ื”ืžื˜ื‘ืขื” ืžื•ื“ืขืช ืœื›ืœ ื”ืคืขื•ืœื•ืช ื•ืžื—ืœื™ื˜ื” ืื™ื–ื• ื”ื’ื™ืขื” ืงื•ื“ื. ื›ื“ื™ ืœื”ืฉื™ื’ ื–ืืช

ืœืœื ืฆื“ ื ืืžืŸ, ื—ื•ื‘ื” ืœื”ื›ืจื™ื– ืขืœ ืคืขื•ืœื•ืช ื‘ืื•ืคืŸ ืคื•ืžื‘ื™ [ 1], ื•ื ื—ื•ืฆื” ืžืขืจื›ืช ืœื”ืกื›ืžื” ื‘ื™ืŸ ืžืฉืชืชืคื™ื ืœื’ื‘ื™

ื”ื™ืกื˜ื•ืจื™ื” ื™ื—ื™ื“ื” ืฉืœ ื”ืกื“ืจ ื‘ื• ื”ืŸ ื”ืชืงื‘ืœื•. ืžืงื‘ืœ ื”ืชืฉืœื•ื ื–ืงื•ืง ืœื”ื•ื›ื—ื” ืฉื‘ื–ืžืŸ ื‘ื• ื›ืœ ืคืขื•ืœื”

ื”ืชื‘ืฆืขื”, ืจื•ื‘ ื”ืฆืžืชื™ื ื”ืกื›ื™ืžื• ื›ื™ ื”ื™ื ื”ื™ืชื” ื”ืจืืฉื•ื ื” ืฉื”ืชืงื‘ืœื”.


3. ืฉืจืช ื—ื•ืชืžื•ืช ื–ืžืŸ

ืฉืจืช ื—ื•ืชืžื•ืช-ื–ืžืŸ .(timestamp server) ื”ืคื™ืชืจื•ืŸ ืื•ืชื• ืื ื• ืžืฆื™ืขื™ื ืžืชื—ื™ืœ ืขื ืฉืจืช ื—ื•ืชืžื•ืช-ื–ืžืŸ

ืฉืœ ืคืจื™ื˜ื™ื ื”ื–ืงื•ืงื™ื ืœื—ื•ืชืžืช ื–ืžืŸ ื•ื”ืคืฆืชื• ื‘ืื•ืคืŸ ื ืจื—ื‘, (block) ืคื•ืขืœ ืขืœ ื™ื“ื™ ืœืงื™ื—ืช ื’ื™ื‘ื•ื‘ ืฉืœ ื’ื•ืฉ

ืจืื” [ 2-5 ]). ื—ื•ืชืžืช ื”ื–ืžืŸ ืžื•ื›ื™ื—ื” ืฉื‘ื”ื›ืจื— ื”ื ืชื•ื ื™ื ื”ื™ื• ืงื™ื™ืžื™ื ื‘ืื•ืชื• ) Usenet- ืœืžืฉืœ ื‘ืขื™ืชื•ืŸ ืื• ื‘

ื–ืžืŸ, ืื—ืจืช ืœื ื”ื™ื• ื™ื›ื•ืœื™ื ืœื”ื™ื•ืช ื›ืœื•ืœื™ื ื‘ื’ื™ื‘ื•ื‘. ื›ืœ ื—ื•ืชืžืช-ื–ืžืŸ ืžื›ื™ืœื” ืืช ื—ื•ืชืžืช-ื”ื–ืžืŸ ื”ืงื•ื“ืžืช

ื‘ื’ื™ื‘ื•ื‘ ืฉืœื”, ืžื” ืฉื™ื•ืฆืจ ืฉืจืฉืจืช ื‘ื” ื›ืœ ื—ื•ืชืžืช-ื–ืžืŸ ื ื•ืกืคืช ืžืชื’ื‘ืจืช ืืช ืืœื• ืฉื‘ืื• ืœืคื ื™ื”.

4. ื”ื•ื›ื—ืช ืขื‘ื•ื“ื”

ื‘ื›ื“ื™ ืœืžืžืฉ ืฉืจืช ื—ื•ืชืžื•ืช-ื–ืžืŸ ืขืœ ื‘ืกื™ืก ืฉื™ืชื•ืคื™ (Proof-of-work) , ืื ื• ื ืฆื˜ืจืš ืžืขืจื›ืช ื”ื•ื›ื—ืช ืขื‘ื•ื“ื”

ื”ื•ื›ื—ืช ื”ืขื‘ื•ื“ื” ื›ืจื•ื›ื” .Usenet- ืฉืœ ืื“ื ื‘ืง [ 6], ื‘ืžืงื•ื ืคืจืกื•ืžื™ื ื‘ืขื™ืชื•ืŸ ืื• ื‘ Hashcash- ื‘ื“ื•ืžื” ืœ

ื”ื’ื™ื‘ื•ื‘ ืžืชื—ื™ืœ ื‘ืžืกืคืจ ืžืกื•ื™ื ืฉืœ ,SHA-256 ื‘ื—ื™ืคื•ืฉ ืื—ืจ ืขืจืš ืฉื›ืืฉืจ ื”ื•ื ืขื•ื‘ืจ ื’ื™ื‘ื•ื‘, ืœืžืฉืœ ืขื

ืกื™ื‘ื™ื•ืช ืืคืก. ื”ื›ืžื•ืช ื”ืžืžื•ืฆืขืช ืฉืœ ื”ืขื‘ื•ื“ื” ื”ื“ืจื•ืฉื” ื”ื™ื ืžืขืจื™ื›ื™ืช ื‘ืžืกืคืจ ืกื™ื‘ื™ื•ืช ื”ืืคืก ื”ื“ืจื•ืฉื•ืช,

ื•ื”ื™ื ื™ื›ื•ืœื” ืœื”ืชืืžืช ืชื•ืš ื‘ื™ืฆื•ืข ื’ื™ื‘ื•ื‘ ื‘ื•ื“ื“.

ื‘ืฉื‘ื™ืœ ืจืฉืช ื—ื•ืชืžื•ืช-ื”ื–ืžืŸ ืฉืœื ื•, ืื ื• ืžืžืžืฉื™ื ืืช ื”ื•ื›ื—ืช ื”ืขื‘ื•ื“ื” ืขืœ ื™ื“ื™ ื”ื’ื“ืœืช ืžืกืคืจ ื—ื“-ืคืขืžื™

ื‘ื’ื•ืฉ ืขื“ ืฉื ืžืฆื ืขืจืš ื”ืžืขื ื™ืง ืœื’ื™ื‘ื•ื‘ ืฉืœ ื”ื’ื•ืฉ ืืช ื”ืžืกืคืจ ื”ื“ืจื•ืฉ ืฉืœ ืกื™ื‘ื™ื•ืช ืืคืก. ืœืื—ืจ (nonce)

ืฉื”ืžืืžืฅ ื”ื—ื™ืฉื•ื‘ื™ ื”ื•ืฉืงืข ื‘ืฉื‘ื™ืœ ืœื’ืจื•ื ืœื’ื•ืฉ ืœืกืคืง ืืช ื”ื•ื›ื—ืช ื”ืขื‘ื•ื“ื”, ืœื ื ื™ืชืŸ ืœืฉื ื•ืช ืื•ืชื• ืžื‘ืœื™

ืœื‘ืฆืข ืืช ื”ืขื‘ื•ื“ื” ืžื—ื“ืฉ. ืžืื—ืจ ื•ื’ื•ืฉื™ื ืžืื•ื—ืจื™ื ื™ื•ืชืจ ืžืฉื•ืจืฉืจื™ื ืื—ืจื™ื•, ื”ืขื‘ื•ื“ื” ื”ื“ืจื•ืฉื” ื›ื“ื™

ืœืฉื ื•ืช ื’ื•ืฉ ืชื›ืœื•ืœ ื‘ื™ืฆื•ืข ืžื—ื“ืฉ ืฉืœ ื›ืœ ื”ื’ื•ืฉื™ื ืฉืœืื—ืจื™ื•.

