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When Homomorphism Becomes a Liability

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Part of the Lecture Notes in Computer Science book series (LNSC,volume 7785)

Abstract

We show that an encryption scheme cannot have a simple decryption function and be homomorphic at the same time, even with added noise. Specifically, if a scheme can homomorphically evaluate the majority function, then its decryption cannot be weakly-learnable (in particular, linear), even if the probability of decryption error is high. (In contrast, without homomorphism, such schemes do exist and are presumed secure, e.g. based on LPN.)

An immediate corollary is that known schemes that are based on the hardness of decoding in the presence of low hamming-weight noise cannot be fully homomorphic. This applies to known schemes such as LPN-based symmetric or public key encryption.

Using these techniques, we show that the recent candidate fully homomorphic encryption, suggested by Bogdanov and Lee (ePrint ’11, henceforth BL), is insecure. In fact, we show two attacks on the BL scheme: One that uses homomorphism, and another that directly attacks a component of the scheme.

Keywords

  • Encryption Scheme
  • Homomorphic Encryption
  • Decryption Function
  • Decryption Error
  • Cryptology ePrint Archive

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Brakerski, Z. (2013). When Homomorphism Becomes a Liability. In: Sahai, A. (eds) Theory of Cryptography. TCC 2013. Lecture Notes in Computer Science, vol 7785. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36594-2_9

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  • DOI: https://doi.org/10.1007/978-3-642-36594-2_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36593-5

  • Online ISBN: 978-3-642-36594-2

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