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

Table 1

$1$

$x$

$xy$

${x}^{2}$

${x}^{2}y$

$x{y}^{2}$

${x}^{2}{y}^{2}$

${x}^{2}{y}^{3}$

${e}^{2}$

${e}^{2}$

${xe}^{2}$

*

${Xe}^{2}$

$fe$

*

*

$XYe$

${x}^{2}{e}^{2}$

*

*

*

${X}^{2}{e}^{2}$

$xfe$

*

*

*

*

${X}^{2}Ye$

$yfe$

*

*

*

*

*

$X{Y}^{2}e$

${f}^{2}$

*

*

*

*

*

*

${X}^{2}{Y}^{2}$

${yf}^{2}$

*

*

*

*

*

*

*

${XY}^{3}$

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