ื”ื•ื›ื—ืช ื”ืขื‘ื•ื“ื” ื’ื ืคื•ืชืจืช ืืช ื‘ืขื™ื™ืช ืงื‘ื™ืขืช ื”ื™ื™ืฆื•ื’ ื‘ืงื‘ืœืช ื”ื—ืœื˜ื•ืช ืžื‘ื•ืกืกืช ืจื•ื‘. ืื ื”ืจื•ื‘ ื”ื™ื”

ื›ืœ ืžื™ ืฉืžืกื•ื’ืœ ืœื”ืงืฆื•ืช ื›ืชื•ื‘ื•ืช ืจื‘ื•ืช ื”ื™ื” ื™ื›ื•ืœ ืœื—ืชื•ืจ ืชื—ืชื™ื•. ,"IP ืžื‘ื•ืกืก ืขืœ "ืงื•ืœ ืœื›ืœ ื›ืชื•ื‘ืช

ื”ื•ื›ื—ืช ืขื‘ื•ื“ื” ื”ื™ื ืœืžืขืฉื” "ืงื•ืœ ืœื›ืœ ืžืขื‘ื“". ื”ื—ืœื˜ืช ื”ืจื•ื‘ ืžื™ื•ืฆื’ืช ืขืœ ื™ื“ื™ ื”ืฉืจืฉืจืช ื”ืืจื•ื›ื” ื‘ื™ื•ืชืจ,

ื‘ื” ืžื•ืฉืงืข ืžืืžืฅ ื”ื•ื›ื—ืช ื”ืขื‘ื•ื“ื” ื”ืจื‘ ื‘ื™ื•ืชืจ. ืื ืจื•ื‘ ืขื•ืฆืžืช ื”ื—ื™ืฉื•ื‘ ื ืฉืœื˜ืช ืขืœ ื™ื“ื™ ืฆืžืชื™ื ื™ืฉืจื™ื,

ื”ืฉืจืฉืจืช ื”ื™ืฉืจื” ืชืฆืžื— ื‘ืงืฆื‘ ื”ืžื”ื™ืจ ื‘ื™ื•ืชืจ ื•ืชืฉื™ื’ ื›ืœ ืฉืจืฉืจืช ืžืชื—ืจื”. ื‘ื›ื“ื™ ืœืฉื ื•ืช ื’ื•ืฉ ืžื”ืขื‘ืจ,

ืชื•ืงืฃ ื™ืฆื˜ืจืš ืœื‘ืฆืข ืžื—ื“ืฉ ืืช ื”ื•ื›ื—ืช ื”ืขื‘ื•ื“ื” ืฉืœ ื”ื’ื•ืฉ ื•ื›ืœ ื”ื’ื•ืฉื™ื ืœืื—ืจื™ื•, ื•ืื– ืœื”ื“ื‘ื™ืง ืืช ื”ืคืขืจ

ื•ืœืขืœื•ืช ืขืœ ื”ืขื‘ื•ื“ื” ืฉืœ ื”ืฆืžืชื™ื ื”ื™ืฉืจื™ื. ืžืื•ื—ืจ ื™ื•ืชืจ ื ืจืื” ืฉื”ื”ืกืชื‘ืจื•ืช ืฉืชื•ืงืฃ ืื™ื˜ื™ ื™ื•ืชืจ ื™ื“ื‘ื™ืง

ืืช ื”ืคืขืจ ืงื˜ื ื” ื‘ืื•ืคืŸ ืžืขืจื™ื›ื™ ื›ื›ืœ ืฉื’ื•ืฉื™ื ืขื•ืงื‘ื™ื ืžืชื•ื•ืกืคื™ื.

ื‘ื›ื“ื™ ืœืคืฆื•ืช ืขืœ ื”ื’ื“ื™ืœื” ื‘ืžื”ื™ืจื•ืช ื”ื—ื•ืžืจื” ื•ื”ืฉืชื ื•ืช ื‘ืจืžืช ื”ืขื ื™ื™ืŸ ื‘ื”ืคืขืœืช ืฆืžืชื™ื ืœืื•ืจืš ื–ืžืŸ,

ื“ืจื’ืช ื”ืงื•ืฉื™ ืฉืœ ื”ื•ื›ื—ืช ื”ืขื‘ื•ื“ื” ื ืงื‘ืขืช ืขืœ ื™ื“ื™ ืžืžื•ืฆืข ื ืข ื”ืฉื ืœืžื˜ืจื” ืžืกืคืจ ืžืžื•ืฆืข ืžืกื•ื™ื ืฉืœ

ื’ื•ืฉื™ื ืœืฉืขื”. ืื ื”ื ื ื•ืฆืจื™ื ืžื”ืจ ืžื“ื™, ื“ืจื’ืช ื”ืงื•ืฉื™ ืขื•ืœื”.


5. ืจืฉืช

ื”ืฉืœื‘ื™ื ื‘ื”ืคืขืœืช ื”ืจืฉืช ื”ื ื›ื“ืœืงืžืŸ:

1) ืคืขื•ืœื•ืช ื—ื“ืฉื•ืช ืžืฉื•ื“ืจื•ืช ืœื›ืœ ื”ืฆืžืชื™ื.

2) ื›ืœ ืฆื•ืžืช ืื•ืกืฃ ืคืขื•ืœื•ืช ื—ื“ืฉื•ืช ืœืชื•ืš ื’ื•ืฉ.

3) ื›ืœ ืฆื•ืžืช ืขื•ื‘ื“ ืขืœ ืžืฆื™ืืช ื”ื•ื›ื—ืช ืขื‘ื•ื“ื” ืงืฉื” ืœื’ื•ืฉ ืฉืœื•.

4) ื›ืฉืฆื•ืžืช ืžื•ืฆื ื”ื•ื›ื—ืช ืขื‘ื•ื“ื”, ื”ื•ื ืžืฉื“ืจ ืื•ืชื• ืœื›ืœ ื”ืฆืžืชื™ื.

5) ืฆืžืชื™ื ืžืกื›ื™ืžื™ื ืขื ื”ื’ื•ืฉ ืจืง ืื ื›ืœ ื”ืคืขื•ืœื•ืช ื‘ื• ื”ืŸ ืชืงื™ื ื•ืช ื•ืœื ื ื•ืฆืœื• ื›ื‘ืจ.

6) ืฆืžืชื™ื ืžื‘ื˜ืื™ื ืืช ื”ืกื›ืžืชื ืขื ื’ื•ืฉ ื‘ืขืฆื ื–ื” ืฉื”ื ืขื•ื‘ื“ื™ื ืขืœ ื™ืฆื™ืจืช ื”ื’ื•ืฉ ื”ื‘ื ื‘ืฉืจืฉืจืช,

ืชื•ืš ืฉื™ืžื•ืฉ ื‘ื’ื™ื‘ื•ื‘ ืฉืœ ื”ื‘ืœื•ืง ืฉื”ืชืงื‘ืœ ื‘ืชื•ืจ ื”ื’ื™ื‘ื•ื‘ ื”ืงื•ื“ื.


