Abstract
XTR public key system was introduced at Crypto 2000, which is based on a method to present elements of a subgroup of a multiplicative group of a finite field. Its application in cryptographic protocols leads to substantial savings both in communication and computational overhead without compromising security. It was shown how the use of finite extension fields and subgroups can be combined in such a way that the number of bits to be exchanged is reduced by a factor 3.
In this paper we show how to more compress the communication overhead. The compressed XTR leads to a factor 6 reduction in the representation size compared to the traditional representation and achieves as twice compactness as XTR. The computational overhead of it is a little worse than that of XTR, however the compressed XTR requires only about additional 6% computational effort. If finding 4-th roots of unity is pre-computed, then the computational overhead is only 1% compared to that of original XTR. Furthermore, the required size of public key data of it reduces about 26% from that of XTR.
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Barreto, P.S.L.M., Kim, H.Y., Lynn, B., Scott, M.: Efficient Algorithms for Pairing-Based Cryptosystems. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 354–369. Springer, Heidelberg (2002)
Brouwer, A.E., Pellikaan, R., Verheul, E.R.: Doing More with Fewer Bits. In: Lam, K.-Y., Okamoto, E., Xing, C. (eds.) ASIACRYPT 1999. LNCS, vol. 1716, pp. 321–332. Springer, Heidelberg (1999)
Cohen, H.: A Course in Computational Algebraic Number Theory. Springer, Heidelberg (1993)
ElGamal, T.: A Public Key Cryptosystem and a Signature scheme Based on Discrete Logarithms. IEEE Transactions on Information Theory 31(4), 469–472 (1985)
Gong, G., Harn, L.: Public key cryptosystems based on cubic finite field extensions. IEEE Transactions on Information Theory 45(7), 2601–2605 (1999)
Itoh, T., Teechai, O., Tsujii, S.: A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases. Information and Computation 78, 171–177 (1988)
Lenstra, A.K., Verheul, E.R.: The XTR Public Key System. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 1–20. Springer, Heidelberg (2000)
Lenstra, A.K.: Using Cyclotomic Polynomials to Construct Efficient Discrete Logarithm Cryptosystems over Finite Fields. In: Mu, Y., Pieprzyk, J.P., Varadharajan, V. (eds.) ACISP 1997. LNCS, vol. 1270, pp. 127–138. Springer, Heidelberg (1997)
Menezes, A.J., van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1997)
Schnorr, C.P.: Efficient signature generation by smart cards. Journal of Cryptology 4, 161–174 (1991)
Smith, P., Skinner, C.: A Public-key cryptosystem and a digital signature system based on the Lucas function analogue to discrete logarithms. In: Safavi-Naini, R., Pieprzyk, J.P. (eds.) ASIACRYPT 1994. LNCS, vol. 917, pp. 357–364. Springer, Heidelberg (1995)
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Shirase, M., Han, DG., Hibino, Y., Kim, H.W., Takagi, T. (2007). Compressed XTR. In: Katz, J., Yung, M. (eds) Applied Cryptography and Network Security. ACNS 2007. Lecture Notes in Computer Science, vol 4521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72738-5_27
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DOI: https://doi.org/10.1007/978-3-540-72738-5_27
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