![]() ![]() ![]() With theory of arrays, we can essentially declare an array with arbitrary indexĭef hack_proof_of_work ( message ): block = md5 ( message ). SMT solvers are so mature, we can use multiple theories to create and solve a ![]() Understand BitVec as index and so wont our model understand our function! Theory of Arrays Good question, it wont the sub is a previously defined python function whichĮxpects python int to index the SBOX and return a value. Rv1 ^= x y = y * ( m LShR ( z, 16 )) ^ RotateLeft ( x, 3 ) rv2 ^= y rv1, rv2 = rv2, rv1 rv1 = sub ( rv1 ) # shift by default but in z3 > is arithmetic while LShR is logical Python ints are infinite, so > means logical shift by # shift right shifts as is whereas arithmetic shift right also retains the # there are two kinds of shift rights, arithmetic and logical. # note that > is replaced with LShR, this is because in theory of bitvecs X = x * ( m LShR ( y, 16 )) ^ RotateLeft ( z, 3 ) # expanding the walrus (:=) # and tries to simplify as much as possible (no effect on truth, can skip) Z, u = blocks ^ z, blocks ^ u x, y, z, u = # simplify tries to evaluate the current symbolic computation of a variable We can make an SMT model in z3 and let it do its wonders!īut first let us demarcate the function so it’s easier to refer function setupįor i in range ( 13 ): x, y = blocks ^ x, blocks ^ y # easy interop with xor "You don't have to add the z3 solver to your firmware ever again. Since the first block provides a subtle hint Over the message and we have to actually expoit the keys.įinding relevant key1 and key2 seems difficult by bare logic, dont worry Insted of a block, md5(block) is hashed, so we have little to no control.Which means rv1, rv2, x, y, z, u are all 32bit values including.Since each operation is preceded by
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