IEICE TRANSACTIONS on Fundamentals
On the Average Length of Secret Key Exchange Eulerian Circuits
Summary :
Designing a protocol to exchange a secret key is one of the most fundamental subjects in cryptography. Using a random deal of cards, pairs of card players (agents) can share secret keys that are information-theoretically secure against an eavesdropper. A key set protocol, which uses a random deal of cards, can perform an Eulerian secret key exchange, in which the pairs of players sharing secret keys form an Eulerian circuit passing through all players. Along the Eulerian circuit any designated player can send a message to the rest of players and the message can be finally sent back to the sender. Checking the returned message with the original one, the sender can know whether the message circulation has not been influenced by a possible single transmission error or false alteration. It has been known that any Eulerian circuit formed by the protocol has length at most 3/2k, where k is the number of players. Note that the length corresponds to the time required to send the message to all players and acknowledge the secure receipt. In this paper, we show that the average length of Eulerian circuits is approximately k+ln k.
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- IEICE TRANSACTIONS on Fundamentals Vol.E83-A No.4 pp.662-670
- Publication Date
- 2000/04/25
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- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
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Takaaki MIZUKI, Zhi-Bo SUI, Hiroki SHIZUYA, Takao NISHIZEKI, "On the Average Length of Secret Key Exchange Eulerian Circuits" in IEICE TRANSACTIONS on Fundamentals,
vol. E83-A, no. 4, pp. 662-670, April 2000, doi: .
Abstract: Designing a protocol to exchange a secret key is one of the most fundamental subjects in cryptography. Using a random deal of cards, pairs of card players (agents) can share secret keys that are information-theoretically secure against an eavesdropper. A key set protocol, which uses a random deal of cards, can perform an Eulerian secret key exchange, in which the pairs of players sharing secret keys form an Eulerian circuit passing through all players. Along the Eulerian circuit any designated player can send a message to the rest of players and the message can be finally sent back to the sender. Checking the returned message with the original one, the sender can know whether the message circulation has not been influenced by a possible single transmission error or false alteration. It has been known that any Eulerian circuit formed by the protocol has length at most 3/2k, where k is the number of players. Note that the length corresponds to the time required to send the message to all players and acknowledge the secure receipt. In this paper, we show that the average length of Eulerian circuits is approximately k+ln k.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e83-a_4_662/_p
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@ARTICLE{e83-a_4_662,
author={Takaaki MIZUKI, Zhi-Bo SUI, Hiroki SHIZUYA, Takao NISHIZEKI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Average Length of Secret Key Exchange Eulerian Circuits},
year={2000},
volume={E83-A},
number={4},
pages={662-670},
abstract={Designing a protocol to exchange a secret key is one of the most fundamental subjects in cryptography. Using a random deal of cards, pairs of card players (agents) can share secret keys that are information-theoretically secure against an eavesdropper. A key set protocol, which uses a random deal of cards, can perform an Eulerian secret key exchange, in which the pairs of players sharing secret keys form an Eulerian circuit passing through all players. Along the Eulerian circuit any designated player can send a message to the rest of players and the message can be finally sent back to the sender. Checking the returned message with the original one, the sender can know whether the message circulation has not been influenced by a possible single transmission error or false alteration. It has been known that any Eulerian circuit formed by the protocol has length at most 3/2k, where k is the number of players. Note that the length corresponds to the time required to send the message to all players and acknowledge the secure receipt. In this paper, we show that the average length of Eulerian circuits is approximately k+ln k.},
keywords={},
doi={},
ISSN={},
month={April},}
Copy
TY - JOUR
TI - On the Average Length of Secret Key Exchange Eulerian Circuits
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 662
EP - 670
AU - Takaaki MIZUKI
AU - Zhi-Bo SUI
AU - Hiroki SHIZUYA
AU - Takao NISHIZEKI
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E83-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2000
AB - Designing a protocol to exchange a secret key is one of the most fundamental subjects in cryptography. Using a random deal of cards, pairs of card players (agents) can share secret keys that are information-theoretically secure against an eavesdropper. A key set protocol, which uses a random deal of cards, can perform an Eulerian secret key exchange, in which the pairs of players sharing secret keys form an Eulerian circuit passing through all players. Along the Eulerian circuit any designated player can send a message to the rest of players and the message can be finally sent back to the sender. Checking the returned message with the original one, the sender can know whether the message circulation has not been influenced by a possible single transmission error or false alteration. It has been known that any Eulerian circuit formed by the protocol has length at most 3/2k, where k is the number of players. Note that the length corresponds to the time required to send the message to all players and acknowledge the secure receipt. In this paper, we show that the average length of Eulerian circuits is approximately k+ln k.
ER -
English
