A New Method of Constructing a Lattice Basis and Its Applications to Cryptanalyse Short Exponent RSA

Table 1

	$1$	$x$	$xy$	$x^2$	$x^{2}y$	$x{y}^2$	$x^2{y}^2$	$x^2{y}^3$
$e^2$	$e^2$
${xe}^2$	*	${Xe}^2$
$fe$	*	*	$XYe$
$x^2{e}^2$	*	*	*	$X^2{e}^2$
$xfe$	*	*	*	*	$X^{2}Ye$
$yfe$	*	*	*	*	*	$X{Y}^{2}e$
$f^2$	*	*	*	*	*	*	$X^2{Y}^2$
${yf}^2$	*	*	*	*	*	*	*	${XY}^3$