Paper 2014/610

Computing on the Edge of Chaos: Structure and Randomness in Encrypted Computation

Craig Gentry


This survey, aimed mainly at mathematicians rather than practitioners, covers recent developments in homomorphic encryption (computing on encrypted data) and program obfuscation (generating encrypted but functional programs). Current schemes for encrypted computation all use essentially the same "noisy" approach: they encrypt via a noisy encoding of the message, they decrypt using an "approximate" ring homomorphism, and in between they employ techniques to carefully control the noise as computations are performed. This noisy approach uses a delicate balance between structure and randomness: structure that allows correct computation despite the randomness of the encryption, and randomness that maintains privacy against the adversary despite the structure. While the noisy approach "works", we need new techniques and insights, both to improve efficiency and to better understand encrypted computation conceptually.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. International Congress of Mathematicians (ICM) 2014
homomorphic encryptionobfuscationlearning with errors
Contact author(s)
cbgentry @ us ibm com
2014-08-13: received
Short URL
Creative Commons Attribution


      author = {Craig Gentry},
      title = {Computing on the Edge of Chaos: Structure and Randomness in Encrypted Computation},
      howpublished = {Cryptology ePrint Archive, Paper 2014/610},
      year = {2014},
      note = {\url{}},
      url = {}
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