Abstract
Pairing-based cryptosystems (PBC) have been attracted by researchers in cryptography. Some implementations show that PBC are relatively slower than the standard public key cryptosystems. We present an efficient implementation for computing Tate pairing on a mobile phone using Java. We implemented the η T pairing (a recent efficient variation of Duursma-Lee algorithm) over some finite fields of characteristic 3 with extension degree m = { 97, 167, 193, 239 }. Our optimized implementation for m = 97 achieved about 0.5 seconds for computing the η T pairing over FOMA SH901iS, NTT DoCoMo. Then our implementation of the η T pairing is compared in the same platform with other Java program of the standard cryptosystems, i.e., RSA cryptosystem and elliptic curve cryptosystem (ECC). The computation speed of the η T pairing is comparable to that of RSA or ECC on the same mobile device.
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References
Barreto, P. S. L. M.: A note on efficient computation of cube roots in characteristic 3, IACR ePrint Archive, Report 2004/305 (2004)
Barreto, P. S. L. M., Galbraith, S., O’hEigeartaigh, C., Scott, M.: Efficient pairing computation on supersingular abelian varieties, To appear in Designs, Codes, and Cryptography
Barreto, P.S.L.M., Kim, H., Lynn, B., Scott, M.: Efficient algorithms for pairing-based cryptosystems. In: Yung, M. (ed.) Advances in Cryptology - CRYPTO 2002. LNCS, vol. 2442, pp. 354–368. Springer, Heidelberg (2002)
Bouncy Castle Crypto APIs, The Legion of the Bouncy Castle. http://www.bouncycastle.org/
Bertoni, G., Guajardo, J., Kumar, S., Orland, G., Paar, C., Wollinger, T.: Efficient GF(p m) arithmetic architectures for cryptographic application. In: Joye, M. (ed.) Topics in Cryptology - CT-RSA 2003. LNCS, vol. 2612, pp. 158–175. Springer, Heidelberg (2003)
Boneh, D., Franklin, M.: Identity based encryption from the Weil pairing. SIAM J. Comput. 32(3), 586–615 (2001)
Boneh, D., Gentry, C., Waters, B.: Collusion resistant broadcast encryption with short ciphertexts and private keys. In: Shoup, V. (ed.) Advances in Cryptology – CRYPTO 2005. LNCS, vol. 3621, pp. 258–275. Springer, Heidelberg (2005)
Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. In: Boyd, C. (ed.) Advances in Cryptology - ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)
Certicom Research: EC 2: Recommended Elliptic Curve Domain Parameters, Version 1.0 (2000)
Duursma, I., Lee, H.: Tate pairing implementation for hyperelliptic curves y 2 = x p − x + d. In: Laih, C.-S. (ed.) Advances in Cryptology - ASIACRYPT 2003. LNCS, vol. 2894, pp. 111–123. Springer, Heidelberg (2003)
Hankerson, D., Menezes, A., Vanstone, S.: Guide to elliptic curve cryptography. Springer, Heidelberg (2004)
Harrison, K., Page, D., Smart, N.: Software implementation of finite fields of characteristic three, for use in pairing-based cryptosystems. LMS J. Comput. Math. 5, 181–193 (2002)
IAIK Provider for the Java Cryptography Extension (IAIK-JCE). http://www.iaik.tugraz.at/
Java 2 Platform, Micro Edition (J2ME). http://java.sun.com/javame/
Java Cryptography Extension (JCE). http://java.sun.com/products/jce/
Kerins, T., Marnane, W., Popovici, E., Barreto, P.S.L.M.: Efficient hardware for the Tate pairing calculation in characteristic three. In: Rao, J.R., Sunar, B. (eds.) Cryptographic Hardware and Embedded Systems – CHES 2005. LNCS, vol. 3659, pp. 412–426. Springer, Heidelberg (2005)
Kwon. S.: Efficient Tate pairing computation for supersingular elliptic curves over binary fields, IACR ePrint Archive, Report, p. 303 (2004)
Scott, M., Costigan, N., Abdulwahab, W.: Implementing Cryptographic Pairings on Smartcards. In: Goubin, L., Matsui, M. (eds.) Cryptographic Hardware and Embedded Systems - CHES 2006. LNCS, vol. 4249, pp. 134–147. Springer, Heidelberg (2006)
Silverman, J.: The arithmetic of elliptic curves. Springer, Heidelberg (1986)
Takagi, T., Reis Jr., D., Yen, S.-M., Wu, B.-C.: Radix-r non-adjacent form and its application to pairing-based cryptosystem. IEICE Transactions E89-A(1), 115–123 (2006)
Tillich, S., Großschadl, J.: A survey of public-key cryptography on J2ME-enabled mobile devices. In: Aykanat, C., Dayar, T., Körpeoğlu, İ. (eds.) Computer and Information Sciences - ISCIS 2004. LNCS, vol. 3280, pp. 935–944. Springer, Heidelberg (2004)
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Kawahara, Y., Takagi, T., Okamoto, E. (2007). Efficient Implementation of Tate Pairing on a Mobile Phone Using Java. In: Wang, Y., Cheung, Ym., Liu, H. (eds) Computational Intelligence and Security. CIS 2006. Lecture Notes in Computer Science(), vol 4456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74377-4_42
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DOI: https://doi.org/10.1007/978-3-540-74377-4_42
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