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See detailKey Recovery Attacks Against NTRU-Based Somewhat Homomorphic Encryption Schemes
Chenal, Massimo UL; Tang, Qiang UL

in Information Security - 18th International Conference, ISC 2015 (2015, September)

A key recovery attack allows an attacker to recover the pri- vate key of an underlying encryption scheme when given a number of decryption oracle accesses. Previous research has shown that most exist- ing ... [more ▼]

A key recovery attack allows an attacker to recover the pri- vate key of an underlying encryption scheme when given a number of decryption oracle accesses. Previous research has shown that most exist- ing Somewhat Homomorphic Encryption (SHE) schemes su er from this attack. In this paper, we propose e cient key recovery attacks against two NTRU-based SHE schemes due to Lopez-Alt et al. (2012) and Bos et al. (2013), which have not gained much attention in the literature. Paral- lel to our work, Dahab, Galbraith and Morais (2015) have also proposed similar attacks but only for speci c parameter settings. In comparison, our attacks apply to all parameter settings and are more e cient. [less ▲]

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See detailOn Key Recovery Attacks against Existing Somewhat Homomorphic Encryption Schemes
Chenal, Massimo UL; Tang, Qiang UL

in Progress in Cryptology - LATINCRYPT 2014, Florianópolis 17-19 September 2014 (2014)

In his seminal paper at STOC 2009, Gentry left it as a future work to investigate (somewhat) homomorphic encryption schemes with IND-CCA1 security. At SAC 2011, Loftus et al. showed an IND-CCA1 attack ... [more ▼]

In his seminal paper at STOC 2009, Gentry left it as a future work to investigate (somewhat) homomorphic encryption schemes with IND-CCA1 security. At SAC 2011, Loftus et al. showed an IND-CCA1 attack against the somewhat homomorphic encryption scheme presented by Gentry and Halevi at Eurocrypt 2011. At ISPEC 2012, Zhang, Plantard and Susilo showed an IND-CCA1 attack against the somewhat homomorphic encryption scheme developed by van Dijk et al. at Eurocrypt 2010. In this paper, we continue this line of research and show that most existing somewhat homomorphic encryption schemes are not IND-CCA1 secure. In fact, we show that these schemes suffer from key recovery attacks (stronger than a typical IND-CCA1 attack), which allow an adversary to recover the private keys through a number of decryption oracle queries. The schemes, that we study in detail, include those by Brakerski and Vaikuntanathan at Crypto 2011 and FOCS 2011, and that by Gentry, Sahai and Waters at Crypto 2013. We also develop a key recovery attack that applies to the somewhat homomorphic encryption scheme by van Dijk et al., and our attack is more efficient and conceptually simpler than the one developed by Zhang et al.. Our key recovery attacks also apply to the scheme by Brakerski, Gentry and Vaikuntanathan at ITCS 2012, and we also describe a key recovery attack for the scheme developed by Brakerski at Crypto 2012. [less ▲]

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