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You can use AES in CTR mode. Well it is generally secure, but not really for large data, since a counter repeats every $2^{128}$ blocks, so you need change keys every $2^{128}$ blocks. See this link here for some more information.


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From §5.1 ‘Data units and tweaks’, p. 4: Each data unit is assigned a tweak value which is a non-negative integer. The tweak values are assigned consecutively, starting from an arbitrary non-negative integer. When encrypting tweak value using AES, the tweak is first converted into a little-endian byte array. For example, tweak value 123456789A16 ...


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You should visit the Homomorphic Encryption Standardization web page. There you can find Homomorphic Encryption Standardization. Also, there is a workshop The Second Homomorphic Encryption Standardization Workshop there you can find this document Homomorphic Encryption Standard see section 2.0.3 I hope, all this will help in your research.


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You can start your learning https://www.coursera.org/learn/crypto/home/welcome An excellent course to start with all about Symmetric/Asymmetric encryption/TLS/MAC etc. A free ebook is also available https://crypto.stanford.edu/~dabo/cryptobook/BonehShoup_0_4.pdf https://www.schneier.com/books/applied_cryptography/


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I found chapter 7 of the (still in progress) book "Graduate Course in Applied Cryptography" by Shoup and Boneh pretty useful as a thorough explanation of authentication based on universal hashing: https://crypto.stanford.edu/~dabo/cryptobook/


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