ืฆืžืชื™ื ืชืžื™ื“ ืžืชื™ื™ื—ืกื™ื ืœืฉืจืฉืจืช ื”ืืจื•ื›ื” ื‘ื™ื•ืชืจ ื›ืืœ ื”ืฉืจืฉืจืช ื”ื ื›ื•ื ื” ื•ื™ืžืฉื™ื›ื• ืœืขื‘ื•ื“ ืขืœ ื”ืืจื›ืชื”.

ืื ืฉื ื™ ืฆืžืชื™ื ืžืฉื“ืจื™ื ื’ืจืกืื•ืช ืฉื•ื ื•ืช ืฉืœ ื”ื’ื•ืฉ ื”ื‘ื ื‘ื•-ื–ืžื ื™ืช, ื—ืœืง ืžื”ืฆืžืชื™ื ื™ืงื‘ืœื• ืืช ื”ืื—ื“ ืื•

ื”ืฉื ื™ ืชื—ื™ืœื”. ื‘ืžืงืจื” ื–ื”, ื”ื ื™ืขื‘ื“ื• ืขืœ ื”ืจืืฉื•ืŸ ืฉื”ื ืงื™ื‘ืœื•, ืื‘ืœ ื™ืฉืžืจื• ืืช ื”ืขื ืฃ ื”ืฉื ื™ ืœืžืงืจื” ืฉื”ื•ื

ื™ื”ืคืš ืœืืจื•ืš ื™ื•ืชืจ. ื”ืชื™ืงื• ื™ื™ืฉื‘ืจ ื›ืฉื”ื•ื›ื—ืช ื”ืขื‘ื•ื“ื” ื”ื‘ืื” ืชื™ืžืฆื ื•ืื—ื“ ืžื”ืขื ืคื™ื ื™ื”ืคืš ืœืืจื•ืš ื™ื•ืชืจ;

ื”ืฆืžืชื™ื ืฉืขื‘ื“ื• ืขืœ ื”ืขื ืฃ ื”ืื—ืจ ื™ืขื‘ืจื• ืœืขื ืฃ ื”ืืจื•ืš ื™ื•ืชืจ.


ืฉื™ื“ื•ืจื™ื ืฉืœ ืคืขื•ืœื•ืช ื—ื“ืฉื•ืช ืœื ืฆืจื™ื›ื™ื ื‘ื”ื›ืจื— ืœื”ื’ื™ืข ืœื›ืœ ื”ืฆืžืชื™ื. ื›ืœ ืขื•ื“ ื”ื ืžื’ื™ืขื™ื ืœืฆืžืชื™ื

ืจื‘ื™ื, ื”ื ื™ื™ื›ื ืกื• ืœืชื•ืš ื’ื•ืฉ ื‘ื—ืœื•ืฃ ื–ืžืŸ ืœื ืจื‘. ืฉื™ื“ื•ืจื™ ื’ื•ืฉ ื”ื ื’ื ืกื•ื‘ืœื ื™ื™ื ืœื’ื‘ื™ ื”ื•ื“ืขื•ืช ืฉื ืฉืžื˜ื•. ืื

ืฆื•ืžืช ืœื ืžืงื‘ืœ ื’ื•ืฉ, ื”ื•ื ื™ื‘ืงืฉ ืื•ืชื• ื›ืฉื”ื•ื ืžืงื‘ืœ ืืช ื”ื’ื•ืฉ ื”ื‘ื ื•ืžื‘ื™ืŸ ืฉื”ื•ื ื”ื—ืžื™ืฅ ืื—ื“.


6. ืชืžืจื™ืฅ

ืขืœ ืคื™ ื”ืžื•ืกื›ืžื”, ื”ืคืขื•ืœื” ื”ืจืืฉื•ื ื” ื‘ื›ืœ ื’ื•ืฉ ื”ื™ื ืคืขื•ืœื” ืžื™ื•ื—ื“ืช ืฉืžืชื—ื™ืœื” ืžื˜ื‘ืข ื—ื“ืฉ ื‘ื‘ืขืœื•ืชื• ืฉืœ

ื™ื•ืฆืจ ื”ื’ื•ืฉ. ื–ื” ืžื•ืกื™ืฃ ืชืžืจื™ืฅ ืœืฆืžืชื™ื ืœืชืžื•ืš ื‘ืจืฉืช, ื•ืžืขื ื™ืง ื“ืจืš ืจืืฉื•ื ื™ืช ืœื”ืคื™ืฅ ืžื˜ื‘ืขื•ืช ืœืžื—ื–ื•ืจ,

ืžืื—ืจ ื•ืื™ืŸ ืกืžื›ื•ืช ืžืจื›ื–ื™ืช ื”ื™ื›ื•ืœื” ืœื”ื ืคื™ืง ืื•ืชื. ื”ืชื•ืกืคืช ื”ืงื‘ื•ืขื” ืฉืœ ืžื˜ื‘ืขื•ืช ื—ื“ืฉื™ื ืžืงื‘ื™ืœื”

ืœื›ื•ืจื™ ื–ื”ื‘ ื”ืžื•ืฆื™ืื™ื ืžืฉืื‘ื™ื ื›ื“ื™ ืœื”ื•ืกื™ืฃ ื–ื”ื‘ ืœืžื—ื–ื•ืจ. ื‘ืžืงืจื” ืฉืœื ื•, ื”ืžืฉืื‘ื™ื ื”ื ื–ืžืŸ ืžืขื‘ื“

ื•ืื ืจื’ื™ื” ื—ืฉืžืœื™ืช.

ื”ืชืžืจื™ืฅ ื™ื›ื•ืœ ื’ื ืœื”ื™ื•ืช ืžืžื•ืžืŸ ืขืœ ื™ื“ื™ ืขืžืœื•ืช ืคืขื•ืœื”. ืื ืขืจืš ื”ืคืœื˜ ืฉืœ ืคืขื•ืœื” ื ืžื•ืš ืžืขืจืš ื”ืงืœื˜,

ื”ื”ืคืจืฉ ื”ื•ื ืขืžืœืช ืคืขื•ืœื” ืฉืžืชื•ื•ืกืคืช ืœืขืจืš ื”ืชืžืจื™ืฅ ืฉืœ ื”ื’ื•ืฉ ื”ืžื›ื™ืœ ืืช ื”ืคืขื•ืœื”. ืœืื—ืจ ืฉืžืกืคืจ

ืงื‘ื•ืข ืžืจืืฉ ืฉืœ ืžื˜ื‘ืขื•ืช ื ื›ื ืก ืœืžื—ื–ื•ืจ, ื”ืชืžืจื™ืฅ ื™ื›ื•ืœ ืœืขื‘ื•ืจ ื‘ืื•ืคืŸ ื‘ืœืขื“ื™ ืœืขืžืœื•ืช ืคืขื•ืœื” ื•ืœื”ื™ื•ืช ื ืงื™

ืœื—ืœื•ื˜ื™ืŸ ืžืื™ื ืคืœืฆื™ื”.

