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The task of function inversion is central to cryptanalysis: breaking block ciphers, forging signatures, and cracking password hashes are all special cases of the function-inversion problem. In 1980, H...
In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DL...
The Shortest Vector Problem (SVP) is one of the mathematical foundations of lattice based cryptography. Lattice sieve algorithms are amongst the foremost methods of solving SVP. The asymptotically fas...
At CRYPTO 2017, Rosca et al. introduce a new variant of the Learning With Errors (LWE) problem, called the Middle-Product LWE (MP-LWE). The hardness of this new assumption is based on the hardness of ...
Fujioka, Takashima, Terada and Yoneyama, in their 2018 work on an authenticated key exchange protocol using supersingular isogenies, use new assumptions in their security proof of the scheme. In parti...
The iterated Even-Mansour construction is an elegant construction that idealizes block cipher designs such as the AES. In this work we focus on the simplest variant, the 2-round Even-Mansour construct...
The Hidden Subgroup Problem (HSP) aims at capturing all problems that are susceptible to be solvable in quantum polynomial time following the blueprints of Shor's celebrated algorithm. Successful solu...
The Modular Inversion Hidden Number Problem (MIHNP), introduced by Boneh, Halevi and Howgrave-Graham in Asiacrypt 2001, is briefly described as follows: Let MSBδ(z)MSBδ(z) refer to the δδ most signifi...
In 2017, Aggarwal, Joux, Prakash, and Santha proposed an innovative NTRU-like public-key cryptosystem that was believed to be quantum resistant, based on Mersenne prime numbers q=2N−1q=2N−...
In this document, we investigate the complexity of an old-time combinatorial problem - namely Permuted Kernel Problem (PKP) - about which no new breakthrough were reported for a while. PKP is an NP-co...
Two recent papers have made significant advances towards a better understanding of the concrete hardness of the computational supersingular isogeny (CSSI) problem; this problem underlies the supersing...
The approximate greatest common divisor problem (ACD) and its variants have been used to construct many cryptographic primitives. In particular, variants of the ACD problem based on Chinese remainder ...
Link Prediction is an important and well-studied problem for social networks. Given a snapshot of a graph, the link prediction problem predicts which new interactions between members are most likely t...
The Learning with Errors problem (LWE) has become a central topic in recent cryptographic research. In this paper, we present a new solving algorithm combining important ideas from previous work on im...
The Multivariate Ring Learning with Errors (mm-RLWE) problem was introduced in 2015 by Pedrouzo-Ulloa, Troncoso-Pastoriza and Pérez-González. Instead of working over a polynomial residue ring with one...

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