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Additional Topics in Cryptography

  • Jeffrey Hoffstein
  • Jill Pipher
  • Joseph H. Silverman
Chapter
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

The emphasis of this book has been on the mathematical underpinnings of public key cryptography. We have developed most of the mathematics from scratch and in sufficient depth to enable the reader to understand both the underlying mathematical principles and how they are applied in cryptographic constructions. Unfortunately, in achieving this laudable goal, we have now reached the end of a hefty textbook with many important cryptographic topics left untouched.

Keywords

Hash Function Advance Encryption Standard Hyperelliptic Curve Secret Sharing Scheme Discrete Logarithm Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [11]
    M. Bellare, Practice oriented provable-security, in Proceedings of the First International Workshop on Information Security—ISW ’97, Tatsunokuchi. Volume of 1396 Lecture Notes in Computer Science (Springer, Berlin, 1998)Google Scholar
  2. [12]
    M. Bellare, P. Rogaway, Random oracles are practical: a paradigm for designing efficient protocols, in Proceedings of the First Annual Conference on Computer and Communications Security, Fairfax, 1993, pp. 62–73Google Scholar
  3. [13]
    M. Bellare, P. Rogaway, Optimal asymmetric encryption, in Advances in Cryptology—EUROCRYPT ’94, Perugia. Volume 950 of Lecture Notes in Computer Science (Springer, Berlin, 1995), pp. 92–111Google Scholar
  4. [15]
    G. Blakley, Safeguarding cryptographic keys, in Proceedings of AFIPS National Computer Conference, Zurich, vol. 48, 1979, pp. 313–317Google Scholar
  5. [16]
    D. Bleichenbacher, Chosen ciphertext attacks against protocols based on RSA encryption standard PKCS #1, in Advances in Cryptology—CRYPTO 1998, Santa Barbara. Volume 1462 of Lecture Notes in Computer Science (Springer, Berlin, 1998), pp. 1–12Google Scholar
  6. [26]
    D. Chaum, Blind signatures for untraceable payments, in Advances in Cryptology—CRYPTO ’82, Santa Barbara. Lecture Notes in Computer Science (Plenum Press, New York/London, 1983), pp. 199–203Google Scholar
  7. [27]
    D. Chaum, A. Fiat, M. Naor, Untraceable electronic cash, in Advances in Cryptology—CRYPTO 1988, Santa Barbara. Volume 403 of Lecture Notes in Computer Science (Springer, 1988), pp. 319–327Google Scholar
  8. [47]
    C. Gentry, A Fully Homomorphic Encryption Scheme, PhD thesis, Stanford University, 2009. crypto.stanford.edu/craig
  9. [48]
    C. Gentry, Fully homomorphic encryption using ideal lattices, in STOC’09—Proceedings of the 2009 ACM International Symposium on Theory of Computing, Bethesda (ACM, New York, 2009), pp. 169–178Google Scholar
  10. [64]
    P. Kaye, R. Laflamme, M. Mosca, An Introduction to Quantum Computing (Oxford University Press, Oxford, 2007)zbMATHGoogle Scholar
  11. [69]
    N. Koblitz, The uneasy relationship between mathematics and cryptography. Not. Am. Math. Soc. 54, 972–979 (2007)MathSciNetzbMATHGoogle Scholar
  12. [70]
    N. Koblitz, A.J. Menezes, Another look at “provable security”. J. Cryptol. 20(1), 3–37 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  13. [87]
    G.L. Miller, Riemann’s hypothesis and tests for primality. J. Comput. Syst. Sci. 13(3), 300–317 (1976). Working papers presented at the ACM-SIGACT Symposium on the Theory of Computing, Albuquerque, 1975Google Scholar
  14. [91]
    S.p. Nakamoto, Bitcoin: a peer-to-peer electronic cash system (2009). https://bitcoin.org/bitcoin.pdf
  15. [96]
    NIST–AES, Advanced Encryption Standard (AES). FIPS Publication 197, National Institue of Standards and Technology, 2001. http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf
  16. [97]
    NIST–DES, Data Encryption Standard (DES). FIPS Publication 46-3, National Institue of Standards and Technology, 1999. http://csrc.nist.gov/publications/fips/fips46-3/fips46-3.pdf
  17. [99]
    NIST–SHS, Secure Hash Standard (SHS). FIPS Publication 180-2, National Institue of Standards and Technology, 2003. http://csrc.nist.gov/publications/fips/fips180-2/fips180-2.pdf
  18. [107]
    J. Proos, C. Zalka, Shor’s discrete logarithm quantum algorithm for elliptic curves. Quantum Inf. Comput. 3(4), 317–344 (2003)MathSciNetzbMATHGoogle Scholar
  19. [108]
    M.O. Rabin, Digitized signatures and public-key functions as intractible as factorization. Technical report, MIT Laboratory for Computer Science, 1979. Technical Report LCS/TR-212Google Scholar
  20. [123]
    A. Shamir, How to share a secret. Commun. ACM 22(11), 612–613 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  21. [128]
    P.W. Shor, Algorithms for quantum computation: discrete logarithms and factoring, in 35th Annual Symposium on Foundations of Computer Science, Santa Fe, 1994 (IEEE Computer Society, Los Alamitos, 1994), pp. 124–134Google Scholar
  22. [129]
    P.W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  23. [131]
    V. Shoup, OAEP reconsidered, in Advances in Cryptology—CRYPTO 2001, Santa Barbara. Volume 2139 of Lecture Notes in Computer Science (Springer, Berlin, 2001), pp. 239–259Google Scholar
  24. [142]
    Standards for Efficient Cryptography, SEC 2: recommended elliptic curve domain parameters (Version 1), 20 Sept 2000. http://www.secg.org/collateral/sec2_final.pdf

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Jeffrey Hoffstein
    • 1
  • Jill Pipher
    • 1
  • Joseph H. Silverman
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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