ื”ืชืžืจื™ืฅ ื™ื›ื•ืœ ืœืขื–ื•ืจ ื‘ืขื™ื“ื•ื“ ืฆืžืชื™ื ืœื”ื™ืฉืืจ ื™ืฉืจื™ื. ืื ืชื•ืงืฃ ื—ืžื“ืŸ ืžืกื•ื’ืœ ืœื›ื ื•ืก ื™ื•ืชืจ ื›ื•ื— ื—ื™ืฉื•ื‘

ืžื›ืœ ื”ืฆืžืชื™ื ื”ื™ืฉืจื™ื, ื”ื•ื ื™ืฆื˜ืจืš ืœื‘ื—ื•ืจ ื‘ื™ืŸ ืฉื™ืžื•ืฉ ื‘ื• ื›ื“ื™ ืœื”ื•ื ื•ืช ืื ืฉื™ื ื‘ื’ื ื™ื‘ืช ื”ืชืฉืœื•ืžื™ื ืฉืœื•

ื‘ื—ื–ืจื”, ืื• ืฉื™ืžื•ืฉ ื‘ื• ืœื™ืฆื•ืจ ืžื˜ื‘ืขื•ืช ื—ื“ืฉื™ื. ืžืชืงื‘ืœ ืขืœ ื”ื“ืขืช ืฉื™ื”ื™ื” ื–ื” ืจื•ื•ื—ื™ ื™ื•ืชืจ ื‘ืขื™ื ื™ื• ืœืฉื—ืง ืœืคื™

ื”ื›ืœืœื™ื, ื›ืœืœื™ื ืืœื• ืฉื—ื•ื ื ื™ื ืื•ืชื• ื‘ื™ื•ืชืจ ืžื˜ื‘ืขื•ืช ื—ื“ืฉื™ื ืžืืฉืจ ื›ืœ ืฉืืจ ื”ืžืฉืชืชืคื™ื ื‘ื™ื—ื“, ืžืืฉืจ

ืœืจื•ืคืฃ ืืช ื”ืžืขืจื›ืช ื•ืืช ืชืงืคื•ืช ื”ื”ื•ืŸ ืฉืœ ืขืฆืžื•.


7. ืฉื—ืจื•ืจ ื ืคื— ื›ื•ื ืŸ

ืžื”ืจื’ืข ื‘ื• ื”ืคืขื•ืœื” ื”ืื—ืจื•ื ื” ื‘ืžื˜ื‘ืข ืงื‘ื•ืจื” ืชื—ืช ืžืกืคื™ืง ื’ื•ืฉื™ื, ื”ืคืขื•ืœื•ืช ื”ืžื ื•ืฆืœื•ืช ืœืคื ื™ื” ื™ื›ื•ืœื•ืช

ืœื”ื™ื–ืจืง ื›ื“ื™ ืœื—ืกื•ืš ื‘ื ืคื— ื›ื•ื ืŸ. ื›ื“ื™ ืœืกื™ื™ืข ื‘ื›ืš ืžื‘ืœื™ ืœืฉื‘ื•ืจ ืืช ื’ื™ื‘ื•ื‘ ื”ื’ื•ืฉ, ื”ืคืขื•ืœื•ืช ืžื’ื•ื‘ื‘ื•ืช ื‘ืขืฅ

7]), ื‘ืื•ืคืŸ ืฉืจืง ื”ืฉื•ืจืฉ ื›ืœื•ืœ ื‘ื’ื™ื‘ื•ื‘ ื”ื’ื•ืฉ. ื’ื•ืฉื™ื ื™ืฉื ื™ื ื™ื›ื•ืœื™ื ][2][ ืจืื” [ 5 ,Merkle Tree) ืžืจืงืœ

ืœืขื‘ื•ืจ ืฆืžืฆื•ื ืขืœ ื™ื“ื™ ื’ื“ื™ืžืช ืขื ืคื™ื ืžื”ืขืฅ. ืื™ืŸ ืฆื•ืจืš ืœืฉืžื•ืจ ืืช ื”ื’ื™ื‘ื•ื‘ื™ื ื”ืคื ื™ืžื™ื™ื.

ื›ื•ืชืจืช ื’ื•ืฉ ืœืœื ืคืขื•ืœื•ืช ืชืชืคื•ืก ื‘ืขืจืš 80 ื‘ืชื™ื. ืื ืื ื• ืžื ื™ื—ื™ื ืฉื’ื•ืฉื™ื ื ื•ืฆืจื™ื ื›ืœ 10 ื“ืงื•ืช, ืžื“ื•ื‘ืจ

2GB 4.2 ืœืฉื ื”. ื‘ื”ื™ื ืชืŸ ืฉืžืขืจื›ื•ืช ืžื—ืฉื‘ ื˜ื™ืคื•ืกื™ื•ืช ื ืžื›ืจื•ืช ืขื MB = 365 * 24 * 6 * ื‘- 80 ื‘ืชื™ื

1.2 ืœืฉื ื”, ืœื ืืžื•ืจื” ืœื”ื™ื•ืช ื‘ืขื™ื™ืช GB ื–ื™ื›ืจื•ืŸ ื ื›ื•ืŸ ืœืฉื ืช 2008 , ื•ื—ื•ืง ืžื•ืจ ืฆื•ืคื” ืฆืžื™ื—ื” ืขื›ืฉื•ื•ื™ืช ืฉืœ

ืื—ืกื•ืŸ ื’ื ืื ื—ื•ื‘ื” ืœืฉืžื•ืจ ืืช ื›ื•ืชืจื•ืช ื”ื’ื•ืฉื™ื ื‘ื–ื™ื›ืจื•ืŸ.


8. ืื™ืžื•ืช ืžืคื•ืฉื˜ ืฉืœ ืคืขื•ืœื•ืช

ื ื™ืชืŸ ืœืืžืช ืคืขื•ืœื•ืช ืžื‘ืœื™ ืœื”ืคืขื™ืœ ืฆื•ืžืช ืจืฉืช ืžืœื. ืžืฉืชืžืฉ ืฆืจื™ืš ืจืง ืœืฉืžื•ืจ ืขื•ืชืง ืฉืœ ื›ื•ืชืจื•ืช ื”ื’ื•ืฉื™ื

ืฉืœ ืฉืจืฉืจืช ื”ื•ื›ื—ื•ืช ื”ืขื‘ื•ื“ื” ื”ืืจื•ื›ื” ื‘ื™ื•ืชืจ, ืื•ืชื• ื”ื•ื ื™ื›ื•ืœ ืœืงื‘ืœ ืขืœ ื™ื“ื™ ืฉืื™ืœืชื•ืช ืœืฆืžืชื™ื ื‘ืจืฉืช ืขื“

ืฉื”ื•ื ืžืฉื•ื›ื ืข ืฉื™ืฉ ืœื• ืืช ื”ืฉืจืฉืจืช ื”ืืจื•ื›ื” ื‘ื™ื•ืชืจ, ื•ืœื”ืฉื™ื’ ืืช ืขื ืฃ ื”ืžืจืงืœ ื”ืžืงืฉืจ ืืช ื”ืคืขื•ืœื” ืœื’ื•ืฉ

ื‘ื• ื™ืฉ ืœื” ื—ื•ืชืžืช ื–ืžืŸ. ื”ื•ื ืœื ื™ื›ื•ืœ ืœื‘ื“ื•ืง ืืช ื”ืคืขื•ืœื” ื‘ืขืฆืžื•, ืื‘ืœ ืขืœ ื™ื“ื™ ืงื™ืฉื•ืจื” ืœืžืงื•ื ื‘ืฉืจืฉืจืช,

ื”ื•ื ื™ื›ื•ืœ ืœืจืื•ืช ืฉืฆื•ืžืช ื‘ืจืฉืช ื”ืกื›ื™ื ืื™ืชื”, ื•ื’ื•ืฉื™ื ืฉืžืชื•ื•ืกืคื™ื ืื—ืจื™ื” ืžื”ื•ื•ื™ื ืื™ืฉื•ืฉ ื ื•ืกืฃ

ืฉื”ืจืฉืช ืžืกื›ื™ืžื” ืื™ืชื”.

