International Association
for Cryptologic Research

We analyze Dieharder statistical randomness tests according to accuracy and correct interpretation of their results. We used all tests, processed 8 TB of quantum-generated data, and obtained null distributions of first-level and second-level p -values. We inspected whether the p -values are uniformly distributed. The analysis showed that more than half (out of 110) of Dierharder atomic tests (test with particular setting) produce null distributions of p -values that are biased from the expected uniform one. Additional analysis of the Kolmogorov–Smirnov (KS) test showed that the key KS test is also biased. This increases the probability of false positives (in the right tail) for all Dieharder tests as KS is used to post-process their results. Moreover, 12 tests (22 atomic) produce results significantly biased from the null distribution of the KS test which may suggest problems with the implementation of these tests.

We present our discovery of a group of side-channel vulnerabilities in implementations of the ECDSA signature algorithm in a widely used Atmel AT90SC FIPS 140-2 certified smartcard chip and five cryptographic libraries (libgcrypt, wolfSSL, MatrixSSL, SunEC/OpenJDK/Oracle JDK, Crypto++). Vulnerable implementations leak the bit-length of the scalar used in scalar multiplication via timing. Using leaked bit-length, we mount a lattice attack on a 256-bit curve, after observing enough signing operations. We propose two new methods to recover the full private key requiring just 500 signatures for simulated leakage data, 1200 for real cryptographic library data, and 2100 for smartcard data. The number of signatures needed for a successful attack depends on the chosen method and its parameters as well as on the noise profile, influenced by the type of leakage and used computation platform. We use the set of vulnerabilities reported in this paper, together with the recently published TPM-FAIL vulnerability [MSE+20] as a basis for real-world benchmark datasets to systematically compare our newly proposed methods and all previously published applicable lattice-based key recovery methods. The resulting exhaustive comparison highlights the methods’ sensitivity to its proper parametrization and demonstrates that our methods are more efficient in most cases. For the TPM-FAIL dataset, we decreased the number of required signatures from approximately 40 000 to mere 900.