Method for testing and hardening software applications
Methods are provided for testing and hardening software applications for the carrying out digital transactions which comprise a white-box implementation of a cryptographic algorithm. The method comprises the following steps: (a) feeding one plaintext of a plurality of plaintexts to the white-box implementation; (b) reading out and storing the contents of the at least one register of the processor stepwise while processing the machine commands of the white-box implementation stepwise; (c) repeating the steps (a) and (b) with a further plaintext of the plurality of plaintexts N-times; and (d) statistically evaluating the contents of the registers and the plaintexts, the intermediate results and/or the ciphertexts generated from the plaintexts by searching for correlations between the contents of the registers and the plaintexts, the intermediate results and/or the ciphertexts generated from the plaintexts to establish the secret key.
1. A method for testing a white-box implementation of a cryptographic algorithm, said implementation being executable on a processor, generating a ciphertext from a plaintext by means of a secret key and being present in the processor in the form of machine commands, wherein the processor comprises at least one register and the method comprises the following steps:
(a) feeding one plaintext of a plurality of plaintexts to the white-box implementation;
(b) reading out and storing the content of the at least one register of the processor stepwise while processing the machine commands of the white-box implementation stepwise, wherein intermediate results are generated while processing the machine commands of the white-box implementation stepwise for generating the ciphertext from the plaintext;
(c) repeating the hereinabove steps (a) and (b) with a further plaintext of the plurality of plaintexts N-times; and
(d) statistically evaluating a contents of the registers and the plaintexts, the intermediate results and/or the ciphertexts generated from the plaintexts by searching for correlations between the contents of the registers and the plaintexts, the intermediate results and/or the ciphertexts generated from the plaintexts to establish the secret key;
wherein N is chosen so large that a static evaluating of the contents of the registers and the plaintexts, the intermediate results and/or the ciphertexts generated from the plaintexts is possible.
2. The method according to claim 1 , wherein
the content of a register for a plaintext is treated as a function of the number of the processed machine commands analogously to a power/current curve in the differential power analysis; or/and
the step (d) of statistically evaluating the contents of the registers and the plaintexts, the intermediate results and/or the ciphertexts generated from the plaintexts comprises the step of evaluating by means of statistical methods which are known from differential power analysis.
3. The method according to claim 1 , wherein the white-box implementation is part of a software application for carrying out a digital transaction.
4. The method according to claim 1 , wherein the steps (a) and (b) are carried out with at least 10, 100 or 1000 different plaintexts.
5. The method according to claim 1 , wherein in the step (b) the readout of the content of the at least one register is carried out only as of a machine command predefined in the white-box implementation and further in the step (b) the readout of the content of the at least one register is carried out as of the predefined machine command for a predefined number M of machine commands.
6. The method according to claim 1 , wherein the white-box implementation of a cryptographic algorithm is a white-box implementation of the AES algorithm.
7. The method according to claim 1 , wherein in the step (d) of statistically evaluating the contents of the registers and the plaintexts, the intermediate results and/or the ciphertexts generated from the plaintexts those intermediate results and/or ciphertexts generated from the plaintexts are employed for the statistical analysis that depend on only as few bits of the secret key as possible.