Abstract
In this paper we propose a new symmetric block cipher with the following paradoxical traceability properties: it is computationally easy to derive many equivalent secret keys providing distinct descriptions of the same instance of the block cipher. But it is computationally difficult, given one or even up to k equivalent keys, to recover the so called meta-key from which they were derived, or to find any additional equivalent key, or more generally to forge any new untraceable description of the same instance of the block cipher. Therefore, if each legitimate user of a digital content distribution system based on encrypted information broadcast (e.g. scrambled pay TV, distribution over the Internet of multimedia content, etc.) is provided with one of the equivalent keys, he can use this personal key to decrypt the content. But it is conjectured infeasible for coalitions of up to k traitors to mix their legitimate personal keys into untraceable keys they might redistribute anonymously to pirate decoders. Thus, the proposed block cipher inherently provides an efficient traitor tracing scheme [4]. The new algorithm can be described as an iterative block cipher belonging to the class of multivariate schemes. It has advantages in terms of performance over existing traitor tracing schemes and furthermore, it allows to restrict overheads to one single block (i.e. typically 80 to 160 bits) per encrypted content payload. Its strength relies upon the difficulty of the “Isomorphism of Polynomials” problem [17], which has been extensively investigated over the past years. An initial security analysis is supplied.
Chapter PDF
Similar content being viewed by others
Keywords
References
Barkan, E., Biham, E.: In how many ways can you write Rijndael?, available from the e-print at: http://eprint.iacr.org/2002/157/
Biryukov, A., De Canniere, C., Braeken, A., Preneel, B.: A Toolbox for Cryptanalysis: Linear and Affine Equivalence Algorithms. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 33–50. Springer, Heidelberg (2003)
Boneh, D., Franklin, M.: An Efficient Public Key Traitor Tracing Scheme. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 338–353. Springer, Heidelberg (1999)
Chor, B., Fiat, A., Naor, M.: Tracing Traitors. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 257–270. Springer, Heidelberg (1994)
Chow, S., Eisen, P., Johnson, H., Van Oorschot, P.C.: White- Box Cryptography and an AES Implementation. In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 250–270. Springer, Heidelberg (2003)
Courtois, N., Goubin, L., Meier, W., Tacier, J.-D.: Solving Underdefined Systems of Multivariate Quadratic Equations. In: Naccache, D., Paillier, P. (eds.) PKC 2002. LNCS, vol. 2274, pp. 211–227. Springer, Heidelberg (2002)
Courtois, N., Goubin, L., Patarin, J.: C*− + and HM: Variations around two schemes of T. Matsumoto and H. Imai. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 35–49. Springer, Heidelberg (1998)
Courtois, N., Klimov, A., Patarin, J., Shamir, A.: Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 392–407. Springer, Heidelberg (2000)
Courtois, N.T., Daum, M., Felke, P.: On the Security of HFE, HFEv- and Quartz. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 337–350. Springer, Heidelberg (2002)
Faugère, J.-C., Joux, A.: Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 44–60. Springer, Heidelberg (2003)
Kipnis, A., Shamir, A.: Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 19–30. Springer, Heidelberg (1999)
Kocher, P., Jaffe, J., Jun, B.: Differential Power Analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999)
Matsumoto, T., Imai, H.: Public Quadratic Polynomial-tuples for Efficient Signature Verification and Message Encryption. In: Günther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol. 330, pp. 419–453. Springer, Heidelberg (1988)
Naor, M., Pinkas, B.: Threshold Traitor Tracing. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 502–517. Springer, Heidelberg (1998)
Patarin, J.: Cryptanalysis of the Matsumoto and Imai Public Key Scheme of Eurocrypt ’88. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 248–261. Springer, Heidelberg (1995)
Patarin, J.: Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 33–48. Springer, Heidelberg (1996)
Patarin, J., Goubin, L., Courtois, N.: Improved Algorithms for Isomorphisms of Polynomials. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 184–200. Springer, Heidelberg (1998)
Stinson, D.R., Wei, R.: Combinatorial Properties and Constructions of Traceability Schemes and Frameproof Codes. SIAM Journal on Discrete Mathematics 11(1), 41–53 (1998)
Specifications of SFLASH, available from the site of the NESSIE workshop at: https://www.cosic.esat.kuleuven.ac.be/nessie/workshop/
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Billet, O., Gilbert, H. (2003). A Traceable Block Cipher. In: Laih, CS. (eds) Advances in Cryptology - ASIACRYPT 2003. ASIACRYPT 2003. Lecture Notes in Computer Science, vol 2894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40061-5_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-40061-5_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20592-0
Online ISBN: 978-3-540-40061-5
eBook Packages: Springer Book Archive