Hypothèse calculatoire

En cryptographie, une hypothèse de difficulté calculatoire est une hypothèse qui sert à évaluer et à démontrer la robustesse des primitives cryptographiques. Dans certains cas, la sécurité est dite inconditionnelle si elle ne repose sur aucune hypothèse de difficulté calculatoire ; un exemple courant est la technique dite du masque jetable, où le masque est aussi grand que le message. Cependant, il est souvent impossible d'atteindre une forme de sécurité aussi forte ; dans de tels cas, les cryptographes doivent s'en remettre à une forme de sécurité dite « calculatoire ». En première approximation, cela signifie que ces systèmes sont sûrs en supposant que tous les adversaires disposent d'une capacité de calcul limitée, comme tous les protagonistes en disposent en pratique. Déterminer la difficulté de résolution d'un problème n’est pas une question facile, et le cryptosystème de Merkle-Hellman a supposé par exemple la difficulté du problème du sac à dos à poids super-croissant, qui s'e

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

Poster: LocalCoin: An Ad-hoc Payment Scheme for Areas with High Connectivity

Dimitrios Chatzopoulos, Boi Faltings, Sujit Prakash Gujar

The popularity of digital currencies, especially cryptocurrencies, has been continuously growing since the appearance of Bitcoin. Bitcoin is a peer-to-peer (P2P) cryptocurrency protocol enabling transactions between individuals without the need of a trusted authority. Its network is formed from resources contributed by individuals known as miners. Users of Bitcoin currency create transactions that are stored in a specialised data structure called a block chain. Bitcoin's security lies in a proof-of-work scheme, which requires high computational resources at the miners. These miners have to be synchronised with any update in the network, which produces high data traffic rates. Despite advances in mobile technology, no cryptocurrencies have been proposed for mobile devices. This is largely due to the lower processing capabilities of mobile devices when compared with conventional computers and the poorer Internet connectivity to that of the wired networking. In this work, we propose LocalCoin, an alternative cryptocurrency that requires minimal computational resources, produces low data traffic and works with off-the-shelf mobile devices. LocalCoin replaces the computational hardness that is at the root of Bitcoin's security with the social hardness of ensuring that all witnesses to a transaction are colluders. It is based on opportunistic networking rather than relying on infrastructure and incorporates characteristics of mobile networks such as users' locations and their coverage radius in order to employ an alternative proof-of-work scheme. Localcoin features (i) a lightweight proof-of-work scheme and (ii) a distributed block chain.

Assoc Computing Machinery2016

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

Novak Kaluderovic

EPFL2022

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

Existence Of Solutions For Jacobian And Hessian Equations Under Smallness Assumptions

Poster: LocalCoin: An Ad-hoc Payment Scheme for Areas with High Connectivity

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

Existence Of Solutions For Jacobian And Hessian Equations Under Smallness Assumptions

Poster: LocalCoin: An Ad-hoc Payment Scheme for Areas with High Connectivity