International Association for Cryptologic Research

International Association
for Cryptologic Research


Michael Reichle


Breaking Parallel ROS: Implication for Isogeny and Lattice-based Blind Signatures
Shuichi Katsumata Yi-Fu Lai Michael Reichle
Many of the three-round blind signatures based on identification protocols are only proven to be $\ell$-concurrently unforgeable for $\ell = \polylog(\secpar)$. It was only recently shown in a seminal work by Benhamouda et al.~(EUROCRYPT'21) that this is not just a limitation of the proof technique. They proposed an elegant polynomial time attack against the $\ell$-concurrently unforgeability of the classical blind Schnorr protocol for $\ell = \poly(\secpar)$. However, there are still many blind signatures following a similar recipe to blind Schnorr where the attack by Benhamouda et al. does not apply. This includes for instance the isogeny-based blind signature CSI-Otter by Katsumata et al (CRYPTO'23), the lattice-based blind signatures BLAZE+ by Alkeilani et al (ACISP'20) and BlindOR by Alkeilani et al (CANS'20). In this work, we provide a simple and novel attack on blind signatures based on identification protocols performing \emph{parallel repetition} to reduce the soundness error. Our attack translates to a polynomial time break for the $\ell$-concurrent unforgeability of CSI-Otter, BLAZE+, and BlindOR for $\ell = \poly(\secpar)$. More formally, we define an intermediate problem called Parallel Random inhomogeneities in an Overdetermined Solvable system of linear equations ($\pROS$) problem and show that an attack against $\pROS$ implies an attack to the above blind signatures. One takeaway of our finding is that while parallel repetition allows to exponentially reduce the soundness error of an identification protocol, this has minimal effect on the resulting blind signature.Our attack is concretely very efficient and for instance breaks 4-concurrent unforgeability of CSI-Otter in time roughly 2^{34} hash computations.
Pairing-Free Blind Signatures from Standard Assumptions in the ROM
Julia Kastner Ky Nguyen Michael Reichle
Blind Signatures are a useful primitive for privacy preserving applications such as electronic payments, e-voting, anonymous credentials, and more. However, existing practical blind signature schemes based on standard assumptions require either pairings or lattices. We present the first construction of a round-optimal blind signature in the random oracle model based on standard assumptions without resorting to pairings or lattices. In particular, our construction is secure under the strong RSA assumption and DDH (in pairing-free groups). For our construction, we provide a NIZK-friendly signature based on strong RSA, and efficiently instantiate a variant of Fischlin’s generic framework (CRYPTO’06). Our Blind Signature scheme has signatures of size 4.28 KB and communication cost 10.98 KB. On the way, we develop techniques that might be of independent interest. In particular, we provide efficient relaxed range- proofs for large ranges with subversion zero-knowledge and compact commitments to elements of arbitrary groups.
Adaptively Secure 5 Round Threshold Signatures from MLWE/MSIS and DL with Rewinding
T-out-of-N threshold signatures have recently seen a renewed interest, with various types now available, each offering different tradeoffs. However, one property that has remained elusive is \emph{adaptive} security. When we target thresholdizing existing efficient signatures schemes based on the Fiat-Shamir paradigm such as Schnorr, the elusive nature becomes clear. This class of signature schemes typically rely on the forking lemma to prove unforgeability. That is, an adversary is \emph{rewound and run twice} within the security game. Such a proof is at odds with adaptive security, as the reduction must be ready to answer $2(T - 1)$ secret key shares in total, implying that it can reconstruct the full secret key. Indeed, prior works either assumed strong idealized models such as the algebraic group model (AGM) or modified the underlying signature scheme so as not to rely on rewinding based proofs. In this work, we propose a new proof technique to construct adaptively secure threshold signatures for existing rewinding-based Fiat-Shamir signatures. As a result, we obtain the following: 1. The first adaptively secure 5 round lattice-based threshold signature under the MLWE and MSIS assumptions in the ROM. The resulting signature is a standard signature of Raccoon, a lattice-based signature scheme by del Pino et al., submitted to the additional NIST call for proposals. 2. The first adaptively secure 5 round threshold signature under the DL assumption in the ROM. The resulting signature is a standard Schnorr signature. To the best of our knowledge, this is the first adaptively secure threshold signature based on DL even assuming stronger models like AGM. Our work is inspired by the recent statically secure lattice-based 3 round threshold signature by del Pino et al. (Eurocrypt~2024) based on Raccoon. While they relied on so-called one-time additive masks to solve lattice specific issues, we notice that these masks can also be a useful tool to achieve adaptive security. At a very high level, we use these masks throughout the signing protocol to carefully control the information the adversary can learn from the signing transcripts. Intuitively, this allows the reduction to return a total of $2(T-1)$ \emph{randomly sampled} secret key shares to the adversary consistently and without being detected, resolving the above paradoxical situation. Lastly, by allowing the parties to maintain a simple state, we can compress our 5 round schemes into 4 rounds.
