Masahiro Mambo (Web page: Japanese version , English version)

Fundamental Cryptography: (back to the top)

Jean-Luc Beuchat, Hiroshi Doi, Kaoru Fujita, Atsuo Inomata, Piseth Ith, Akira Kanaoka, Masayoshi Katouno, Masahiro Mambo, Eiji Okamoto, Takeshi Okamoto, Takaaki Shiga, Masaaki Shirase, Ryuji Soga, Tsuyoshi Takagi, Ananda Vithanage, and Hiroyasu Yamamoto,
FPGA and ASIC Implementations of the η_T Pairing in Characteristic Three,
Computers and Electrical Engineering, Vol.36, Issue 1, pp.73-87 (January 2010).
Abstract & Paper (ScienceDirect)

Shingo HASEGAWA, Shuji ISOBE, Masahiro MAMBO, Hiroki SHIZUYA, Yuichi FUTA, Motoji OHMORI,
A Countermeasure for Protecting NTRUSign against the Transcript Attack,
Interdisciplinary Information Sciences, Vol.13, No.2, pp.181-188 (2007).
Abstract & Paper (IIS on J-STAGE (Japan Science and Technology Information Aggregator, Electronic))

Shuji ISOBE, Wataru KUMAGAI, Masahiro MAMBO, Hiroki SHIZUYA,
Toward Separating Integer Factoring from Discrete Logarithm mod p,
IEICE Trans. on Fundamentals, Vol.E90-A, No.1, pp.48-53 (January 2007).
Abstract & Paper (IEICE Transactions Online)

Chisato KONOMA, Masahiro MAMBO and Hiroki SHIZUYA,
The Computational Difficulty of Solving Cryptographic Primitive Problems Related to the Discrete Logarithm Problem,
IEICE Trans. on Fundamentals, Vol.E88-A, No.1, pp.81-88 (January 2005).
Abstract & Paper (IEICE Transactions Online)

Chisato KONOMA, Masahiro MAMBO and Hiroki SHIZUYA,
Complexity Analysis of the Cryptographic Primitive Problems through Square-Root Exponent,
IEICE Trans. on Fundamentals, Vol.E87-A, No.5, pp.1083-1091 (May 2004).
Abstract & Paper (IEICE Transactions Online)

Soo-Hyun OH, Masahiro MAMBO, Hiroki SHIZUYA and Dong-Ho WON,
On the Security of Girault Key Agreement Protocols against Active Attacks,
IEICE Trans. on Fundamentals, Vol.E86-A, No.5, pp.1181-1189 (May 2003).
Abstract & Paper (IEICE Transactions Online)

Shintaro ITAGAKI, Masahiro MAMBO and Hiroki SHIZUYA,
On the Strength of Strong RSA Assumption,
IEICE Trans. on Fundamentals, Vol.E86-A, No.5, pp.1164-1170 (May 2003).
Abstract & Paper (IEICE Transactions Online)

Seungjoo Kim, Masahiro Mambo and Yuliang Zheng,
Rethinking Chosen-Ciphertext Security under Kerckhoffs' Assumption,
Topics in Cryptology-CT-RSA 2003, M. Joye (Ed.), Lecture Notes in Computer Science 2612, Springer-Verlag, pp.226-242 (April 2003).
LNCS Volume 2612 (SpringerLink)

Seungjoo Kim, Jung Hee Cheon, Marc Joye, Seongan Lim, Masahiro Mambo, Dongho Won and Yuliang Zheng,
Strong Adaptive Chosen-Ciphertext Attacks with Memory Dump (Or: The Importance of the Order of Decryption and Validation),
Cryptography and Coding, B. Honary (Ed.), Lecture Notes in Computer Science 2260, Springer-Verlag, pp.114-127 (December 2001).
LNCS Volume 2260 (SpringerLink)

Seungjoo KIM, Masahiro MAMBO, Takeshi OKAMOTO, Hiroki SHIZUYA, Mitsuru TADA and Dongho WON,
On the Security of the Okamoto-Tanaka ID-Based Key Exchange Scheme against Active Attacks,
IEICE Trans. on Fundamentals, Vol.E84-A, No.1, pp.231-238 (January 2001).
Abstract & Paper (IEICE Transactions Online)

Masato YAMAMICHI, Masahiro MAMBO and Hiroki SHIZUYA,
On the Complexity of Constructing an Elliptic Curve of a Given Order,
IEICE Trans. on Fundamentals, Vol.E84-A, No.1, pp.140-145 (January 2001).
Abstract & Paper (IEICE Transactions Online)

Seungjoo Kim, Masahiro Mambo, Hiroki Shizuya and Dongho Won,
On the Security of the Okamoto-Tanaka ID-Based Key Exchange Scheme against Active Attacks,
Proc. of Japan-Korea Joint Workshop on Information Security and Cryptology, JW-ISC2000 pp.191-198 (January 2000).

