68 problems

The supplied source describes the Jouart conjecture as asserting that the indices $m$ for which $P(m)=3m+i(m)$ is prime exhibit a regular exclusion structure characterized by two f…

Determine the supremum of the exponents $\alpha$ for which the following holds: for every fixed $\varepsilon>0$, there is a deterministic polynomial-time algorithm that, given a ba…

For every pair of positive integers $n,k$ with $\gcd(k,n)=1$, let $F:\mathbb{F}_{2^n}\to\mathbb{F}_{2^n}$ be defined by $F(x)=x^{4^k-2^k+1}$, and let…

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For an $n$-party monotone access structure $\Gamma\subseteq 2^{[n]}$, let $\ell_{\Gamma}$ be the minimum, over all linear secret-sharing schemes for one-bit secrets realizing…

For $N=2^n$, let $s\in\mathbb{Z}_N$ be hidden. Given polynomially many independent copies of the mixed coset state…

Given a modular polynomial equation $f(x_1,\ldots,x_n)\equiv 0\pmod N$ and the associated lattice-based Coppersmith method, determine the optimal asymptotic region of exponents…

Let $X,Y \in \{0,1\}$ have joint distribution … then $I(X;Y) = 1 - h(\alpha)$ for $0 \leq \alpha \leq 1/2$ where…

Let $a_1, a_2, a_3, \ldots$ be a sequence of real numbers (a signal) transmitted in the presence of additive noise such that…

It is known that it is possible to establish correspondence between certain NP-hard graph problems and problems in group theory; we would like to expand our portfolio of such probl…

We would like to use computational problems in group theory to derive fundamental cryptographic objects including one-way functions and multilinear maps.

Several cryptanalytic methods against group-based cryptography suggest possible use cases for infinite non-abelian groups; for example, non-Hopfian groups. We would like to develop…

Generally speaking the field does not seem to offer methods of key establishment. It remains open to construct standard key exchange protocols as well as more complicated multi-par…

In general very little work exists on efficient implementation of group-based protocols; over time we would like to build up a software library of such implementations.

Across the various group-based protocols there is a general lack of precision on which parameter specification. As the field matures we should make available challenge instances of…

We would like to use generic group-action tools to build ring signatures, blind signatures, threshold signatures and more. We would also like to apply the "twist" technique present…

There have been some results in the application of machine learning to the cryptanalysis of lattice-based schemes; whether these methods translate to the group-theoretic realm rema…

We would like to solidify the credentials of group-theoretic cryptography as post-quantum by developing lower bounds for the quantum complexity of problems arising in group theory.…

On the quantum side the question of quantum equivalence of SDLP and the CDH-type problem underpinning semidirect product key exchange (SCDH) remains unproven, though we have strong…

In the design of the hash function one has control over two parameters; the dimension of the special linear group considered, and the characteristic of the underlying field. We wou…

Compute short units in the ring of integers of $\mathbb Q[x]/(x^{312} - x^{156} -1)$. How short can they be, and how fast can you find them?

Is there a crypto problem that is solved by Simon's algorithm without superposition attackers? Which hidden subgroup problems have crypto applications? Or non-crypto instances?

Solve Decisional Diffie-Hellman (DDH) in the context of CSIDH: Let $E_0$ be a supersingular elliptic curve defined over $\mathbb F_p$ with endomorphism ring $\mathbb Z[\pi]$. Disti…

Are there CSIDH attacks better than hidden shift? What is the cost of the hidden shift attack?

Can quantum algorithms be used to attack SIDH by using the extra points? Are there SIDH attacks better than claw-finding?