| 摘要 |
The aim of the present invention is to propose an alternative scheme to the classical Boneh-Franklin scheme in order to simplify the generation and the use of the asymmetric keys. According to the present invention, it is proposed a method to generate an i-th private key in a public key encryption scheme with traceable private keys formed by a public component gamma(i) and a secret component thetai, according to a maximal coalition factor k, with all arithmetic operations performed within a multiplicative group Z/qZ where q is a prime number, said public component being defined as: <?in-line-formulae description="In-line Formulae" end="lead"?>gamma(i)pl =(1, i mod q, i2 mod q, . . . , ik-1 mod q)<?in-line-formulae description="In-line Formulae" end="tail"?> and said secret component being defined as: <maths id="MATH-US-00001" num="00001"> <math overflow="scroll"> <mrow> <msub> <mi>theta</mi> <mi>i</mi> </msub> <mo>=</mo> <mrow> <mfrac> <mrow> <mo>∑</mo> <mrow> <msub> <mi>r</mi> <mi>j</mi> </msub> <mo></mo> <msub> <mi>alpha</mi> <mi>j</mi> </msub> </mrow> </mrow> <mrow> <mo>∑</mo> <mrow> <msub> <mi>r</mi> <mi>j</mi> </msub> <mo></mo> <msubsup> <mi>gamma</mi> <mi>j</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </msubsup> </mrow> </mrow> </mfrac> <mo></mo> <mi>mod</mi> <mo></mo> <mstyle> <mspace width="0.3em" height="0.3ex"/> </mstyle> <mo></mo> <mi>q</mi> </mrow> </mrow> </math> </maths> where rj and alphaj are random values in the group Z/Z.
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