ื‘ืชื•ืจ ืฉื›ื–ื”, ื”ืื™ืžื•ืช ื”ื•ื ืืžื™ืŸ ื›ืœ ืขื•ื“ ืฆืžืชื™ื ื™ืฉืจื™ื ืฉื•ืœื˜ื™ื ื‘ืจืฉืช, ืื‘ืœ ื”ื•ื ืคื’ื™ืข ื™ื•ืชืจ ืื

ืชื•ืงืฃ ื’ื•ื‘ืจ ืขืœ ื”ืจืฉืช. ื‘ืขื•ื“ ืฆืžืชื™ื ื‘ืจืฉืช ื™ื›ื•ืœื™ื ืœืืžืช ืคืขื•ืœื•ืช ื‘ืขืฆืžื, ื”ืฉื™ื˜ื” ื”ืžืคื•ืฉื˜ืช ื™ื›ื•ืœื”

ืœืœื›ืช ืฉื•ืœืœ ืื—ืจ ืคืขื•ืœื•ืช ื‘ื“ื™ื•ื ื™ื•ืช ืฉืœ ืชื•ืงืฃ ื›ืœ ืขื•ื“ ื”ื•ื ื™ื›ื•ืœ ืœื”ืžืฉื™ืš ืœื’ื‘ื•ืจ ืขืœ ื”ืจืฉืช. ืืกื˜ืจื˜ื’ื™ื”

ืื—ืช ืœื”ื’ืŸ ืžืคื ื™ ื–ื” ื”ื™ื ืœืงื‘ืœ ื”ืชืจืขื•ืช ืžืฆืžืชื™ื ื‘ืจืฉืช ื›ืฉื”ื ื—ื•ืฉืคื™ื ื’ื•ืฉ ืœื ืงื‘ื™ืœ, ื•ืœื”ื ื™ืข ืืช

ื”ืชื•ื›ื ื” ืฉืœ ื”ืžืฉืชืžืฉ ืœื”ื•ืจื™ื“ ืืช ื”ื’ื•ืฉ ื”ืžืœื ื•ื”ืคืขื•ืœื•ืช ื”ื—ืฉื•ื“ื•ืช ื›ื“ื™ ืœืืฉืจ ืืช ื—ื•ืกืจ ื”ืขืงื‘ื™ื•ืช

ืฉืœื”ืŸ. ืขืกืงื™ื ืฉืžืงื‘ืœื™ื ืชืฉืœื•ืžื™ื ื‘ืื•ืคืŸ ืชื“ื™ืจ ื›ื ืจืื” ื™ืจืฆื• ืขื“ื™ื™ืŸ ืœื”ืคืขื™ืœ ืฆืžืชื™ื ืžืฉืœ ืขืฆืžื ืœืฆื•ืจืš

ืžื™ื“ื” ืจื‘ื” ื™ื•ืชืจ ืฉืœ ืื‘ื˜ื—ื” ื‘ืœืชื™-ืชืœื•ื™ื” ื•ืื™ืžื•ืช ืžื”ื™ืจ ื™ื•ืชืจ.


9. ืฆื™ืจื•ืฃ ื•ืคื™ืฆื•ืœ ืขืจืš

ืืฃ ืขืœ ืคื™ ืฉื”ื™ื” ืืคืฉืจ ืœื˜ืคืœ ื‘ืžื˜ื‘ืขื•ืช ื‘ืื•ืคืŸ ืคืจื˜ื ื™, ื™ื”ื™ื” ื–ื” ืžืกื•ืจื‘ืœ ืœืงื™ื™ื ืคืขื•ืœื” ื ืคืจื“ืช ืœื›ืœ ืื’ื•ืจื”

ื‘ื”ืขื‘ืจื”. ื›ื“ื™ ืœืืคืฉืจ ืœืขืจืš ืœืขื‘ื•ืจ ืฆื™ืจื•ืฃ ื•ืคื™ืฆื•ืœ, ืคืขื•ืœื•ืช ืžื›ื™ืœื•ืช ืงืœื˜ื™ื ื•ืคืœื˜ื™ื ืžืจื•ื‘ื™ื. ื‘ืื•ืคืŸ ืจื’ื™ืœ

ื™ื”ื™ื• ืื• ืงืœื˜ ืื—ื“ ืžืคืขื•ืœื” ืงื•ื“ืžืช ื’ื“ื•ืœื” ื™ื•ืชืจ ืื• ืงืœื˜ื™ื ืžืจื•ื‘ื™ื ื”ืžืฆืจืคื™ื ื›ืžื•ื™ื•ืช ืงื˜ื ื•ืช ื™ื•ืชืจ, ื•ืœื›ืœ

ื”ื™ื•ืชืจ ืฉื ื™ ืคืœื˜ื™ื: ืื—ื“ ื‘ืฉื‘ื™ืœ ื”ืชืฉืœื•ื, ื•ืื—ื“ ื‘ืฉื‘ื™ืœ ืœื”ื—ื–ื™ืจ ืืช ื”ืขื•ื“ืฃ, ืื ืงื™ื™ื, ื‘ื—ื–ืจื” ืืœ

ื”ืฉื•ืœื—.

ืจืื•ื™ ืœืฆื™ื™ืŸ ืฉื”ืกืชืขืคื•ืช, ื‘ื” ื›ืœ ืคืขื•ืœื” ืชืœื•ื™ื” ื‘ืžืกืคืจ ืคืขื•ืœื•ืช, ื•ืคืขื•ืœื•ืช ืืœื” ืชืœื•ื™ื•ืช ื‘ืจื‘ื•ืช ื ื•ืกืคื•ืช,

ืื™ื ื” ื‘ืขื™ื” ื›ืืŸ. ืœืขื•ืœื ืื™ืŸ ืฆื•ืจืš ืœื”ืคื™ืง ืขื•ืชืง ืฉืœื ื”ืขื•ืžื“ ื‘ืคื ื™ ืขืฆืžื• ืฉืœ ื”ื”ื™ืกื˜ื•ืจื™ื” ืฉืœ ืคืขื•ืœื”.


