Size | Timing (evaluations of hash function) | Security level | |||||
---|---|---|---|---|---|---|---|
Scheme | Signature key | Verification key | Signature | Gen | Sig | Ver | |
Biba | tn | tn | kn | t | (t + 1)/Ps | 2k + 1 | \(\begin{aligned} & (kr - 1)\log n - \log C_{kr}^{{}} k \\ & - (kr - k)\log (n - 1) \\ \end{aligned}\) |
Hors | tn | tn | kn | t | 1/Ps | k + 1 | \(k\left( {\log t - \log k - \log r} \right)\) |
Pors | tn | tn | kn | t | 1/Ps | k + 1 | \(k\left( {\log t - \log k - \log r} \right)\) |
Fors | ktn | n | (k + logt)n | kt | 1/Ps | klogt + k−1 | \(- \log \left[ {\begin{array}{*{20}c} {(1 + q)\sum\limits_{\gamma } {((1 - (1 - \frac{1}{t})} ^{\gamma } )^{k} } \\ {\left( {\begin{array}{*{20}c} {q{\prime }} \\ \gamma \\ \end{array} } \right)(1 - \frac{1}{{2^{h} }})^{{q{\prime } - \gamma }} \frac{1}{{2^{{h\gamma }} }})} \\ \end{array} } \right]\) |