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CCA Secure PKE with Auxiliary Input Security and Leakage Resiliency

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Information Security (ISC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9290))

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Abstract

Under the strengthened subgroup indistinguishability assumption, we present a new generic construction of chosen ciphertext attack (CCA) secure public key encryption scheme, achieve resilience to auxiliary input information as well as resilience to secret key leakage, from an all-but-one lossy function. In particular, under a special case of SSI assumption, we construct a scheme, if chose the proper parameters for 80-bit security, then it remains CCA secure if any \(2^{-2048}\)-weakly uninvertible functions of secret key is given to the adversary. Furthermore, our scheme also remains CCA secure if any efficient leakage function of secret key is given to the adversary. The leakage rate is \(1-\frac{1690}{l}\), where l is the length of binary representation of secret key. If we choose a sufficiently large l, then the leakage rate is arbitrarily close to 1.

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Notes

  1. 1.

    Indistinguishability under chosen ciphertext attack (CCA) uses a definition similar to that of CPA. However, in addition to the public key, the adversary is given access to a decryption oracle which decrypts arbitrary ciphertexts at the adversary’s request, returning the plaintext.

  2. 2.

    RSI assumption only requires that \(G_{\omega _1}\) and \(G_{\omega _2}\) are both cyclic groups.

  3. 3.

    \(\mathfrak {C}\) is a tag space.

  4. 4.

    For any \(x\ne y\), we have \(Pr_{H\leftarrow _R\mathcal {H}}[H(x)=H(y)]\le \frac{1}{2^{\lfloor \log \omega _2\rfloor -1}}\).

  5. 5.

    We assume that G is q-order elliptic curve group over finite field \(\mathbb {F}_p\). For 80-bit security, p and q can be chosen to be 160-bit prime. Thus, in such a group, each element can be denoted as a 160-bit strings. So, in this case, the hash function H maps a \((l+1)\times 160\)-bit string to a \(\lfloor \log \omega _2\rfloor -1\)-bit string.

  6. 6.

    Here, \(d\log \) denote the discrete logarithm.

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Acknowledgments

This research is partially supported by the National Natural Science Foundation of China under Grant No.61373006.

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Authors and Affiliations

  1. College of Computer, Nanjing University of Posts and Telecommunications, Nanjing, 210003, Jiangsu, China

    Zhiwei Wang

  2. University of Hong Kong, Pokfulam, Hong Kong

    Zhiwei Wang & Siu Ming Yiu

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  1. Zhiwei Wang
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  2. Siu Ming Yiu
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Correspondence to Zhiwei Wang .

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Editors and Affiliations

  1. University of Malaga, Malaga, Spain

    Javier Lopez

  2. Royal Holloway University of London, Egham, United Kingdom

    Chris J. Mitchell

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Wang, Z., Yiu, S.M. (2015). CCA Secure PKE with Auxiliary Input Security and Leakage Resiliency. In: Lopez, J., Mitchell, C. (eds) Information Security. ISC 2015. Lecture Notes in Computer Science(), vol 9290. Springer, Cham. https://doi.org/10.1007/978-3-319-23318-5_18

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  • DOI: https://doi.org/10.1007/978-3-319-23318-5_18

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