Khadijeh Bagheri

Hassan Khodaiemehr, Khadijeh Bagheri, Chen Feng et al.

SILMARILS is built from a minimal algebraic core over $\mathbb{F}_p$ using true randomness and perfect $2$-out-of-$2$ Shamir secret sharing. The framework supports both two-party and three-party modes. In the two-party setting, SILMARILS realizes a transferable designated-verifier (TDV) signature scheme. The designated verifier can simulate accepting transcripts indistinguishable from real ones, achieving Jakobsson-Sako-Impagliazzo DV security. The verifier may publish a receipt $r$ enabling public verification, yet even with $r$, no external party can tell whether a transcript was signed or simulated. As DV signatures permit simulation, standard EUF-CMA cannot hold for the designated verifier; instead, we prove $\mathsf{EUF\text{-}CMA}^{\neg\mathsf{DV}}$ security for all non-designated verifiers in both the random oracle model (ROM) and quantum random oracle model (QROM). In the three-party mode, adopting the broadcast model of Fitzi et al., we obtain a statistically secure signature protocol with simulation-based security and error~$1/p$. We analyze security in the Pure IT model, the IT+ROM, and the QROM, extending the Fitzi et al. framework to quantum adversaries with classical I/O. Correctness, secrecy, transferability, and unforgeability for non-designated parties remain equivalent to simulation-based security. Thanks to its simple algebraic structure, SILMARILS achieves substantially smaller keys and signatures than standardized post-quantum schemes such as Dilithium, Falcon, and SPHINCS$^+$, while providing post-quantum security in a TDV setting well suited to blockchain applications.

Khadijeh Bagheri, Mohammad-Reza Sadeghi, Daniel Panario

We propose BQTRU, a non-commutative NTRU-like cryptosystem over quaternion algebras. This cryptosystem uses bivariate polynomials as the underling ring. The multiplication operation in our cryptosystem can be performed with high speed using quaternions algebras over finite rings. As a consequence, the key generation and encryption process of our cryptosystem is faster than NTRU in comparable parameters. Typically using Strassen's method, the key generation and encryption process is approximately $16/7$ times faster than NTRU for an equivalent parameter set. Moreover, the BQTRU lattice has a hybrid structure that makes inefficient standard lattice attacks on the private key. This entails a higher computational complexity for attackers providing the opportunity of having smaller key sizes. Consequently, in this sense, BQTRU is more resistant than NTRU against known attacks at an equivalent parameter set. Moreover, message protection is feasible through larger polynomials and this allows us to obtain the same security level as other NTRU-like cryptosystems but using lower dimensions.