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- W105649968 abstract "Lattice-based cryptography plays an important role in modern cryptography. Apart from being a perfect alternative of classic public key cryptosystems, should the quantum computers become available, the lattice-based cryptography also enables many applications that conventional cryptosystems, such as RSA encryption scheme, can not deliver. One of the most significant aspects from this point of view is the fully homomorphic encryption schemes. A fully homomorphic encryption scheme allows one to arbitrarily operate on the encrypted messages, without decrypting it. This notion was raised in 1978, and it becomes a “holy grail” for the cryptographers for 30 years until 2009, Craig Gentry presented a framework to construct a fully homomorphic encryption using ideal lattice. The fully homomorphic encryption schemes, although they may be lacking of efficiency at its current stage, enable many important applications, such as secured cloud searching verifiable outsourced computing. Nevertheless, just like other cryptosystems, and perhaps all other inventions at the initial stage, the fully homomorphic encryption is young, prospective, and hence requires more research. In this thesis, we focus on the security of fully homomorphic encryption schemes. The security of all known fully homomorphic encryption schemes can be reduced to some lattice problems. Therefore, our main tool, not surprisingly, is lattice. Previous work has shown that some of the fully homomorphic encryption schemes can be broken using lattice reduction algorithms. Indeed, there exist several lattice reduction algorithms, such as LLL and L, that run in polynomial time, that can break a homomorphic encryption scheme. However, the running time, even though it is a polynomial algorithm, is still beyond tolerance. Hence, our first step is to optimize those algorithms. In this thesis, we show three different improvements. To sum up, combining those techniques, we are able to accelerate the reduction form O(dβ + dβ) to O(dβ + dβ) when the algorithm is dedicated for those cryptosystems, where d is the dimension of the lattice, and β is the maximum bit-length of the norm of input" @default.
- W105649968 created "2016-06-24" @default.
- W105649968 creator A5003284833 @default.
- W105649968 date "2014-01-01" @default.
- W105649968 modified "2023-09-24" @default.
- W105649968 title "Revisiting fully homomorphic encryption schemes and their cryptographic primitives" @default.
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