Abstract
In this article, we investigate the question of equivalent keys for two \({\mathcal M}\)ultivariate \({\mathcal Q}\)uadratic public key schemes HFE and C* − − and improve over a previously known result, which appeared at PKC 2005. Moreover, we show a new non-trivial extension of these results to the classes HFE-, HFEv, HFEv-, and C* − −, which are cryptographically stronger variants of the original HFE and C* schemes. In particular, we are able to reduce the size of the private — and hence the public — key space by at least one order of magnitude and several orders of magnitude on average. While the results are of independent interest themselves as they broaden our understanding of \({\mathcal M}\)ultivariate \({\mathcal Q}\)uadratic schemes, we also see applications both in cryptanalysis and in memory efficient implementations.
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Wolf, C., Preneel, B. (2005). Equivalent Keys in HFE, C*, and Variations. In: Dawson, E., Vaudenay, S. (eds) Progress in Cryptology – Mycrypt 2005. Mycrypt 2005. Lecture Notes in Computer Science, vol 3715. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11554868_4
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DOI: https://doi.org/10.1007/11554868_4
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