Vladimír Sedláček

Rutgers, The State University of New Jersey | Rutgers · Department of Mathematics

It can be tricky to trust elliptic curves standardized in a non-transparent way. To rectify this, we propose a systematic methodology for analyzing curves and statistically comparing them to the expected values of a large number of generic curves with the aim of identifying any deviations in the standard curves.For this purpose, we put together the...

It can be tricky to trust elliptic curves standardized in a non-transparent way. To rectify this, we propose a systematic methodology for analyzing curves and statistically comparing them to the expected values of a large number of generic curves with the aim of identifying any deviations in the standard curves. For this purpose, we put together t...

The Refined Power Analysis, Zero-Value Point, and Exceptional Procedure attacks introduced side-channel techniques against specific cases of elliptic curve cryptography. The three attacks recover bits of a static ECDH key adaptively, collecting information on whether a certain multiple of the input point was computed. We unify and generalize these...

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 u...

We analyse whether the smartcards of the JavaCard platform correctly validate primality of domain parameters. The work is inspired by Prime and prejudice: primality testing under adversarial conditions, where the authors analysed many open-source libraries and constructed pseudoprimes fooling the primality testing functions. However, in the case of...

We analyse whether the smartcards of the JavaCard platform correctly validate primality of domain parameters. The work is inspired by Albrecht et al. [1], where the authors analysed many open-source libraries and constructed pseudoprimes fooling the primality testing functions. However, in the case of smartcards, often there is no way to invoke the...

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 u...

In this paper we study the groups of circular numbers and circular units in Sinnott’s sense in real abelian fields with exactly four ramified primes under certain conditions. More specifically, we construct ℤ-bases for them in five special infinite families of cases. We also derive some results about the corresponding module of relations (in one fa...