Masahiro MAMBO and Hiroki SHIZUYA,
A Note on the Complexity of Breaking Okamoto-Tanaka ID-Based Key Exchange Scheme,
IEICE Trans. on Fundamentals, Vol.E82-A, No.1, pp.77-80 (January 1999).
Abstract & Paper (IEICE Transactions Online)
(Conference presentation:
Masahiro Mambo and Hiroki Shizuya,
A Note on the Complexity of Breaking Okamoto-Tanaka ID-Based Key Exchange Scheme,
Public Key Cryptography, PKC'98, Hideki Imai and Yuliang Zheng (Eds.), Lecture Notes in Computer Science 1431, Springer-Verlag, pp.258-262 (March 1998).
LNCS Volume 1431 (SpringerLink) )

Kouichi Itoh, Eiji Okamoto and Masahiro Mambo,
Proposal of a Fast Public Key Cryptosystem,
Workshop Record of Workshop on Selected Areas in Cryptography, SAC'97, pp.224-230 (1997).

Rene PERALTA, Masahiro MAMBO and Eiji OKAMOTO,
Factoring Hard Integers on a Parallel Machine,
IEICE Trans. on Fundamentals, Vol.E80-A, No.4, pp.658-662 (April 1997).
Abstract & Paper (IEICE Transactions Online)

Eiji OKAMOTO, Tomohiko UYEMATSU and Masahiro MAMBO,
Permutation Cipher Scheme Using Polynomials over a Field,
IEICE Trans. on Information and Systems, Vol.E78-D, No.2, pp.138-142 (February 1995).
Abstract & Paper (IEICE Transactions Online)　

Kaoru KUROSAWA, Masahiro MAMBO and Shigeo TSUJII,
5-Move Statistical Zero Knowledge,
IEICE Trans. on Fundamentals, Vol.E76-A, No.1, pp.40-45 (January 1993).
Abstract & Paper (IEICE Transactions Online)

Cryptographic protocols: (back to the top)

Yunho Lee, Sangjoon Park, Masahiro Mambo, Seungjoo Kim, Dongho Won,
Towerds Trustworthy e-Voting using Paper Receipts,
Computer Standards & Interfaces, Elsevier, Vol.32, Issues.5-6, pp.305-311 (October 2010).
Abstract & Paper (ScienceDirect)

Hisao SAKAZAKI, Eiji OKAMOTO and Masahiro MAMBO,
Constructing Identity-Based Key Distribution Systems over Elliptic Curves,
IEICE Trans. on Fundamentals, Vol.E81-A, No.10, pp.2138-2143 (October 1998).
Abstract & Paper (IEICE Transactions Online)
(Related conference presentations:
Hisao Sakazaki, Eiji Okamoto and Masahiro Mambo,
ID-Based Key Distribution System over an Elliptic Curves,
Finite Fields: Theory, Applications, and Algorithms, Contemporary Mathematics Vol.225, AMS, pp.215-224 (1999). (Note: Published after the conference)
Hisao Sakazaki, Eiji Okamoto and Masahiro Mambo,
The Application of ID-Based Key Distribution Systems to an Elliptic Curve,
Information Security, ISW'97, Eiji Okamoto, George Davida and Masahiro Mambo (Eds.), Lecture Notes in Computer Science 1396, Springer-Verlag (1998), 335-344.
Volume 1396 (SpringerLink) )　

Kazuomi OISHI, Masahiro MAMBO and Eiji OKAMOTO,
Anonymous Public Key Certificates and Their Applications,
IEICE Trans. on Fundamentals, Vol.E81-A, No.1, pp.56-64 (January 1998).
Abstract & Paper (IEICE Transactions Online)

