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SCA on Kyber with Low-Cost Countermeasures

This project contains the source code for our paper

Ravi, P., Paiva, T., Jap, D., D’Anvers, J.-P., & Bhasin, S. (2024). Defeating Low-Cost Countermeasures against Side-Channel Attacks in Lattice-based Encryption: A Case Study on Crystals-Kyber. IACR Transactions on Cryptographic Hardware and Embedded Systems, 2024(2), 795–818. https://doi.org/10.46586/tches.v2024.i2.795-818

Contents

  • belief_propagation_solver_from_roulette/:

  • data/:

    • data/confusion_matrices/: Preliminary confusion matrices corresponding to some SCA setups.
    • data/gaussian_confusion_matrices/: Confusion matrices with gaussian noise.

  • kyber_sca_simulation: C code for simulating the attack.

    • kyber_sca_simulation/kyber_sca_full_attack.c: The full attack for given parameters.
    • kyber_sca_simulation/solver.c: The new fast solver in C.
    • kyber_sca_simulation/kyber768/: Original reference implementation of Kyber.
      • Notice: There is a small change in crypto_kem_enc to simulate the shuffled implementation, triggered by the definition SIMULATE_ATTACK_ON_SHUFFLED_IMPLEMENTATION.
    • kyber_sca_simulation/indcpa.c: Modified source with injected code for simulating SCA information.

  • kyber_sca_simulation: C code for simulating the attack.

  • results: CSV files with the results on the number of ciphertexts for successful attacks

  • plotters: Python scripts to generate the paper plots based on the result files

Dependencies

Kyber requires OpenSSL (-lcrypto). The solver and attack simulation do not have any dependencies. However, to use the clock_gettime(CLOCK_MONOTONIC_RAW, _); call we define #define _XOPEN_SOURCE 700. This may be a problem in Windows but it should not be difficult to substitute the timing functions with appropriate ones.

Setup

$ uname -a
Linux 6.4.11-arch2-1 #1 SMP PREEMPT_DYNAMIC Sat, 19 Aug 2023 15:38:34 +0000 x86_64 GNU/Linux
$ cat /proc/cpuinfo | grep "model name" | head -n 1
model name  : Intel(R) Core(TM) i7-8700 CPU @ 3.20GHz
$ cat /proc/meminfo | head -n 1
MemTotal:       32789148 kB
$ gcc --version | head -n 1
gcc (GCC) 13.2.1 20230801

Compiling

$ cd kyber_sca_simulation
$ cmake -B build
$ cd build
$ make

This will generate a number of executables:

build_bias_matrices
build_bias_matrices_masked
find_n_ciphertexts_needed
find_n_ciphertexts_needed_masked
kyber_sca_full_attack
kyber_sca_full_attack_grid
kyber_sca_full_attack_masked
kyber_sca_full_attack_shuffled
kyber_sca_generate_inequalities
kyber_sca_solve_inequalities

The simplest ones to use are the kyber_full_attack*. These run the full attack, simulating SCA and then building and solving the inequalities. Each of the 3 executables is responsible for simulating the attack on the unprotected, masked and shuffled implementation, respectively.

kyber_sca_full_attack
kyber_sca_full_attack_masked
kyber_sca_full_attack_shuffled

The executables find_n_ciphertexts_needed and find_n_ciphertexts_needed_masked essentially run a binary search to find the average number of ciphertext needed for a successful attack. Executable build_bias_matrices and build_bias_matrices_masked are used for generating the matrices in kyber_sca_simulation/bias_matrices.h, that are used for to generate the inequalities for key recovery.

Executables kyber_sca_generate_inequalities and kyber_sca_solve_inequalities are auxiliary files to generate inequalities for other solvers to

Usage

The three kyber_full_attack* have a similar usage.

$ ./kyber_sca_full_attack
Usage: ./kyber_sca_full_attack n_simulations seed n_inequalities confusion_matrix_filepath

The parameters meaning are as follows:

  • n_simulations: Number of secret keys to attack for each parameter set
  • seed: A seed used to initialize randombytes (uint64_t)
  • n_inequalities: Number of inequalities to generate
  • confusion_matrix_filepath: Path to the confusion matrix used to simulate errors in SCA measurement

Examples

Right now, the solver outputs some extra information to stderr. So in this README we will use 2> /dev/null to redirect the stderr output and get a cleaner output.

Here we use the ./kyber_sca_full_attack to recover 10 keys using 20000 inequalities and assuming perfect classification. Notice that the output is a CSV file, that can then be used for plotting.

In this case, all keys were recovered with less than 350 ciphertexts.

$ ./kyber_sca_full_attack 10 1 20000 ../../data/gaussian_confusion_matrices/scale_0.00.csv 2> /dev/null
confusion_matrix_filepath,spread,n_inequalities,n_ciphertexts,n_wrong_inequalities,recovered_key,fraction_of_solution_recovered,n_iterations,time_seconds_build_inequalities,time_seconds_solve_inequalities,max_ciphertext_exceeded
../../data/gaussian_confusion_matrices/scale_0.00.csv,317,20000,328,1,True,1.00,40,0.30,9.97,False
../../data/gaussian_confusion_matrices/scale_0.00.csv,317,20000,333,0,True,1.00,70,0.30,16.17,False
../../data/gaussian_confusion_matrices/scale_0.00.csv,317,20000,333,0,True,1.00,160,0.30,36.12,False
../../data/gaussian_confusion_matrices/scale_0.00.csv,317,20000,335,0,True,1.00,50,0.30,11.98,False
../../data/gaussian_confusion_matrices/scale_0.00.csv,317,20000,340,0,True,1.00,170,0.31,74.91,False
../../data/gaussian_confusion_matrices/scale_0.00.csv,317,20000,333,0,True,1.00,50,0.31,12.36,False
../../data/gaussian_confusion_matrices/scale_0.00.csv,317,20000,333,0,True,1.00,70,0.30,16.25,False
../../data/gaussian_confusion_matrices/scale_0.00.csv,317,20000,338,0,True,1.00,71,0.31,16.61,False
../../data/gaussian_confusion_matrices/scale_0.00.csv,317,20000,333,0,True,1.00,51,0.30,12.45,False
../../data/gaussian_confusion_matrices/scale_0.00.csv,317,20000,335,0,True,1.00,70,0.31,16.57,False