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We propose two polynomial memory collision finding algorithms for the low Hamming weight discrete logarithm problem in any abelian group GG. The first one is a direct adaptation of the Becker-Coron-Jo...
For enabling post-quantum cryptanalytic experiments on a meaningful scale, there is a strong need for low-memory algorithms. We show that the combination of techniques from representations, multiple c...
Iterative collision search procedures play a key role in developing combinatorial algorithms for the subset sum and learning parity with noise (LPN) problems. In both scenarios, the single-list pair-w...
We construct a public-key encryption (PKE) scheme whose security is polynomial-time equivalent to the hardness of the Subset Sum problem. Our scheme achieves the standard notion of indistinguishabil...
In this paper, we describe the families of block ciphers named SHipher. We show a symmetric encryption framework based on the SubSet-Sum problem. This framework can provide families of secure, flexi...
This paper introduces a subset-sum algorithm with heuristic asymptotic cost exponent below 0.25. The new algorithm combines the 2010 Howgrave-Graham--Joux subset-sum algorithm with a new streamlined d...
In Gentry's fully homoomrphic cryptosystem, a sparse subset sum problem is used and a big set is included in the public key. In the implementation of a variant of Gentry's scheme, to reduce the size o...
It is well known that the general subset sum problem is NP-complete. However, almost all subset sum problems with density less than $0.9408\ldots$ can be solved in polynomial time with an oracle that ...
Given a prime $p$, an elliptic curve $\mathcal{E}/\mathbb{F}_p$ over the finite field $\mathbb{F}_p$ of $p$ elements and a binary linear recurrence sequence $\(u(n)\)_{n =1}^\infty$ of order~$r$, we s...
Given a prime $p$, an elliptic curve $\mathcal{E}/\mathbb{F}_p$ over the finite field $\mathbb{F}_p$ of $p$ elements and a binary linear recurrence sequence $\(u(n)\)_{n =1}^\infty$ of order~$r$, we s...
We propose a semantically-secure public-key encryption scheme whose security is polynomial- time equivalent to the hardness of solving random instances of the subset sum problem. The subset sum assu...

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