Masahiro Mambo, Eiji Okamoto and Kouichi Sakurai,
Protection of Data and Delegated Keys in Digital Distribution,
Information Security and Privacy, ACISP '97, Vijay Varadharajan and Josef Pieprzyk and Yi Mu (Eds.), Lecture Notes in Computer Science 1270, Springer-Verlag, pp.271-282 (July 1997).
Volume 1270 (SpringerLink)

Masahiro Mambo, Kouichi Sakurai and Eiji Okamoto,
How to Utilize the Transformability of Digital Signatures for Solving the Oracle Problem,
Advances in Cryptology -- Asiacrypt'96, Kwangjo Kim and Tsutomu Matsumoto (Eds.), Lecture Notes in Computer Science 1163, Springer-Verlag, pp.322-333 (November 1996).
Volume 1163 (SpringerLink)

Masahiro MAMBO, Akinori NISHIKAWA, Eiji OKAMOTO and Shigeo TSUJII,
A Secure Broadcast Communication Method with Short Messages,
IEICE Trans. on Fundamentals, Vol.E77-A, No.8, pp.1319-1327 (August 1994).
Abstract & Paper (IEICE Transactions Online)
(Conference presentation:
Masahiro Mambo, Akinori Nishikawa, Shigeo Tsujii and Eiji Okamoto,
Efficient Secure Broadcast Communication Systems,
Proc. of 1993 Korea-Japan Joint Workshop on Information Security and Cryptology pp.23-33 (1993).)

Digital Commerce: (back to the top)

嘉賀光儀, 満保雅浩, 岡本栄司,
効率的な改良PayWord小額決済方式,
電子情報通信学会論文誌, Vol.J91-D, No.12, pp.2809-2818, (December 2008).
Mitsuyoshi KAGA, Masahiro MAMBO, Eiji OKAMOTO,
An Efficient Improved PayWord Micropayment Scheme,
The IEICE Trans. on Information and Systems (Japanese Edition), Vol.J91-D, No.12, pp.2809-2818, (December 2008). (in Japanese)
Abstract & Paper (IEICE Transactions Online)

Masahiro Mambo, Moises Rosales Salinas, Kazuo Ohta, Noboru Kunihiro,
Problems on the MR Micropayment Schemes,
Proc. of the ACM Symposium on Information, Computer and Communications Security (ASIACCS’06), ISBN 1-59593-272-0, page 363, (March 2006).
Paper (ACM Digital Library)

Eikoh Chida, Yosuke Kasai, Masahiro Mambo and Hiroki Shizuya,
Spending Offline Divisible Coins with Combining Capability,
Progress in Cryptology - INDOCRYPT 2002, A. Menezes, P. Sarkar (Eds.), Lecture Notes in Computer Science 2551, Springer-Verlag, pp.339-353 (December 2002).
LNCS Volume 2551 (SpringerLink)

Eikoh CHIDA, Masahiro MAMBO and Hiroki SHIZUYA,
Digital Money -- A Survey,
Interdisciplinary Information Sciences, Vol.7, No.2, pp.135-165 (2001).
Abstract & Paper (IIS on J-STAGE (Japan Science and Technology Information Aggregator, Electronic))

Proxy cryptography: (back to the top)

Lihua Wang, Licheng Wang, Masahiro Mambo, Eiji Okamoto, Identity-Based Proxy Cryptosystems with Revocability and Hierarchical Confidentialities, ICICS 2010, LNCS, pp.-, Springer-Verlag (December 2010) Accepted, To be published.

Lihua Wang, Licheng Wang, Masahiro Mambo, Eiji Okamoto, New Identity-Based Proxy Re-Encryption Schemes to Prevent Collusion Attacks, Pairing 2010, LNCS, pp.-, Springer-Verlag (December 2010) Accepted, To be published.

Lihua Wang, Jun Shao, Zhenfu Cao, Masahiro Mambo, Akihiro Yamamura,
A Certificate-Based Proxy Cryptosystem with Revocable Proxy Decryption Power,
K. Srinathan, C. Pandu Rangan, Moti Yung (eds.), INDCRYPT 2007, Springer-Verlag, LNCS4859, pp.297-311 (2007).
LNCS Volume 4859 (SpringerLink)

Masahiro Mambo and Shahrokh Saeednia,
Signature Schemes Based on the DSA and the Related Atomic Proxy Functions,
Proc. 2003 IEEE International Symposium on Information Theory, page 138 (2003). 　

