4 research outputs found
Evaluation of Resilience of randomized RNS implementation
Randomized moduli in Residue Number System (RNS) generate effectively large noise and
make quite difficult to attack a secret key from only few observations of Hamming distances
that result from the changes on the state variable. Since Hamming distances have gaussian distribution and most of the statistic tests, like NIST\u27s ones, evaluate discrete and uniform distribution, we choose to use side-channel attacks as a tool in order to evaluate randomisation of Hamming distances . This paper analyses the resilience against Correlation Power Analysis (CPA), Differential Power Analysis (DPA) when the cryptographic system is protected against Simple Power Analysis (SPA) by a Montgomery Powering Ladder (MPL). While both analysis use only information on the current state, DPA Square crosses the information of all the states. We emphasize that DPA Square performs better than DPA and CPA and we show that the number of observations needed to perform an attack increases with respect to the number of moduli . For Elliptic Curves Cryptography (ECC) and using a Monte Carlo simulation, we conjecture that
Key Randomization Countermeasures to Power Analysis Attacks on Elliptic Curve Cryptosystems
It is essential to secure the implementation of cryptosystems in
embedded devices agains side-channel attacks. Namely, in order to
resist differential (DPA) attacks, randomization techniques should be
employed to decorrelate the data processed by the device from
secret key parts resulting in the value of this data. Among the
countermeasures that appeared in the literature were those that
resulted in a random representation of the key known as the binary
signed digit representation (BSD). We have discovered some interesting
properties related to the number of possible BSD representations for
an integer and we have proposed a different randomization
algorithm. We have also carried our study to the -adic
representation of integers which is employed in elliptic curve
cryptosystems (ECCs) using Koblitz curves. We have then dealt with
another randomization countermeasure which is based on randomly
splitting the key. We have investigated the secure employment of this
countermeasure in the context of ECCs