CryptoDB
Luciano Maino
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Publications
Year
Venue
Title
2023
EUROCRYPT
A Direct Key Recovery Attack on SIDH
★
Abstract
We present an attack on SIDH utilising isogenies between polarized products of two supersingular elliptic curves. In the case of arbitrary starting curve, our attack (discovered independently from [8]) has subexponential complexity, thus significantly reducing the security of SIDH and SIKE. When the endomorphism ring of the starting curve is known, our attack (here derived from [8]) has polynomial-time complexity assuming the generalised Riemann hypothesis. Our attack applies to any isogeny-based cryptosystem that publishes the images of points under the secret isogeny, for example Séta [13] and B-SIDH [11]. It does not apply to CSIDH [9], CSI-FiSh [3], or SQISign [14].
2023
ASIACRYPT
FESTA: Fast Encryption from Supersingular Torsion Attacks
Abstract
We introduce FESTA, an efficient isogeny-based public-key encryption (PKE) protocol based on a constructive application of the SIDH attacks.
At its core, FESTA is based on a novel trapdoor function, which uses an improved version of the techniques proposed in the SIDH attacks to develop a trapdoor mechanism. Using standard transformations, we construct an efficient PKE that is IND-CCA secure in the QROM. Additionally, using a different transformation, we obtain the first isogeny-based PKE that is IND-CCA secure in the standard model.
Lastly, we propose a method to efficiently find parameters for FESTA, and we develop a proof-of-concept implementation of the protocol. We expect FESTA to offer practical performance that is competitive with existing isogeny-based constructions.
Coauthors
- Andrea Basso (1)
- Luciano Maino (2)
- Chloe Martindale (1)
- Lorenz Panny (1)
- Giacomo Pope (2)
- Benjamin Wesolowski (1)