Practical Round-Optimal Blind Signatures in the ROM from Standard Assumptions
Blind signatures serve as a foundational tool for privacy-preserving applications and have recently seen renewed interest due to new applications in blockchains and privacy-authentication tokens. With this, constructing practical round-optimal (i.e., signing consists of the minimum two rounds) blind signatures in the random oracle model (ROM) has been an active area of research, where several impossibility results indicate that either the ROM or a trusted setup is inherent. In this work, we present two round-optimal blind signatures under standard assumptions in the ROM with different approaches: one achieves the smallest sum of the signature and communication sizes, while the other achieves the smallest signature size. Both of our instantiations are based on standard assumptions over asymmetric pairing groups, i.e., CDH, DDH, and/or SXDH. Our first construction is a highly optimized variant of the generic blind signature construction by Fischlin (CRYPTO’06) and has signature and communication sizes 447 B and 303 B, respectively. We progressively weaken the building blocks required by Fischlin and we result in the first blind signature where the sum of the signature and communication sizes fit below 1 KB based on standard assumptions. Our second construction is a semi-generic construction from a specific class of randomizable signature schemes that admits an all-but-one reduction. The signature size is only 96 B while the communication size is 2.2 KB. This matches the previously known smallest signature size while improving the communication size by several orders of magnitude. Finally, both of our constructions rely on a (non-black box) fine-grained analysis of the forking lemma that may be of independent interest.
Hermes: I/O-Efficient Forward-Secure Searchable Symmetric Encryption
Brice Minaud Michael Reichle
Dynamic Symmetric Searchable Encryption (SSE) enables a user to outsource the storage of an encrypted database to an untrusted server, while retaining the ability to privately search and update the outsourced database. The performance bottleneck of SSE schemes typically comes from their I/O efficiency. Over the last decade, a line of work has substantially improved that bottleneck. However, all existing I/O-efficient SSE schemes have a common limitation: they are not forward-secure. Since the seminal work of Bost at CCS 2016, forward security has become a de facto standard in SSE. In the same article, Bost conjectures that forward security and I/O efficiency are incompatible. This explains the current status quo, where users are forced to make a difficult choice between security and efficiency. The central contribution of this paper it to show that, contrary to what the status quo suggests, forward security and I/O efficiency can be realized simultaneously. This result is enabled by two new key techniques. First, we make use of a controlled amount of client buffering, combined with a deterministic update schedule. Second, we introduce the notion of SSE supporting dummy updates. In combination, those two techniques offer a new path to realizing forward security, which is compatible with I/O efficiency. Our new SSE scheme, Hermes, achieves sublogarithmic I/O efficiency O(log log N/p), storage efficiency O(1), with standard leakage, as well as backward and forward security. Practical experiments confirm that Hermes achieves excellent performance.
Dynamic Local Searchable Symmetric Encryption 📺
Michael Reichle Brice Minaud
In this article, we tackle for the first time the problem of \emph{dynamic} memory-efficient Searchable Symmetric Encryption (SSE). In the term ``memory-efficient'' SSE, we encompass both the goals of \emph{local} SSE, and \emph{page-efficient} SSE. The centerpiece of our approach is a novel connection between those two goals. We introduce a map, called the Generic Local Transform, which takes as input a \emph{page-efficient} SSE scheme with certain special features, and outputs an SSE scheme with strong \emph{locality} properties. We obtain several results. (1) First, for page-efficient SSE with page size $p$, we build a \emph{dynamic} scheme with storage efficiency $\bigO{1}$ and page efficiency $O(\log \log (N/p))$, called LayeredSSE. The main technical innovation behind LayeredSSE is a novel weighted extension of the two-choice allocation process, of independent interest. (2) Second, we introduce the Generic Local Transform, and combine it with LayeredSSE to build a \emph{dynamic} SSE scheme with storage efficiency $O{1}$, locality $O{1}$, and read efficiency $O(\log\log N)$, under the condition that the longest list is of size $O(N^{1-1/\log \log \lambda})$. This matches, in every respect, the purely \emph{static} construction of Asharov et al. presented at STOC 2016: dynamism comes at no extra cost. (3) Finally, by applying the Generic Local Transform to a variant of the Tethys scheme by Bossuat et al. from Crypto 2021, we build an unconditional static SSE with storage efficiency $O(1)$, locality $O(1)$, and read efficiency $O(\log^\varepsilon N)$, for an arbitrarily small constant $\varepsilon > 0$. To our knowledge, this is the construction that comes closest to the lower bound presented by Cash and Tessaro at Eurocrypt 2014.
