International Association
for Cryptologic Research

<p> In this work, we assess the real-world practicality of CSIDH, an isogeny-based non-interactive key exchange. We provide the first thorough assessment of the practicality of CSIDH in higher parameter sizes for conservative estimates of quantum security, and with protection against physical attacks.</p><p> This requires a three-fold analysis of CSIDH. First, we describe two approaches to efficient high-security CSIDH implementations, based on SQALE and CTIDH. Second, we optimize such high-security implementations, on a high level by improving several subroutines, and on a low level by improving the finite field arithmetic. Third, we benchmark the performance of high-security CSIDH. As a stand-alone primitive, our implementations outperform previous results by a factor up to 2.53×.</p><p> As a real-world use case considering network protocols, we use CSIDH in TLS variants that allow early authentication through a NIKE. Although our instantiations of CSIDH have smaller communication requirements than post-quantum KEM and signature schemes, even our highly-optimized implementations result in too-large handshake latency (tens of seconds), showing that CSIDH is only practical in niche cases. </p>

The Linear Code Equivalence (LCE) Problem has received increased attention in recent years due to its applicability in constructing efficient digital signatures. Notably, the LESS signature scheme based on LCE is under consideration for the NIST post-quantum standardization process, along with the MEDS signature scheme that relies on an extension of LCE to the rank metric, namely Matrix Code Equivalence (MCE) Problem. Building upon these developments, a family of signatures with additional properties, including linkable ring, group, and threshold signatures, has been proposed. These novel constructions introduce relaxed versions of LCE (and MCE), wherein multiple samples share the same secret equivalence. Despite their significance, these variations have often lacked a thorough security analysis, being assumed to be as challenging as their original counterparts. Addressing this gap, our work delves into the sample complexity of LCE and MCE --- precisely, the sufficient number of samples required for efficient recovery of the shared secret equivalence. Our findings reveal, for instance, that one should not use the same secret twice in the LCE setting since this enables a polynomial time (and memory) algorithm to retrieve the secret. Consequently, our results unveil the insecurity of two advanced signatures based on variants of the LCE Problem.

The Refined Power Analysis, Zero-Value Point, and Exceptional Procedure attacks introduced side-channel techniques against specific cases of elliptic curve cryptography. The three attacks recover bits of a static ECDH key adaptively, collecting information on whether a certain multiple of the input point was computed. We unify and generalize these attacks in a common framework, and solve the corresponding problem for a broader class of inputs. We also introduce a version of the attack against windowed scalar multiplication methods, recovering the full scalar instead of just a part of it. Finally, we systematically analyze elliptic curve point addition formulas from the Explicit-Formulas Database, classify all non-trivial exceptional points, and find them in new formulas. These results indicate the usefulness of our tooling, which we released publicly, for unrolling formulas and finding special points, and potentially for independent future work.