10. ืคืจื˜ื™ื•ืช

ื”ืžื•ื“ืœ ื”ื‘ื ืงืื™ ื”ืžืกื•ืจืชื™ ืžืฉื™ื’ ืจืžื” ืžืกื•ื™ืžืช ืฉืœ ืคืจื˜ื™ื•ืช ื‘ื›ืš ืฉื”ื•ื ืžื’ื‘ื™ืœ ืืช ื”ื’ื™ืฉื” ืœืžื™ื“ืข ืœืฆื“ื“ื™ื

ื”ืžืขื•ืจื‘ื™ื ื•ืœืฆื“ ื”ืฉืœื™ืฉื™ ื”ื ืืžืŸ. ื”ื”ื›ืจื— ื‘ื”ื›ืจื–ืช ื›ืœ ื”ืคืขื•ืœื•ืช ื‘ืื•ืคืŸ ืคื•ืžื‘ื™ ืžื•ืฆื™ื ืžื›ืœืœ ื—ืฉื‘ื•ืŸ ืืช

ื”ืฉื™ื˜ื” ื”ื–ืืช, ืื‘ืœ ืขื“ื™ื™ืŸ ื ื™ืชืŸ ืœืฉืžื•ืจ ืขืœ ืคืจื˜ื™ื•ืช ืขืœ ื™ื“ื™ ืฉื‘ื™ืจืช ื–ืจื™ืžืช ื”ืžื™ื“ืข ื‘ืžืงื•ื ืื—ืจ: ืฉืžื™ืจืช

ื”ืืœืžื•ื ื™ื•ืช ืฉืœ ืžืคืชื—ื•ืช ืฆื™ื‘ื•ืจื™ื™ื. ื”ืฆื™ื‘ื•ืจ ื™ื›ื•ืœ ืœืจืื•ืช ืฉืžื™ืฉื”ื• ืฉื•ืœื— ื›ืžื•ืช ืžืกื•ื™ืžืช ืœืžื™ืฉื”ื• ืื—ืจ,

ืืš ืœืœื ืžื™ื“ืข ื”ืžืงืฉืจ ืืช ื”ืคืขื•ืœื” ืœื’ื•ืจื ื›ืœืฉื”ื•. ื“ื•ืžื” ื”ื“ื‘ืจ ืœืจืžืช ื”ืžื™ื“ืข ื”ืžืฉื—ืจืจื•ืช ื‘ื•ืจืกื•ืช ืžื ื™ื•ืช,

ื‘ื”ืŸ ื”ื–ืžืŸ ื•ื”ื’ื•ื“ืœ ืฉืœ ืคืขื•ืœื•ืช ืคืจื˜ื ื™ื•ืช, ื”"ืคืกื ื•ืข", ืžื•ืฆื’ ื‘ืื•ืคืŸ ื’ืœื•ื™, ืืš ืžื‘ืœื™ ืœื•ืžืจ ืžื™ ื”ื™ื• ื”ืฆื“ื“ื™ื.

ื›ืืžืฆืขื™ ื”ื’ื ื” ื ื•ืกืฃ, ื™ืฉ ืœื”ืฉืชืžืฉ ื‘ื–ื•ื’ ืžืคืชื—ื•ืช ื—ื“ืฉ ืœื›ืœ ืคืขื•ืœื” ื›ื“ื™ ืœืžื ื•ืข ืžื”ื ืœื”ื™ื•ืช ืžืงื•ืฉืจื™ื

ืœื‘ืขืœื™ื ืžืฉื•ืชืฃ. ืžื™ื“ื” ืžืกื•ื™ืžืช ืฉืœ ืงื™ืฉื•ืจ ื”ื™ื ืขื“ื™ื™ืŸ ื‘ืœืชื™-ื ืžื ืขืช ืขื ืคืขื•ืœื•ืช ืžืจื•ื‘ื•ืช ืงืœื˜ื™ื,

ืฉื‘ื”ื›ืจื— ื—ื•ืฉืคื•ืช ืฉื”ืงืœื˜ื™ื ืฉืœื”ืŸ ื”ื™ื• ืฉื™ื™ื›ื™ื ืœืื•ืชื• ื‘ืขืœื™ื. ื”ืกื™ื›ื•ืŸ ื”ื•ื ืฉืื ื”ื‘ืขืœื™ื ืฉืœ ืžืคืชื—

ื ื—ืฉืฃ, ืงื™ืฉื•ืจ ื™ื›ื•ืœ ืœื—ืฉื•ืฃ ืคืขื•ืœื•ืช ื ื•ืกืคื•ืช ืฉืฉื™ื™ื›ื•ืช ืœืื•ืชื• ื‘ืขืœื™ื.


11. ื—ื™ืฉื•ื‘ื™ื

ืื ื• ื‘ื•ื—ื ื™ื ืชืจื—ื™ืฉ ื‘ื• ืชื•ืงืฃ ืžื ืกื” ืœื™ืฆื•ืจ ืฉืจืฉืจืช ื—ืœื•ืคื™ืช ืžื”ืจ ื™ื•ืชืจ ืžื”ืฉืจืฉืจืช ื”ื™ืฉืจื”. ื’ื ืื ื”ื“ื‘ืจ

ืžืชื‘ืฆืข, ื”ืžืขืจื›ืช ืื™ื ื” ื ืคืชื—ืช ืœืฉื™ื ื•ื™ื™ื ืฉืจื™ืจื•ืชื™ื™ื, ื›ืžื• ื™ืฆื™ืจืช ืขืจืš ื™ืฉ ืžืื™ืŸ ืื• ืœืงื™ื—ืช ื›ืกืฃ

ืฉืžืขื•ืœื ืœื ื”ื™ื” ืฉื™ื™ืš ืœืชื•ืงืฃ. ืฆืžืชื™ื ืœื ื™ืกื›ื™ืžื• ืœืงื‘ืœ ืคืขื•ืœื” ื‘ืœืชื™-ืงื‘ื™ืœื” ื›ืชืฉืœื•ื, ื•ืฆืžืชื™ื ื™ืฉืจื™ื

ืœืขื•ืœื ืœื ื™ืกื›ื™ืžื• ืขื ื’ื•ืฉ ื”ืžื›ื™ืœ ืื•ืชืŸ. ืชื•ืงืฃ ื™ื›ื•ืœ ืจืง ืœื ืกื•ืช ืœืฉื ื•ืช ืื—ืช ืžื”ืคืขื•ืœื•ืช ืฉืœื• ื›ื“ื™ ืœืงื—ืช

ื‘ื—ื–ืจื” ื›ืกืฃ ืฉื”ื•ื ื”ื•ืฆื™ื ืœืื—ืจื•ื ื”.

ื ื™ืชืŸ ืœืืคื™ื™ืŸ ืืช ื”ืžื™ืจื•ืฅ ื‘ื™ืŸ ื”ืฉืจืฉืจืช ื”ื™ืฉืจื” ื•ืฉืจืฉืจืช ืฉืœ ืชื•ืงืฃ ื‘ืชื•ืจ ื”ื™ืœื•ืš ืืงืจืื™ ื‘ื™ื ื•ืžื™.