Efficient Range Proofs with Transparent Setup from Bounded Integer Commitments 📺
We introduce a new approach for constructing range proofs. Our approach is modular, and leads to highly competitive range proofs under standard assumption, using less communication and (much) less computation than the state of the art methods, and without relying on a trusted setup. Our range proofs can be used as a drop-in replacement in a variety of protocols such as distributed ledgers, anonymous transaction systems, and many more, leading to significant reductions in communication and computation for these applications. At the heart of our result is a new method to transform any commitment over a finite field into a commitment scheme which allows to commit to and efficiently prove relations about bounded integers. Combining these new commitments with a classical approach for range proofs based on square decomposition, we obtain several new instantiations of a paradigm which was previously limited to RSA-based range proofs (with high communication and computation, and trusted setup). More specifically, we get: - Under the discrete logarithm assumption, we obtain the most compact and efficient range proof among all existing candidates (with or without trusted setup). Our proofs are 12% to 20% shorter than the state of the art Bulletproof (Bootle et al., CRYPTO'18) for standard choices of range size and security parameter, and are more efficient (both for the prover and the verifier) by more than an order of magnitude. - Under the LWE assumption, we obtain range proofs that improve over the state of the art in a batch setting when at least a few dozen range proofs are required. The amortized communication of our range proofs improves by up to two orders of magnitudes over the state of the art when the number of required range proofs grows. - Eventually, under standard class group assumptions, we obtain the first concretely efficient standard integer commitment scheme (without bounds on the size of the committed integer) which does not assume trusted setup.
SSE and SSD: Page-Efficient Searchable Symmetric Encryption 📺
Searchable Symmetric Encryption (SSE) enables a client to outsource a database to an untrusted server, while retaining the ability to securely search the data. The performance bottleneck of classic SSE schemes typically does not come from their fast, symmetric cryptographic operations, but rather from the cost of memory accesses. To address this issue, many works in the literature have considered the notion of locality, a simple design criterion that helps capture the cost of memory accesses in traditional storage media, such as Hard Disk Drives. A common thread among many SSE schemes aiming to improve locality is that they are built on top of new memory allocation schemes, which form the technical core of the constructions. The starting observation of this work is that for newer storage media such as Solid State Drives (SSDs), which have become increasingly common, locality is not a good predictor of practical performance. Instead, SSD performance mainly depends on page efficiency, that is, reading as few pages as possible. We define this notion, and identify a simple allocation problem, Data-Independent Packing, that captures the main technical challenge required to build page-efficient SSE. As our main result, we build a page-efficient and storage-efficient data-independent packing scheme, and deduce an SSE scheme with the same properties. The technical core of the result is a new generalization of cuckoo hashing to items of variable size. Practical experiments show that this approach achieves excellent performance.
Non-interactive Keyed-Verification Anonymous Credentials
Geoffroy Couteau Michael Reichle
Anonymous credential ($$\mathsf {AC}$$) schemes are protocols which allow for authentication of authorized users without compromising their privacy. Of particular interest are non-interactive anonymous credential ($$\mathsf {NIAC}$$) schemes, where the authentication process only requires the user to send a single message that still conceals its identity. Unfortunately, all known $$\mathsf {NIAC}$$ schemes in the standard model require pairing based cryptography, which limits them to a restricted set of specific assumptions and requires expensive pairing computations. The notion of keyed-verification anonymous credential ($$\mathsf {KVAC}$$) was introduced in (Chase et al., CCS’14) as an alternative to standard anonymous credential schemes allowing for more efficient instantiations; yet, making existing $$\mathsf {KVAC}$$ non-interactive either requires pairing-based cryptography, or the Fiat-Shamir heuristic.In this work, we construct the first non-interactive keyed-verification anonymous credential ($$\mathsf {NIKVAC}$$) system in the standard model, without pairings. Our scheme is efficient, attribute-based, supports multi-show unlinkability, and anonymity revocation. We achieve this by building upon a combination of algebraic $$\mathsf {MAC}$$ with the recent designated-verifier non-interactive zero-knowledge ($$\mathsf {DVNIZK}$$) proof of knowledge of (Couteau and Chaidos, Eurocrypt’18). Toward our goal of building $$\mathsf {NIKVAC}$$, we revisit the security analysis of a $$\mathsf {MAC}$$ scheme introduced in (Chase et al., CCS’14), strengthening its guarantees, and we introduce the notion of oblivious non-interactive zero-knowledge proof system, where the prover can generate non-interactive proofs for statements that he cannot check by himself, having only a part of the corresponding witness, and where the proof can be checked efficiently given the missing part of the witness. We provide an efficient construction of an oblivious $$\mathsf {DVNIZK}$$, building upon the specific properties of the $$\mathsf {DVNIZK}$$ proof system of (Couteau and Chaidos, Eurocrypt’18).