Cryptanalysis of the m-Permutation Protection Schemes

Anderson and Kuhn have proposed the EEPROM modification attack to recover the secret key stored in the EEPROM. At ACISP’98, Fung and Gray proposed an m-permutation protection scheme against the EEPROM modification attack. At ACISP’99, Fung and Gray pointed out that in their original scheme, a secret key with too small or too large Hamming weight could be recovered easily. Then they proposed a revised m- permutation protection scheme and claimed that their revised scheme does not leak any information of the secret key. In this paper, we break completely both the original and the revised m-permutation protection schemes. The original scheme is broken with about 2log2 n devices from the same batch and about (3log2 n +2 ) ×m ×n probes (n is the length of the secret key and m is the amount of permutations). The revised m-permutation protection scheme is more vulnerable than the original one. It could be broken with only one device and about m ×n 3/3 probes.