A More Efficient Fully Homomorphic Encryption Scheme Based on GSW and DM Schemes

Table 1

List of mathematical symbols with their meanings.

Symbol	Meaning
Regular letters (with possibly superscripts and subscripts), e.g. .	Scalars.
Bold lowercase letters (with possibly superscripts and subscripts), e.g. .	Vectors.
Bold uppercase letters (with possibly superscripts and subscripts), e.g. .	Matrices.
	The set of all integers.
	The set of all complex numbers.
	The set of all positive integers.
	The set of integers modulo an integer , which are reduced to .
	The set of matrices with all coefficients in .
	The set of all polynomials with integer coefficients.
	Binomial distribution with parameters .
	Rounding of to the nearest integer.
or	Inner product of vectors .
	The horizontal concatenation of matrix and vector .
	The infinite norm of vector , .
	If is a distribution, is sampled according to ; If is a set, is uniformly sampled from .
	A negligible amount: for any constant as .