Abstract
In this paper, we study the indifferentiable security of the domain extension algorithm of the PHOTON hash function that was proven to be indifferentiable from a random oracle up to \(\mathcal{O}(2^{\min\{ c/2, c^\prime/2 \}})\) query complexity, where c is the capacity in the absorbing step of PHOTON and c ′ is that in the squeezing step. By reducing the size c ′, one can reduce the processing time spent by PHOTON, while the indifferentiable security is degraded. Note that there is no generic attack on PHOTON with \(\mathcal{O}(2^{c^\prime/2})\) query complexity. Thus it is interesting to investigate the optimality of the indifferentiable security and the size of c ′ ensuring the \(\mathcal{O}(2^{c/2})\) security.
For these motivations, first, we prove that PHOTON is indifferentiable from a random oracle up to \(\mathcal{O}(\min \{ q_{\mathsf{mcoll}} (d^\ast,c-c^\prime ), 2^{c/2} \})\) query complexity where q mcoll (d ∗ ,c − c ′) is the query complexity to find a d ∗ -multi-collision of (c − c ′) bits of hash values and d ∗ satisfies \(q_{\mathsf{mcoll}} (d^\ast,c-c^\prime ) = 2^{c^\prime }/d^\ast\). We also show that there exists a generic attack on PHOTON with the same query complexity. Thus the indifferentiable security of our proof is optimal.
Second, by using this bound we study the parameter c ′ ensuring the \(\mathcal{O}(2^{c/2})\) security. We show that the \(\mathcal{O}(2^{c/2})\) security is ensured if c ′ ≥ c/2 + log2 c, which implies that we can reduce the processing time by PHOTON with keeping the same indifferentiable security.
Finally, we propose a faster construction than PHOTON with keeping the same indifferentiable security, where the length of the first message block is modified from r bits to r + c/2 bits.
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Naito, Y., Ohta, K. (2014). Improved Indifferentiable Security Analysis of PHOTON . In: Abdalla, M., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2014. Lecture Notes in Computer Science, vol 8642. Springer, Cham. https://doi.org/10.1007/978-3-319-10879-7_20
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DOI: https://doi.org/10.1007/978-3-319-10879-7_20
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