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International Workshop on Public Key Cryptography

PKC 2007: Public Key Cryptography – PKC 2007 pp 266–281Cite as

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ℓ-Invertible Cycles for \(\mathcal{M}\)ultivariate \(\mathcal{Q}\)uadratic (\({\mathcal{MQ}}\)) Public Key Cryptography

ℓ-Invertible Cycles for \(\mathcal{M}\)ultivariate \(\mathcal{Q}\)uadratic (\({\mathcal{MQ}}\)) Public Key Cryptography

  • Jintai Ding1,
  • Christopher Wolf2 &
  • Bo-Yin Yang3 
  • Conference paper

  • 2033 Accesses

  • 28 Citations

Part of the Lecture Notes in Computer Science book series (LNSC,volume 4450)

Abstract

We propose a new basic trapdoor \(\mathcal{\ell}\)IC (ℓ-Invertible Cycles) of the mixed field type for \(\mathcal{M}\)ultivariate \(\mathcal{Q}\)uadratic public key cryptosystems. This is the first new basic trapdoor since the invention of Unbalanced Oil and Vinegar in 1997. \(\mathcal{\ell}\)IC can be considered an extended form of the well-known Matsumoto-Imai Scheme A (also MIA or C  ∗ ), and share some features of stagewise triangular systems. However \({\mathcal{\ell}}\)IC has very distinctive properties of its own. In practice, \({\mathcal{\ell}}\)IC is much faster than MIA, and can even match the speed of single-field \({\mathcal{MQ}}\) schemes.

Keywords

  • Public Key
  • \({\mathcal{MQ}}\)
  • Trapdoor
  • Encryption
  • Signing

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Author information

Authors and Affiliations

  1. University of Cincinnati and Technische Universität Darmstadt,  

    Jintai Ding

  2. Ecole Normale Superieur,  

    Christopher Wolf

  3. Institute of Information Science, Academia Sinica and TWISC,  

    Bo-Yin Yang

Authors
  1. Jintai Ding
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  2. Christopher Wolf
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  3. Bo-Yin Yang
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Tatsuaki Okamoto Xiaoyun Wang

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Ding, J., Wolf, C., Yang, BY. (2007). ℓ-Invertible Cycles for \(\mathcal{M}\)ultivariate \(\mathcal{Q}\)uadratic (\({\mathcal{MQ}}\)) Public Key Cryptography. In: Okamoto, T., Wang, X. (eds) Public Key Cryptography – PKC 2007. PKC 2007. Lecture Notes in Computer Science, vol 4450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71677-8_18

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