Method to generate a private key in a Boneh-Franklin scheme

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 γ⁽ⁱ⁾ and a secret component θ_i, 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 : $\mathop{\mathrm{image}} \[ {\mathrm{\gamma }}^{\left(i\right)}=\left(1,\mathrm{imodq},i^2\mathrm{modq},\dots ,i^{2k-1}\mathrm{mod\; q}\right) \]$and said secret component being defined as : $\mathop{\mathrm{image}} \[ {\theta }_i=\frac{{\mathrm{\Sigma r}}_j{\alpha }_j}{\mathrm{\Sigma }{r}_j{\mathit{\gamma }}_j^{\left(i\right)}}\mathrm{mod\; q} \]$where r_j and α_j are random values in the group Z/qZ.