• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.6
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• pp.125-135
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• 2002

The electronic payment system based on blind signature is susceptible to the blackmailing attack as opposed to keep the lifestyle of users private. In this paper. we suggest an efficient electronic cash system using a blind XTR-DSA scheme, which improves the method of defeating blackmailing in online electronic cash systems of ［6,9］. In case of blackmailing, to issue the marked coins we use the blind XTR-DSA scheme at withdrawal. In ［6,9］, to cheat the blackmailer who takes the marked coins the decryption key of a user had to be transferred to the Bank. But in our proposed method the delivery of the decryption key is not required. Also, in the most serious attack of blackmailing. kidnapping, we can defeat blackmailing with a relatively high probability of 13/18 compared with 1/2 in ［9］ and 2/3 in ［6］. If an optimal extension field of XTR suggested in ［7］ is used, then we can implement our system more efficiently.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.13 no.3
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• pp.111-117
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• 2003

The XTR public key system has advantage of short key length and fast computing speed. So, the XTR is used usefully in complicated operation. In this paper, we propose a new algorithm of double exponentiation operation and a proxy signature protocol based on the XTR. The double exponentiation operation should be executed to apply XTR for the proxy signature protocol. But this algorithm is inappropriate, because two secret key has to be blown in existent operation algorithm. New algorithm enable double exponentiation operation with proxy signer's secret key and public information. And the XTR is used to generation and verification of proxy at proxy signature protocol. Therefore proxy signature based on the XTR has basic advantage of the XTR. These advantage can be used in internet as well as mobile.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.6
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• pp.17-28
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• 2002

XTR is a new method to represent elements of a subgroup of a multiplicative group of a finite field GF( $p^{6m}$) and it can be generalized to the field GF( $p^{6m}$)$^{[6,9]}$ This paper progress optimal extention fields for XTR among Galois fields GF ( $p^{6m}$) which can be aplied to XTR. In order to select such fields, we introduce a new notion of Generalized Opitimal Extention Fields(GOEFs) and suggest a condition of prime p, a defining polynomial of GF( $p^{2m}$) and a fast method of multiplication in GF( $p^{2m}$) to achieve fast finite field arithmetic in GF( $p^{2m}$). From our implementation results, GF( $p^{36}$ )longrightarrowGF( $p^{12}$ ) is the most efficient extension fields for XTR and computing Tr( $g^{n}$ ) given Tr(g) in GF( $p^{12}$ ) is on average more than twice faster than that of the XTR system on Pentium III/700MHz which has 32-bit architecture.$^{［6,10］/ ［6,10］/6,10］}$