A Secure Multi-Party Computation Protocol Suite Inspired by Shamir’s Secret Sharing Scheme

Tänapäeva maailm on täis saladusi. Mõnikord me sooviks teada midagi nende kohta ilma oma saladusi avalikustamata. Näiteks võib kedagi huvitada, kas ta on rikkam kui mõni tema sõber. Valitsusi võib huvitada, et nende satelliidid ei satuks kokkupõrkesse, kuid samas ei tahaks nad välismaailmale oma strateegiliste satelliitide liikumise kohta liiga palju infot jagada. Turvaline ühisarvutus võimaldab osapooltel ühiselt arvutada mingi funktsiooni väärtusi ilma sisendeid avalikustamata. Sharemind on üks praktiline raamistik turvaliste ühisarvutuste tegemiseks. Selles töös loomegi protokollide komplekti Sharemindi jaoks. Meie protokollid on inspireeritud Shamiri ühissalastusest, mis võimaldab saladusi osadeks jagada. Me anname algoritmid liitmise, korrutamise ja võrdlustehete jaoks koos vastavate turvatõestustega. Lisaks võrdleme realiseeritud protokollide jõudlust juba varasemalt olemasoleva protokollistikuga. Esialgsed keerukus- ja jõudlustulemused on lubavad, kuid on arenguruumi.The world today is full of secrets. Sometimes, we would like to know something about them without revealing the secrets themselves. For example, whether I have more money than my friend or whether two satellites would collide without publishing their moving trajectories. Secure multi-party computation allows us to jointly compute some functions while keeping the privacy of our inputs. Sharemind is a practical framework for performing secure multi-party computations. In this work, we added a protocol suite to Sharemind. This protocol suite was inspired by Shamir's secret sharing scheme, which describes a way to divide a secret into pieces. We describe algorithms for addition, multiplication, equality-testing and less-than comparison. We also give correctness and security proofs for the protocols. The resulting implementations were compared to an existing protocol suite inspired by additive secret sharing. The initial complexities and benchmarking results are promising, but there is room for improvement

Heuristically secure threshold lattice-based cryptography schemes

In public-key encryption, a long-term private key can be an easy target for hacking and deserves extra protection. One way to enhance its security is to share the long-term private key among multiple (say n) distributed servers; any threshold number (t, t ≤ n) of these servers are needed to collectively use the shared private key without reconstructing it. As a result, an attacker who has compromised less than t servers will still not be able to reconstruct the shared private key. In this thesis, we studied threshold decryption schemes for lattice-based public-key en- cryption, which is one of the most promising post-quantum public-key encryption schemes. We developed threshold decryption schemes for Stinson’s, the standard NTRU, and NTRU with Ring Learning with Errors (R-LWE) cryptosystems. Prototype implementations were developed for validating the functionality of these threshold decryption schemes. Our de- signs achieve heuristic security, and its security is supported by mechanisms similar to that of R-LWE

RYDE: A Digital Signature Scheme based on Rank-Syndrome-Decoding Problem with MPCitH Paradigm

We present a signature scheme based on the Syndrome-Decoding problem in rank metric. It is a construction from multi-party computation (MPC), using a MPC protocol which is a slight improvement of the linearized-polynomial protocol used in [Fen22], allowing to obtain a zero-knowledge proof thanks to the MPCitH paradigm. We design two different zero-knowledge proofs exploiting this paradigm: the first, which reaches the lower communication costs, relies on additive secret sharings and uses the hypercube technique [AMGH+22]; and the second relies on low-threshold linear secret sharings as proposed in [FR22]. These proofs of knowledge are transformed into signature schemes thanks to the Fiat-Shamir heuristic [FS86].Comment: arXiv admin note: substantial text overlap with arXiv:2307.0857