Masahiro MAMBO and Eiji OKAMOTO,
Proxy Cryptosystems: Delegation of the Power to Decrypt Ciphertexts,
IEICE Transactions on Fundamentals, Vol.E80-A, No.1, pp.54-63, (January 1997).
Abstract & Paper (IEICE Transactions Online)

Masahiro MAMBO, Keisuke USUDA and Eiji OKAMOTO,
Proxy Signatures: Delegation of the Power to Sign Messages,
IEICE Trans. on Fundamentals, E79-A, No.9, pp.1338-1354 (September 1996).
Abstract & Paper (IEICE Transactions Online)
(Conference presentation:
Masahiro Mambo, Keisuke Usuda and Eiji Okamoto,
Proxy Signatures for Delegating Signing Operation,
Proc. of the 3rd ACM Conference on Computer and Communications Security, pp.48-57 (1996).)

A paper applying the proxy signature to compilers

Special signatures: (back to the top)

Naoto Yanai, Eikoh Chida, Masahiro Mambo, A Structured Aggregate Signature Scheme, Proc. of the 2010 International Symposium on Information Theory and its Applications, pp.- (October 2010) Accepted, To be published.

Naoto Yanai, Eikoh Chida and Masahiro Mambo, A Structured Multisignature based on a Non-Commutative Ring Homomorphism, CD-ROM of the Fourth Joint Workshop on Information Security, JWIS 2009, 1B-3 (August 2009).

土井洋, 満保雅浩, 岡本栄司,
様々な署名構造に適用可能なRSA型多重署名方式,
情報処理学会論文誌, 第41巻, 第8号, pp.2080-2091 (Aug. 2000)
Hiroshi Doi, Masahiro Mambo and Eiji Okamoto,
RSA-based Multisignature Scheme for Various Group Structures,
IPSJ Journal, Vol.41, No.8, pp.2080-2091 (August 2000) (in Japanese)
Abstract & Paper (IPSJ Bookpark)
(Conference presentations:
Hiroshi Doi, Masahiro Mambo and Eiji Okamoto,
On the Security of the RSA-Based Multisignature Scheme for Various Group Structures,
Information Security and Privacy, ACISP2000, Ed Dawson, Andrew Clark and Colin Boyd (Eds.), Lecture Notes in Computer Science 1841, Springer-Verlag, pp.352-367 (July 2000).
Volume 1841 (SpringerLink)
Hiroshi Doi, Eiji Okamoto and Masahiro Mambo,
Multisignature Schemes for Various Group Structures,
Proc. of The 36th Annual Allerton Conference on Communication, Control, and Computing, pp.713-722 (1999).
Hiroshi Doi, Eiji Okamoto and Masahiro Mambo,
Multisignature Schemes Using Structured Group ID,
Proc. of First Japan-Singapore Joint Workshop on Information Security, pp.51-60 (1998).)

Mike Burmester, Yvo Desmedt, Hiroshi Doi, Masahiro Mambo, Eiji Okamoto, Mitsuru Tada and Yuko Yoshifuji,
A Structured ElGamal-Type Multisignature Scheme,
Public Key Cryptography, PKC2000, Hideki Imai and Yuliang Zheng (Eds.), Lecture Notes in Computer Science 1751, Springer-Verlag, pp.466-483 (January 2000).
LNCS Volume 1751 (SpringerLink)

Message/key recovery: (back to the top)

Seungjoo Kim, Insoo Lee, Masahiro Mambo and Sungjun Park,
On the Difficulty of Key Recovery Systems,
Information Security, ISW'99, Masahiro Mambo and Yuliang Zheng (Eds.), Lecture Notes in Computer Science 1729, Springer-Verlag, pp.205-222 (November 1999).
LNCS Volume 1729 (SpringerLink)

Masahiro Mambo and Eiji Okamoto,
The Importance of Randomness in Message Recovery,
Proc. of 1997 Joint Workshop on Information Security and Cryptology, pp.181-185 (1997).

