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An Elliptic Curve Backdoor Algorithm for RSASSA

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Information Hiding (IH 2006)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4437))

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Abstract

We present the first (1,2)-SETUP algorithm for the RSA digital signature scheme with appendix. A SETUP algorithm C′ is an algorithmic modification of algorithm C that (1) contains an asymmetric backdoor that can only be used by the designer, even if the backdoor algorithm is fully public, and (2) ensures that the public outputs of C and C′ are computationally indistinguishable under black-box queries. The SETUP is presented in RSASSA-PSS and it transmits the RSA private key within two w.l.o.g consecutive digital signatures. This problem has been solved for DSA and other discrete-log based digital signature algorithms, but not RSA. We therefore solve a long-standing problem in kleptography.

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References

  1. Adleman, L.M., Manders, K., Miller, G.: On Taking Roots in Finite Fields. In: IEEE Foundations of Computer Science—FOCS 1977, pp. 175–177 (1977)

    Google Scholar 

  2. Anderson, R.J.: A Practical RSA Trapdoor. Elec. Letters 29(11) (1993)

    Google Scholar 

  3. Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: 1st Annual ACM CCCS, pp. 62–73 (1993)

    Google Scholar 

  4. Bellare, M., Rogaway, P.: The Exact Security of Digital Signatures—How to Sign with RSA and Rabin. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 399–416. Springer, Heidelberg (1996)

    Google Scholar 

  5. Bellare, M., Rogaway, P.: PSS: Provably Secure Encoding Method for Digital Signatures. IEEE P1363 working group August 1998 (submission)

    Google Scholar 

  6. Bohli, J.M., Steinwandt, R.: On Subliminal Channels in Deterministic Signature Schemes. In: Park, C.-s., Chee, S. (eds.) ICISC 2004. LNCS, vol. 3506, pp. 182–194. Springer, Heidelberg (2005)

    Google Scholar 

  7. Boneh, D.: The Decision Diffie-Hellman Problem. In: Third Algorithmic Number Theory Symposium, pp. 48–63 (1998)

    Google Scholar 

  8. Coppersmith, D.: Finding a small root of a bivariate integer equation; Factoring with high bits known. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 178–189. Springer, Heidelberg (1996)

    Google Scholar 

  9. Crépeau, C., Slakmon, A.: Simple Backdoors for RSA Key Generation. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 403–416. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  10. Diffie, W., Hellman, M.: New Directions in Cryptography. IEEE Transactions on Information Theory IT-22(6), 644–654 (1976)

    Article  MathSciNet  Google Scholar 

  11. NIST. Announcing Draft FIPS 180-2, Secure Hash Standard, and RFC. Federal Register, vol. 66(104), p. 29287 (2001)

    Google Scholar 

  12. NIST. Announcing Approval of FIPS 180-2, Secure Hash Standard; a Revision of FIPS 180-2. Federal Register, vol. 67(165), pp. 54785–54787 (2002)

    Google Scholar 

  13. Gaudry, P., Hess, F., Smart, N.: Constructive and Destructive Facets of Weil Descent on Elliptic Curves. Journal of Cryptology 15(1), 19–46 (2002)

    Article  MathSciNet  Google Scholar 

  14. IEEE P1363 working group. IEEE P1363a D10: Standard Specifications for Public Key Cryptography: Additional Techniques (November 1, 2001), available from http://grouper.ieee.org/groups/1363/

  15. Joux, A., Nguyen, K.: Separating DDH from CDH in Cryptographic Groups. Journal of Cryptology 16(4), 239–247 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  16. Kaliski, B.S.: A Pseudo-Random Bit Generator Based on Elliptic Logarithms. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 84–103. Springer, Heidelberg (1987)

    Google Scholar 

  17. Kaliski, B.S.: Elliptic Curves and Cryptography: A Pseudorandom Bit Generator and Other Tools. PhD Thesis, MIT (February 1988)

    Google Scholar 

  18. Kaliski, B.S.: One-Way Permutations on Elliptic Curves. Journal of Cryptology 3(3), 187–199 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  19. Luby, M.: Pseudorandomness and Cryptographic Applications. Princeton Computer Science Notes (1996)

    Google Scholar 

  20. Möller, B.: A Public-Key Encryption Scheme with Pseudo-Random Ciphertexts. In: Samarati, P., Ryan, P.Y A., Gollmann, D., Molva, R. (eds.) ESORICS 2004. LNCS, vol. 3193, pp. 335–351. Springer, Heidelberg (2004)

    Google Scholar 

  21. PKCS #1 v2.1: RSA Cryptography Standard. RSA Labs (June 14, 2002)

    Google Scholar 

  22. Rabin, M.: Probabilistic Algorithms in Finite Fields. SIAM Journal on Computing 9, 273–280 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  23. Rivest, R., Shamir, A., Adleman, L.: A Method for Obtaining Digital Signatures and Public-Key Cryptosystems. CACM 21(2), 120–126 (1978)

    MATH  MathSciNet  Google Scholar 

  24. Wang, X., Yu, H.: How to Break MD5 and Other Hash Functions. In: Cramer, R.J.F. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 19–35. Springer, Heidelberg (2005)

    Google Scholar 

  25. Wang, X., Ying, Y., Yu, H.: Finding Collisions in the Full SHA-1. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 17–36. Springer, Heidelberg (2005)

    Google Scholar 

  26. Young, A., Yung, M.: The Dark Side of Black-Box Cryptography, or: Should we trust Capstone? In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 89–103. Springer, Heidelberg (1996)

    Google Scholar 

  27. Young, A., Yung, M.: Kleptography: Using Cryptography Against Cryptography. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 62–74. Springer, Heidelberg (1997)

    Google Scholar 

  28. Young, A., Yung, M.: The Prevalence of Kleptographic Attacks on Discrete-Log Based Cryptosystems. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 264–276. Springer, Heidelberg (1997)

    Google Scholar 

  29. Young, A., Yung, M.: A Space Efficient Backdoor in RSA and its Applications. In: Preneel, B., Tavares, S. (eds.) SAC 2005. LNCS, vol. 3897, pp. 128–143. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Cryptovirology Labs,  

    Adam Young

  2. RSA Labs and Columbia University,  

    Moti Yung

Authors
  1. Adam Young
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  2. Moti Yung
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Editor information

Jan L. Camenisch Christian S. Collberg Neil F. Johnson Phil Sallee

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© 2007 Springer-Verlag Berlin Heidelberg

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Young, A., Yung, M. (2007). An Elliptic Curve Backdoor Algorithm for RSASSA. In: Camenisch, J.L., Collberg, C.S., Johnson, N.F., Sallee, P. (eds) Information Hiding. IH 2006. Lecture Notes in Computer Science, vol 4437. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74124-4_24

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  • DOI: https://doi.org/10.1007/978-3-540-74124-4_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74123-7

  • Online ISBN: 978-3-540-74124-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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