Randomization | EPFL Graph Search

Randomization is the process of making something random. Randomization is not haphazard; instead, a random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. For example, a random sample of individuals from a population refers to a sample where every individual has a known probability of being sampled. This would be contrasted with nonprobability sampling where arbitrary individuals are selected. In various contexts, randomization may involve:

generating a random permutation of a sequence (such as when shuffling cards);
selecting a random sample of a population (important in statistical sampling);
allocating experimental units via random assignment to a treatment or control condition;
generating random numbers (random number generation); or
transforming a data stream (such as when using a scrambler in telecommunications).

Applications Ap

Online Matching with General Arrivals

Buddhima Ruwanmini Gamlath Gamlath Ralalage, Mikhail Kapralov, Andreas Maggiori, Ola Nils Anders Svensson, David Wajc

The online matching problem was introduced by Karp, Vazirani and Vazirani nearly three decades ago. In that seminal work, they studied this problem in bipartite graphs with vertices arriving only on one side, and presented optimal deterministic and randomized algorithms for this setting. In comparison, more general arrival models, such as edge arrivals and general vertex arrivals, have proven more challenging and positive results are known only for various relaxations of the problem. In particular, even the basic question of whether randomization allows one to beat the trivially-optimal deterministic competitive ratio of 1/2 for either of these models was open. In this paper, we resolve this question for both these natural arrival models, and show the following. 1) For edge arrivals, randomization does not help no randomized algorithm is better than 1/2 competitive. 2) For general vertex arrivals, randomization helps - there exists a randomized (1/2+Omega (1))-competitive online matching algorithm.

IEEE COMPUTER SOC2019

Attacks on some post-quantum cryptographic protocols: The case of the Legendre PRF and SIKE

Novak Kaluderovic

Post-quantum cryptography is a branch of cryptography which deals with cryptographic algorithms whose hardness assumptions are not based on problems known to be solvable by a quantum computer, such as the RSA problem, factoring or discrete logarithms.This thesis treats two such algorithms and provides theoretical and practical attacks against them.The first protocol is the generalised Legendre pseudorandom function - a random bit generator computed as the Legendre symbol of the evaluation of a secret polynomial at an element of a finite field. We introduce a new point of view on the protocol by analysing the action of the group of Möbius transformations on the set of secret keys (secret polynomials).We provide a key extraction attack by creating a table which is cubic in the number of the function queries, an improvement over the previous algorithms which only provided a quadratic yield. Furthermore we provide an ever stronger attack for a new set of particularly weak keys.The second protocol that we cover is SIKE - supersingular isogeny key encapsulation.In 2017 the American National Institute of Standards and Technology (NIST) opened a call for standardisation of post-quantum cryptographic algorithms. One of the candidates, currently listed as an alternative key encapsulation candidate in the third round of the standardisation process, is SIKE.We provide three practical side-channel attacks on the 32-bit ARM Cortex-M4 implementation of SIKE.The first attack targets the elliptic curve scalar multiplication, implemented as a three-point ladder in SIKE. The lack of coordinate randomisation is observed, and used to attack the ladder by means of a differential power analysis algorithm.This allows us to extract the full secret key of the target party with only one power trace.The second attack assumes coordinate randomisation is implemented and provides a zero-value attack - the target party is forced to compute the field element zero, which cannot be protected by randomisation. In particular we target both the three-point ladder and isogeny computation in two separate attacks by providing maliciously generated public keys made of elliptic curve points of irregular order.We show that an order-checking countermeasure is effective, but comes at a price of 10% computational overhead. Furthermore we show how to modify the implementation so that it can be protected from all zero-value attacks, i.e., a zero-value is never computed during the execution of the algorithm.Finally, the last attack targets a point swapping procedure which is a subroutine of the three-point ladder. The attack successfully extracts the full secret key with only one power trace even if the implementation is protected with coordinate randomisation or order-checking. We provide an effective countermeasure --- an improved point swapping algorithm which protects the implementation from our attack.

EPFL2022

Effect of power randomization on saturation throughput of IEEE 802.11 WLAN

Saeid Sahraei

In this paper, we evaluate the saturation throughput for an IEEE 802.11 based wireless network considering capture effect at the receiver, while nodes transmit with random powers. In this respect, we consider a scenario consisting of a specific number of wireless nodes. Then, we derive the transmission as well as collision probabilities with respect to the perfect capture effect. In order to maximize the saturation throughput we set up an optimization problem and obtain how to compute optimum values for the probabilities corresponding to different power levels. By providing the numerical results, we deduce that power randomization may lead to a significant improvement in saturation throughput.

2010

Attacks on some post-quantum cryptographic protocols: The case of the Legendre PRF and SIKE

Novak Kaluderovic

EPFL2022