# Biblio

Secret Sharing Schemes with Hidden Sets. 2018 IEEE Symposium on Computers and Communications (ISCC). :00713–00718.

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2018. Shamir's Secret Sharing Scheme is well established and widely used. It allows a so-called Dealer to split and share a secret k among n Participants such that at least t shares are needed to reconstruct k, where 0 \textbackslashtextbackslashtextless; t ≤ n. Nothing about the secret can be learned from less than t shares. To split secret k, the Dealer generates a polynomial f, whose independent term is k and the coefficients are randomly selected using a uniform distribution. A share is a pair (x, f(x)) where x is also chosen randomly using a uniform distribution. This scheme is useful, for example, to distribute cryptographic keys among different cloud providers and to create multi-factor authentication. The security of Shamir's Secret Sharing Scheme is usually analyzed using a threat model where the Dealer is trusted to split and share secrets as described above. In this paper, we demonstrate that there exists a different threat model where a malicious Dealer can compute shares such that a subset of less than t shares is allowed to reconstruct the secret. We refer to such subsets as hidden sets. We formally define hidden sets and prove lower bounds on the number of possible hidden sets for polynomials of degree t - 1. Yet, we show how to detect hidden sets given a set of n shares and describe how to create hidden sets while sharing a secret using a modification of Shamir's scheme.

You Shall Not Pass! (Once Again): An IoT Application of Post-Quantum Stateful Signature Schemes. Proceedings of the 5th ACM on ASIA Public-Key Cryptography Workshop. :19–24.

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2018. This paper presents an authentication protocol specifically tailored for IoT devices that inherently limits the number of times that an entity can authenticate itself with a given key pair. The protocol we propose is based on a stateful hash-based digital signature system called eXtended Merkle Signature Scheme (XMSS), which has increased its popularity of late due to its resistance to quantum-computer-aided attacks. We propose a 1-pass authentication protocol that can be customized according to the server capabilities to keep track of the key pair state. In addition, we present results when ported to ARM Cortex-M3 and M0 processors.