We are generally content with the project outcomes, both the planned research and the
unexpected, fruitful new research lines discovered along the way. Many articles were published,
predominantly in the top-tier conferences and journals.
The project attracted many talented young international researchers.
Below we give selected highlights.
SPD$$\mathbb {Z}_{2^k}$$: Efficient MPC mod $$2^k$$ for Dishonest Majority.
Ronald Cramer, Ivan Damgård, Daniel Escudero, Peter Scholl, Chaoping Xing.
CRYPTO 2018. We introduce novel techniques to achieve MPC modulo powers-of-p
instead of over a field, with noticeable efficiency benefits in important applications. In those cases, it can be a replacement for the popular SPDZ protocol.
Blackbox Secret Sharing Revisited: A Coding-Theoretic Approach with Application to Expansionless Near-Threshold Schemes. Ronald Cramer, Chaoping Xing. EUROCRYPT 2020. We give a new method for blackbox secret-sharing,
achieving an error-free and constant-rate rate solution.
Efficient Information-Theoretic Secure Multiparty Computation over $$\mathbb {Z}/p^k\mathbb {Z}$$ via Galois Rings. Mark Abspoel, Ronald Cramer, Ivan Damgård, Daniel Escudero, Chen Yuan. TCC 2019. A follow-up to CDESX19, but now in
the information-theoretic case (threshold, non-asymptotic).
Random Self-reducibility of Ideal-SVP via Arakelov Random Walks. Koen de Boer, Léo Ducas, Alice Pellet-Mary, Benjamin Wesolowski. CRYPTO 2020.
We show, for certain cyclotomic lattices, a worst-case to average-case reduction for ideal-SVP
(i.e. shortest-vector finding in such lattices) by using Arakelov theory.
Compressed $$\varSigma $$-Protocol Theory and Practical Application to Plug & Play Secure Algorithmics. Thomas Attema, Ronald Cramer. CRYPTO 2020.
We introduce an abstract paradigm for logarithmic-communication zero knowledge
based on arithmetic secret sharing and adaptation of powerful protocol
compression technique.
Asymptotically Good Multiplicative LSSS over Galois Rings and Applications to MPC over ℤ/p^kℤ. Mark Abspoel, Ronald Cramer, Ivan Damgård, Daniel Escudero, Matthieu Rambaud, Chaoping Xing, Chen Yuan. ASIACRYPT 2020.
Another follow-up to CDESX19: the
the information-theoretic case (asymptotic, passive adversary), with a general treatment of lifting multiplicative secret sharing to work over rings.
Mildly Short Vectors in Cyclotomic Ideal Lattices in Quantum Polynomial Time.
Ronald Cramer; Léo Ducas; Benjamin Wesolowski. JACM 2021.
Journal version of EUROCRYPT 2017 paper. We show that, under a suitable number-theoretic hypothesis, the shortest vector problem in cyclotomic lattices is considerably less hard than in generic lattices.
Compressed Σ-Protocols for Bilinear Group Arithmetic Circuits and Application to Logarithmic Transparent Threshold Signatures. Thomas Attema, Ronald Cramer, Matthieu Rambaud. ASIACRYPT 2021. We show a useful generalization of [AC20], with application to threshold signatures.
Compressing Proofs of k-Out-Of-n
Partial Knowledge. Thomas Attema, Ronald Cramer, and Serge Fehr. CRYPTO 2021.
We show how to compress a well-known ZKP for proving knowledge
of k out of n secrets.
Asymptotically-Good Arithmetic Secret Sharing over Z/(p^\ell Z) with Strong Multiplication and Its Applications to Efficient MPC. Ronald Cramer, Matthieu Rambaud, and Chaoping Xing. CRYPTO 2021.
Using advanced methods from algebraic geometry, we show to to lift
asymptotically-good arithmetic secret sharing over finite fields to work over Galois-rings.
The final follow-up to CDESX19 (information-theoretic, asymptotic, active adversary).
A Compressed Σ-Protocol Theory for Lattices. Thomas Attema, Ronald Cramer, Lisa Kohl. CRYPTO 2021.
We further enhance the framework from [AC20] and show to instantiate it from lattice-based cryptography.