, ืžืื•ืจืข ื”ื”ืฆืœื—ื” ื”ื•ื ืฉื”ืฉืจืฉืจืช ื”ื™ืฉืจื” ืžืชืืจื›ืช ื‘ื’ื•ืฉ ืื—ื“, ืžื” ืฉืžื’ื“ื™ืœ ืืช ื”ื”ื•ื‘ืœื” ื‘ืฉื™ืขื•ืจ +1

. ื•ืžืื•ืจืข ื”ื›ื™ืฉืœื•ืŸ ื”ื•ื ืฉื”ืฉืจืฉืจืช ืฉืœ ื”ืชื•ืงืฃ ืžืชืืจื›ืช ื‘ื’ื•ืฉ ื—ื“, ืžื” ืฉืžืคื—ื™ืช ืืช ื”ืคืขืจ ื‘ืฉื™ืขื•ืจ -1

ื”ื”ืกืชื‘ืจื•ืช ืฉืชื•ืงืฃ ื™ื“ื‘ื™ืง ืืช ื”ืคืขืจ ืžื’ืจืขื•ืŸ ื ืชื•ืŸ ืžืงื‘ื™ืœ ืœื‘ืขื™ื™ืช ืžืคื•ืœืช ื”ืžื”ืžืจ. ื ื ื™ื— ื›ื™ ืžื”ืžืจ ืขื

ืืฉืจืื™ ื‘ืœืชื™-ืžื•ื’ื‘ืœ ืžืชื—ื™ืœ ืขื ื’ื™ืจืขื•ืŸ ื•ืžืฉื—ืง ื‘ื ื™ืกื™ื•ืŸ ืœื”ื’ื™ืข ืœืื™ื–ื•ืŸ ืžืกืคืจ ื ืกื™ื•ื ื•ืช ื”ื™ื›ื•ืœ ืœื”ื™ื•ืช

ืื™ื ืกื•ืคื™. ืื ื• ื™ื›ื•ืœื™ื ืœื—ืฉื‘ ืืช ื”ื”ืกืชื‘ืจื•ืช ืฉื”ื•ื ื™ื’ื™ืข ืื™-ืคืขื ืœืื™ื–ื•ืŸ, ื›ืœื•ืžืจ ืฉื”ืชื•ืงืฃ ื™ื“ื‘ื™ืง ืื™-ืคืขื

ืืช ื”ืคืขืจ ืขื ื”ืฉืจืฉืจืช ื”ื™ืฉืจื”, ื›ื“ืœืงืžืŸ [8]


ื”ื”ืกืชื‘ืจื•ืช ืฉืฆื•ืžืช ื™ืฉืจ ื™ืžืฆื ืืช ื”ื’ื•ืฉ ื”ื‘ื = p

ื”ื”ืกืชื‘ืจื•ืช ืฉื”ืชื•ืงืฃ ื™ืžืฆื ืืช ื”ื’ื•ืฉ ื”ื‘ื = q

qz = ื’ื•ืฉื™ื z ื”ื”ืกืชื‘ืจื•ืช ืฉื”ืชื•ืงืฃ ื™ื“ื‘ื™ืง ืื™-ืคืขื ืืช ื”ืคืขืจ ืžืคื™ื’ื•ืจ ืฉืœ


ื‘ื”ื ืชืŸ ื”ื”ื ื—ื” ื›ื™ p>q, ื”ื”ืกืชื‘ืจื•ืช ืงื˜ื ื” ื‘ืื•ืคืŸ ืžืขืจื™ื›ื™ ื›ื›ืœ ืฉื’ื“ืœ ืžืกืคืจ ื”ื’ื•ืฉื™ื ืื™ืชื ื”ืชื•ืงืฃ ืฆืจื™ืš ืœื”ื“ื‘ื™ืจ ืืช ื”ืคืขืจ. ื”ื™ื•ืช ื•ื”ืกื™ื›ื•ื™ื™ื ืคื•ืขืœื™ื ื ื’ื“ื•, ืื ืื™ืŸ ืœื• ืืช ื”ืžื–ืœ ื‘ื–ื™ื ื•ืง ืงื“ื™ืžื” ื‘ืชื—ื™ืœื”, ื”ืกื™ื›ื•ื™ื™ื ืฉืœื• ื ื”ื™ื™ื ืืคืกื™ื™ื ื›ื›ืœ ืฉื”ืคื™ื’ื•ืจ ืฉืœื• ื’ื“ืœ. ืขืชื” ื ื‘ื—ืŸ ื›ืžื” ื”ืžืงื‘ืœ ืฉืœ ืคืขื•ืœื” ื—ื“ืฉื” ืฆืจื™ืš ืœื”ืžืชื™ืŸ ื›ื“ื™ ืœื”ื™ื•ืช ื‘ื˜ื•ื— ื‘ืžื™ื“ื” ืžืกืคื™ืงื” ืฉื”ืฉื•ืœื—

ืื™ื ื• ื™ื›ื•ืœ ืœืฉื ื•ืช ืืช ื”ืคืขื•ืœื”. ืื ื• ืžื ื™ื—ื™ื ืฉื”ืฉื•ืœื— ื”ื•ื ืชื•ืงืฃ ื”ืจื•ืฆื” ืœื’ืจื•ื ืœืžืงื‘ืœ ืœื”ืืžื™ืŸ ืœื–ืžืŸ-ืžื”

ืฉื”ื•ื ืฉื™ืœื ืœื•, ื•ืื– ืœื”ื—ืœื™ืฃ ืืช ื”ืคืขื•ืœื” ื›ื“ื™ ืœืฉืœื ื‘ื—ื–ืจื” ืœืขืฆืžื•. ื”ืžืงื‘ืœ ื™ืงื‘ืœ ื”ืชืจืขื” ื›ืฉื–ื” ื™ืงืจื”,

ืืš ื”ืชื•ืงืฃ ืžืงื•ื•ื” ืฉื–ื” ื™ื”ื™ื” ืžืื•ื—ืจ ืžื“ื™.

ื”ืžืงื‘ืœ ื™ื•ืฆืจ ื–ื•ื’ ืžืคืชื—ื•ืช ื—ื“ืฉ ื•ื ื•ืชืŸ ืืช ื”ืžืคืชื— ื”ืฆื™ื‘ื•ืจื™ ืœืฉืœื•ื— ื–ืžืŸ ืงืฆืจ ืœืคื ื™ ื”ื—ืชื™ืžื”. ื–ื” ืžื•ื ืข

ืžื”ืชื•ืงืฃ ืœื”ื›ื™ืŸ ืฉืจืฉืจืช ื’ื•ืฉื™ื ืžื‘ืขื•ื“ ืžื•ืขื“ ืขืœ ื™ื“ื™ ืขื‘ื•ื“ื” ืจืฆื•ืคื” ืขืœื™ื” ืขื“ ืฉื™ืฉ ืœื• ืžืกืคื™ืง ืžื–ืœ ื›ื“ื™

ืœื”ื•ื‘ื™ืœ ื‘ืžื™ื“ื” ืžืกืคืงืช, ื•ืื– ืœื‘ืฆืข ืืช ื”ืคืขื•ืœื” ื‘ืื•ืชื• ื”ืจื’ืข. ื‘ืจื’ืข ื‘ื• ื”ืคืขื•ืœื” ื ืฉืœื—ืช, ื”ืฉื•ืœื— ื”ืœื-

ื™ืฉืจ ืžืชื—ื™ืœ ืœืขื‘ื•ื“ ื‘ื—ืฉืื™ ืขืœ ืฉืจืฉืจืช ืžืงื‘ื™ืœื” ื”ืžื›ื™ืœื” ื’ืจืกื” ื—ืœื•ืคื™ืช ืฉืœ ื”ืคืขื•ืœื” ืฉืœื•.

