On the Number of Messages Which Cannot be Concealed in LUC

Wen-Chung KUO; Chi-Sung LAIH; Min Jea GAU; Chin Chen CHANG

On the Number of Messages Which Cannot be Concealed in LUC

Wen-Chung KUO, Chi-Sung LAIH, Min Jea GAU, Chin Chen CHANG

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Recently, Smith and Lennon proposed a new public key cryptosystem, called LUC, which uses the Lucas function as the one-way function in their cryptographic mechanisms instead of using the exponentiation function. They conjectured that LUC is cryptographically stronger than RSA in 1993. Since then, many weaknesses of LUC have been discoverd, e. g., similar to RSA, LUC also suffers from the chosen-message attacks and the evaluation in LUC is slightly less efficient than that in RSA. In this paper, we analyze another possible weakness of LUC that was not pointed out before. We show that the number of messages which cannot be concealed in LUC is at least as the same as that in RSA regardless of the choice of public keys. In particular, in many cases, the number of messages which cannot be concealed in LUC is greater than that in RSA. This implies that the choice of public keys in LUC needs more limitations than that used in RSA. Our results are useful to designers who consider to use LUC type systems.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E80-A No.11 pp.2218-2224

Publication Date: 1997/11/25

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Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)

Category: Security

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Wen-Chung KUO, Chi-Sung LAIH, Min Jea GAU, Chin Chen CHANG, "On the Number of Messages Which Cannot be Concealed in LUC" in IEICE TRANSACTIONS on Fundamentals, vol. E80-A, no. 11, pp. 2218-2224, November 1997, doi: .
Abstract: Recently, Smith and Lennon proposed a new public key cryptosystem, called LUC, which uses the Lucas function as the one-way function in their cryptographic mechanisms instead of using the exponentiation function. They conjectured that LUC is cryptographically stronger than RSA in 1993. Since then, many weaknesses of LUC have been discoverd, e. g., similar to RSA, LUC also suffers from the chosen-message attacks and the evaluation in LUC is slightly less efficient than that in RSA. In this paper, we analyze another possible weakness of LUC that was not pointed out before. We show that the number of messages which cannot be concealed in LUC is at least as the same as that in RSA regardless of the choice of public keys. In particular, in many cases, the number of messages which cannot be concealed in LUC is greater than that in RSA. This implies that the choice of public keys in LUC needs more limitations than that used in RSA. Our results are useful to designers who consider to use LUC type systems.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e80-a_11_2218/_p

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@ARTICLE{e80-a_11_2218,
author={Wen-Chung KUO, Chi-Sung LAIH, Min Jea GAU, Chin Chen CHANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Number of Messages Which Cannot be Concealed in LUC},
year={1997},
volume={E80-A},
number={11},
pages={2218-2224},
abstract={Recently, Smith and Lennon proposed a new public key cryptosystem, called LUC, which uses the Lucas function as the one-way function in their cryptographic mechanisms instead of using the exponentiation function. They conjectured that LUC is cryptographically stronger than RSA in 1993. Since then, many weaknesses of LUC have been discoverd, e. g., similar to RSA, LUC also suffers from the chosen-message attacks and the evaluation in LUC is slightly less efficient than that in RSA. In this paper, we analyze another possible weakness of LUC that was not pointed out before. We show that the number of messages which cannot be concealed in LUC is at least as the same as that in RSA regardless of the choice of public keys. In particular, in many cases, the number of messages which cannot be concealed in LUC is greater than that in RSA. This implies that the choice of public keys in LUC needs more limitations than that used in RSA. Our results are useful to designers who consider to use LUC type systems.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - On the Number of Messages Which Cannot be Concealed in LUC
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2218
EP - 2224
AU - Wen-Chung KUO
AU - Chi-Sung LAIH
AU - Min Jea GAU
AU - Chin Chen CHANG
PY - 1997
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E80-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 1997
AB - Recently, Smith and Lennon proposed a new public key cryptosystem, called LUC, which uses the Lucas function as the one-way function in their cryptographic mechanisms instead of using the exponentiation function. They conjectured that LUC is cryptographically stronger than RSA in 1993. Since then, many weaknesses of LUC have been discoverd, e. g., similar to RSA, LUC also suffers from the chosen-message attacks and the evaluation in LUC is slightly less efficient than that in RSA. In this paper, we analyze another possible weakness of LUC that was not pointed out before. We show that the number of messages which cannot be concealed in LUC is at least as the same as that in RSA regardless of the choice of public keys. In particular, in many cases, the number of messages which cannot be concealed in LUC is greater than that in RSA. This implies that the choice of public keys in LUC needs more limitations than that used in RSA. Our results are useful to designers who consider to use LUC type systems.
ER -