Protecting Against Faults by Permutation Embedding Sample Clauses

Protecting Against Faults by Permutation Embedding. ◦ ◦ As each codeword represents a message word, f induces a permutation over the space of all k-symbol vectors. We denote this permutation by fC. We can express fC as the composition of three steps: fC = decC f encC with encC encoding the k-symbol input as a n-symbol codeword in C and decC decoding the resulting n-symbol to a k-symbol output. We call fC the embedding of f by C. In general, the decoding decC of the output of f to a k-symbol message word can fail: it only succeeds if the output of f is in C. It follows that if there is a fault in the computation of f , it is likely that decoding fails. As a matter of fact, the probability that a random fault is undetected is αk−n. Concretely, if f is y bits wider than fC, this probability is 2−y . Hence, we can build a fault-resistant k-symbol permutation ƒC by choosing a code C, designing a permutation ƒ that abides C and embedding ƒC in ƒ by C. We call this design approach code embedding. Note that the datapath and key (or tweakey) schedule of block ciphers are also permutations and can therefore be designed with the code embedding approach.