ื’ื•ืฉื™ื ืฉื•ืจืฉืจื• ืœืื—ืจื™ื•. ื”ื•ื ืœื ื™ื•ื“ืข ืืช ืžื™ื“ืช z - ื”ืžืงื‘ืœ ืžื—ื›ื” ืขื“ ืฉื”ืคืขื•ืœื” ื”ืชื•ื•ืกืคื” ืœื’ื•ืฉ ื•

ื”ื”ืชืงื“ืžื•ืช ื”ืžื“ื•ื™ืงืช ืฉืœ ื”ืชื•ืงืฃ, ืื‘ืœ ื‘ื”ื ื—ื” ืฉื”ื’ื•ืฉื™ื ื”ื™ืฉืจื™ื ืœืงื—ื• ืคืจืง ื–ืžืŸ ืžืžื•ืฆืข ืœื›ืœ ื’ื•ืฉ,

ื”ื”ืชืงื“ืžื•ืช ื”ืืคืฉืจื™ืช ืฉืœ ื”ืชื•ืงืฃ ื”ื™ื ืžืฉืชื ื” ืคื•ืืกื•ืŸ ืขื ืชื•ื—ืœืช:


.z ืžื”ืจืฆืช ืžืกืคืจ ืชื•ืฆืื•ืช, ืื ื• ื™ื›ื•ืœื™ื ืœืจืื•ืช ืฉื”ื”ืกืชื‘ืจื•ืช ืงื˜ื ื” ื‘ืื•ืคืŸ ืžืขืจื™ื›ื™ ืขื



12. ืกื™ื›ื•ื

ื”ืฆืขื ื• ืžืขืจื›ืช ืœืขืกืงืื•ืช ืืœืงื˜ืจื•ื ื™ื•ืช ืฉืื™ื ื” ืžืกืชืžื›ืช ืขืœ ืืžื•ืŸ. ื”ืชื—ืœื ื• ืขื ื”ืžืกื’ืจืช ื”ืจื’ื™ืœื” ืฉืœ

ืžื˜ื‘ืขื•ืช ื”ืขืฉื•ื™ื™ื ืžื—ืชื™ืžื•ืช ื“ื™ื’ื™ื˜ืœื™ื•ืช, ื”ืžืกืคืงืช ืฉืœื™ื˜ื” ื—ื–ืงื” ื‘ื‘ืขืœื•ืช, ืืš ืื™ื ื” ืฉืœืžื” ืœืœื ื“ืจืš

ืœืžื ื•ืข ื ื™ืฆื•ืœ ื›ืคื•ืœ. ื›ื“ื™ ืœืคืชื•ืจ ื–ืืช, ื‘ืฆืขื ื• ืจืฉืช ืฉื™ืชื•ืคื™ืช ื”ืžืฉืชืžืฉืช ื‘ื”ื•ื›ื—ืช ืขื‘ื•ื“ื” ื›ื“ื™ ืœื ื”ืœ ืจื™ืฉื•ื

ืฉืœ ื”ื™ืกื˜ื•ืจื™ื” ืคื•ืžื‘ื™ืช ืฉืœ ืคืขื•ืœื•ืช, ืฉื‘ืžื”ืจื” ื”ื•ืคื›ืช ืœื‘ืœืชื™-ืžืขืฉื™ืช ืžื‘ื—ื™ื ื” ื—ื™ืฉื•ื‘ื™ืช ืœื”ืฉืชื ื•ืช ืขืœ ื™ื“ื™

ืชื•ืงืฃ ืื ืฆืžืชื™ื ื™ืฉืจื™ื ืฉื•ืœื˜ื™ื ื‘ืžืจื‘ื™ืช ื›ื•ื— ื”ื—ื™ืฉื•ื‘. ื”ืจืฉืช ืขืžื™ื“ื” ืžืขืฆื ื”ืคืฉื˜ื•ืช ื—ืกืจืช ื”ืžื‘ื ื”

ืฉืœื”. ืฆืžืชื™ื ืขื•ื‘ื“ื™ื ื‘ื•-ื–ืžื ื™ืช ืขื ืžืขื˜ ืชื™ืื•ื. ื”ื ืื™ื ื ืฆืจื™ื›ื™ื ืœื”ื–ื“ื”ื•ืช, ื”ื™ื•ืช ื•ื”ื•ื“ืขื•ืช ืื™ื ืŸ

ืžื ื•ืชื‘ื•ืช ืœืžืงื•ื ืžืกื•ื™ื ื•ืฆืจื™ื›ื•ืช ืœื”ื™ืžืกืจ ืจืง ืขืœ ื‘ืกื™ืก ืžื™ื˜ื‘ ื”ืžืืžืฆื™ื. ืฆืžืชื™ื ื™ื›ื•ืœื™ื ืœืขื–ื•ื‘ ืืช

ื”ืจืฉืช ื•ืœื”ืฆื˜ืจืฃ ืืœื™ื” ืžื—ื“ืฉ ื›ืจืฆื•ื ื, ืชื•ืš ืงื‘ืœืช ืฉืจืฉืจืช ื”ื•ื›ื—ืช ื”ืขื‘ื•ื“ื” ื›ื”ื•ื›ื—ื” ืœืžื” ืฉืงืจื”

ื‘ื”ื™ืขื“ืจื. ื”ื ืžืฆื‘ื™ืขื™ื ืขื ืขื•ืฆืžืช ื—ื™ืฉื•ื‘, ื•ืžื‘ื™ืขื™ื ืืช ื”ืกื›ืžืชื ืขื ื’ื•ืฉื™ื ืชืงื™ื ื™ื ื‘ืขื‘ื•ื“ื” ืขืœ

ื”ืžืฉื›ืชื, ื•ื“ื•ื—ื™ื ื’ื•ืฉื™ื ื‘ืœืชื™-ืงื‘ื™ืœื™ื ื‘ืกื™ืจื•ื‘ ืœืขื‘ื•ื“ ืขืœื™ื”ื. ื ื™ืชืŸ ืœืื›ื•ืฃ ื›ืœ ื›ืœืœ ืื• ืชืžืจื™ืฅ ืฉื™ื™ื“ืจืฉ

ืขื ืžื ื’ื ื•ืŸ ื”ื”ืกื›ืžื” ื”ื›ืœืœื™ืช ื”ื–ื”.



ื”ืคื ื™ื•ืช:

[1] W. Dai, "b-money," http://www.weidai.com/bmoney.txt, 1998.

[2] H. Massias, X.S. Avila, and J.-J. Quisquater, "Design of a secure timestamping service with minimal

trust requirements," In 20th Symposium on Information Theory in the Benelux, May 1999.

[3] S. Haber, W.S. Stornetta, "How to time-stamp a digital document," In Journal of Cryptology, vol 3, no

2, pages 99-111, 1991.

[4] D. Bayer, S. Haber, W.S. Stornetta, "Improving the efficiency and reliability of digital time-stamping,"

In Sequences II: Methods in Communication, Security and Computer Science, pages 329-334, 1993.

[5] S. Haber, W.S. Stornetta, "Secure names for bit-strings," In Proceedings of the 4th ACM Conference

on Computer and Communications Security, pages 28-35, April 1997.

[6] A. Back, "Hashcash - a denial of service counter-measure,"

http://www.hashcash.org/papers/hashcash.pdf, 2002.

[7] R.C. Merkle, "Protocols for public key cryptosystems," In Proc. 1980 Symposium on Security and

Privacy, IEEE Computer Society, pages 122-133, April 1980.

[8] W. Feller, "An introduction to probability theory and its applications," 1957.

Hebrew translation by: Meni Rosenfeld


ืื ื’ื ืืชื ืจื•ืฆื™ื ืœืœืžื•ื“ ืœืกื—ื•ืจ ื‘ืฉื•ืง ื”ืžื˜ื•ืจืฃ ื”ื–ื” ื•ื›ืžื•ื‘ืŸ ืœื”ืจื•ื•ื™ื— ืื– ื”ืฆื˜ืจืคื• ืืœื™ื ื• >> ืงื•ืจืก ืžืกื—ืจ ื‘ืงืจื™ืคื˜ื•

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