満保雅浩, 岡本栄司,
社会での暗号技術の取り扱いとClipper Chipについて,
情報処理学会誌, Vol.37, No.6, pp.503-510 (1996).
Masahiro Mambo and Eiji Okamoto,
On the Treatment of Cryptographic Techniques in the Society and Clipper Chip,
IPSJ Magazine(Joho Shori), Vol.37, No.6, pp.503-510 (1996) (in Japanese).
Paper (IPSJ Bookpark)

Computer/Network security: (back to the top)

Yukie Unno, Masahiro Mambo, Eiji Okamoto,
Refinement of the Blass-Zitterbart Key Establishment Scheme for Secure Aggregating Sensor Networks,
Proc. of JWIS 2008, pp.449-461 (July 2008).

Sk. Md. Mizanur Rahman, Nidal Nasser, Atsuo Inomata, Takeshi Okamoto, Masahiro Mambo, Eiji Okamoto,
Anonymous authentication and secure communication protocol for wireless mobile ad hoc networks,
Security and Communication Networks, Wiley InterScience, Vol.1, Issue 2, pp.179-189 (February 2008).
Abstract & Paper (InterScience Online Journals)
(Conference presentation:
Sk. Md. Mizanur Rahman, Atsuo Inomata, Takeshi Okamoto, Masahiro Mambo, Eiji Okamoto, Anonymous Secure Communication in Wireless Mobile Ad-hoc Networks, F. Stajano et.al. (eds.), ICUCT2006, Springer-Verlag, LNCS4412, pp.140-149 (2007).
LNCS Volume 4412 (SpringerLink) )

Sk. Md. Mizanur Rahman, Atsuo Inomata, Masahiro Mambo, Eiji Okamoto,
Anonymous On-Demand Position-based Routing in Mobile Ad Hoc Networks,
IPSJ Journal Vol.47, No.8, pp.2396-2408 (August 2006).
(Sk. Md. Mizanur Rahman, Atsuo Inomata, Masahiro Mambo, Eiji Okamoto,
Anonymous On-Demand Position-based Routing in Mobile Ad Hoc Networks,
IPSJ Digital Courier Vol.2, pp.524-536 (2006).)
Abstract & Paper (IPSJ Bookpark), Abstract & Paper (IPSJ Digital Courier)
(Conference presentation:
Sk. Md. Mizanur Rahman, Atsuo Inomata, Masahiro Mambo, Eiji Okamoto,
An Anonymous On-Demand Position-based Routing in Mobile Ad Hoc Networks,
Proc. the 2006 International Symposium on Applications and the Internet(SAINT2006), IEEE Computer Society, ISBN 0-7695-2508-3, pp.300-306 (January 2006).
Abstract & Paper (IEEE Computer Society digital library) )

Masahiro Mambo, Eiji Okamoto, Yasushi Sengoku and Takashi Tanaka,
Simple and Secure Mobile Access under the Flexible Organization Management,
Proc. of the Thirteenth International Workshop on Database and Expert Systems Applications, IEEE Computer Society, pp.456-460 (2002).
Abstract & Paper (IEEE Computer Society digital library) 　

後藤英昭, 満保雅浩, 靜谷啓樹,
廉価なスイッチと Secure Shell を利用した安全な情報コンセントの構成方法,
電子情報通信学会論文誌, Vol.J84-D-I, No.10, pp.1502-1505 (2001年10月)
Hideaki GOTO, Masahiro MAMBO, Hiroki SHIZUYA,
Secure Access Ports with Authentication Using Inexpensive Switches and the Secure Shell,
Trans. of IEICE, Vol.J84-D-I, No.10, pp.1502-1505 (October 2001) (in Japanese)
Abstract & Paper (IEICE Transactions Online)

Shigeki KITAZAWA, Xun YI, Eiji OKAMOTO and Masahiro MAMBO,
Improvement of Secure Access Control Agent for Distributed Files,
Proc. of International Workshop on Security, IWSEC'99, IEEE Computer Society, pp.185-190 (1999).

Shigeki Kitazawa, Eiji Okamoto and Masahiro Mambo,
Secure Access Control; Agent For Distributed Files,
Proc. of First Japan-Singapore Joint Workshop on Information Security, pp.83-90 (1998).　

Sangjin Nam, Eiji Okamoto, Youichi Shinoda and Masahiro Mambo,
A Design and Implementation of a Platform for Self-Deciphering Secret Communication,
Proc. of 1996 International Symposium on Information Theory and Its Applications, pp.242-245 (1996).

