Cryptology ePrint Archive: Report 2016/512

Security Analysis of ePrint Report 2016/500 "Efficient Identity-Based Encryption and Public-Key Signature from Trapdoor Subgroups"

Lucjan Hanzlik and Kamil Kluczniak

Abstract: In this short report we analyse the security of three schemes proposed by J. H. Park et al. in "Efficient Identity-Based Encryption and Public-Key Signature from Trapdoor Subgroups". The schemes make use of trapdoor subgroups of $\ZZ_n^*$ and are secure under new assumptions called $q$-Trapdoor Subgroup Diffie-Hellman (TSDH) and $q$-Trapdoor Subgroup Exponent Inversion (TSEI). We show that given several secret keys in case of IBE or several signatures in case of PKS, one can easily extract the trapdoor and break security of the proposed schemes.

Category / Keywords: public-key cryptography / attack, trapdoor subgroup, congruential equations