満保 雅浩, 木下 宏揚, 辻井 重男,
送受信者追跡の不可能な通信プロトコルに関する研究,
電子情報通信学会論文誌, Vol.J74-D-I, No.7, pp.429-434 (July 1991).
Masahiro MAMBO, Hirotsugu KINOSHITA, Shigeo TSUJII,
Communication Protocols with Untraceability of Sender and Receiver,
IEICE Trans. Vol.J74-D-I, No.7, pp.429-434 (July 1991). (in Japanese)
Abstract & Paper (IEICE Transactions Online)

Software protection: (back to the top)

Hideaki Goto, Masahiro Mambo, Hiroki Shizuya and Yasuyoshi Watanabe,
Evaluation of Tamper-Resistant Software Deviating from Structured Programming Rules,
Information Security and Privacy, ACISP2001, Vijay Varadharajan and Yi Mu (Eds.), Lecture Notes in Computer Science 2119, Springer-Verlag, pp.145-158 (July 2001).
LNCS Volume 2119 (SpringerLink)

Hideaki Goto, Masahiro Mambo, Kenjiro Matsumura and Hiroki Shizuya,
An Approach to the Objective and Quantitative Evaluation of Tamper-Resistant Software,
Information Security Workshop, ISW2000, J. Pieprzyk, E. Okamoto, J. Seberry (Eds.), Lecture Notes in Computer Science 1975, Springer-Verlag, pp.82-96 (December 2000).
LNCS Volume 1975 (SpringerLink)

Masahiro Mambo, Takanori Murayama and Eiji Okamoto,
A Tentative Approach to Constructing Tamper-Resistant Software,
1997 New Security Paradigms Workshop, ACM Press, pp.23-33 (1998).　
Paper (ACM Digital Library)

千石 靖, 岡本栄司, 満保雅浩, 植松友彦,
コンピュータウイルスの拡散と消滅の大域的振舞について,
情報処理学会論文誌, Vol.37, No.4, pp.579-587 (April 1996).
Yasushi Sengoku, Eiji Okamoto, Masahiro Mambo and Tomohiko Uyematsu,
Global Behavior of Computer Virus Diffusion and Extinction,
IPSJ Journal, Vol.37, No.4, pp.579-587 (April 1996). (in Japanese)
Abstract & Paper (IPSJ Bookpark)
(Conference presentation:
Yasushi Sengoku, Eiji Okamoto, Masahiro Mambo and Tomohiko Uyematsu,
Analysis of Infection and Distinction of Computer Viruses in Computer Networks,
Proc. of 1996 International Symposium on Information Theory and Its Applications pp.163-166 (1996).

Keisuke USUDA, Masahiro MAMBO, Tomohiko UYEMATSU and Eiji OKAMOTO,
Proposal of an Automatic Signature Creation Using a Compiler,
IEICE Trans. on Fundamentals, Vol.E79-A, No.1, pp.94-101 (January 1996).
Abstract & Paper (IEICE Transactions Online)　
(Conference presentation: Keisuke Usuda, Masahiro Mambo, Tomohiko Uyematsu and Eiji Okamoto,
A Signature Scheme Using a Compiler,
Proc. of 1995 Japan-Korea Joint Workshop on Information Security and Cryptology, pp.111-119 (1995).)

Biometrics/Human identification: (back to the top)

Agus Fanar Syukri, Eiji Okamoto and Masahiro Mambo,
A User Identification System Using Signature Written with Mouse,
Information Security and Privacy, ACISP'98, Colin Boyd and Ed Dawson (Eds.), Lecture Notes in Computer Science 1438, Springer-Verlag, pp.403-414 (July 1998).
LNCS Volume 1438 (SpringerLink)

Kenichi Hayashi, Eiji Okamoto and Masahiro Mambo,
Proposal of User Identification Scheme Using Mouse,
International Conference on Information and Communications Security, ICICS'97, Yongfei Han, Tatsuaki Okamoto and Sihan Qing (Eds.), Lecture Notes in Computer Science 1334, Springer-Verlag, pp.144-148 (1997).
Volume 1334 (SpringerLink)

Algorithm and others: (back to the top)

Shuji ISOBE, Tetsuo KURIYAMA, Masahiro MAMBO and Hiroki SHIZUYA,
On the Polynomial Time Computability of Abstract Ray-Tracing Problems,
IEICE Trans. on Fundamentals, Vol.E88-A, No.5, pp.1209-1213 (May 2005).
Abstract & Paper (IEICE Transactions Online)