Traceable Receipt-free Encryption (TREnc) has recently been introduced by Devillez, Pereira and Peters (Asiacrypt’22) as a verifiable public-key encryption primitive allowing to randomize ciphertexts in order to remove any subliminal information up to a public trace which prevents the malleability of the underlying plaintexts. This unique feature generically enables the construction of voting systems by allowing voters to encrypt their votes, tracing whether a published ballot takes their choices into account, and preventing them from proving how they voted. While being a very promising primitive, the few existing TREnc mechanisms solely rely on discrete-logarithm related assumptions making them vulnerable to the well-known harvest now, decrypt later attack in the wait of quantum computers. In this article, we address this limitation by building the first TREnc which can be safely used today until the advent of quantum adversaries. More precisely, based on the observation that security must hold at the time the primitive is used while only privacy should withstand in the post-quantum era, our solution relies on a mix of pre-quantum and post-quantum cryptography. As a first contribution, we generalize the original TREnc primitive that is too restrictive to be easily compatible with built-in lattice-based semantically-secure encryption. Our more flexible model keeps all the ingredients generically implying receipt-free voting. Next, we design our construction with the following essential properties for trustworthy elections: (i) it is provably-secure in the standard model; (ii) it relies on standard assumptions, namely Ring Learning With Errors (RLWE) coupled with pairing-based statistical zero-knowledge simulation-sound SXDH-based proofs; and (iii) it further enjoys a public-coin common reference string removing the need of a trusted setup.

The Fujisaki-Okamoto transform is a popular solution to design post-quantum public key encryption schemes, or key encapsulation mechanisms. In order to ensure security against chosen-ciphertext attacks, it checks the validity of ciphertexts by re-encrypting decrypted messages. This operation in turn leads to severe side-channel weaknesses, because the re-encrypted messages can be made key-dependent. Hence, distinguishing them thanks to leakage is sufficient to extract (long-term) secret key information. As a result, recent works suggested to ensure the validity of ciphertexts by other means than re-encryption. For now, the main candidate for this purpose, integrated in the Polka encryption scheme (PKC 2023) and analyzed more generically by Hövelmanns et al. (EUROCRYPT 2025), is to use continuous norm checks through the decryption process. In this paper, we evaluate the extent to which replacing the FO-transform by such norm checks helps resistance against leakage. Negatively, we exhibit new attack vectors that were not anticipated in previous (heuristic) analyzes. Positively, we observe that the removal of the FO-transform nevertheless reduces the attack surface and we identify possible tracks to further minimize it. Overall, our results therefore shed light on the challenge of designing post-quantum public-key encryption schemes, or key encapsulation mechanisms, that can be efficiently protected against side-channel attacks. We hope they can inform theory about leakage sources that could be better taken over by design, to develop new schemes allowing a scarcer use of implementation-level countermeasures.

We provide a simpler and more efficient way to prove knowledge of the plaintext in (a variant of) the Joye-Libert additively homomorphic cryptosystem. We also extend it into a proof that two ciphertexts encrypt the same plaintext under different public keys. This provides a more efficient instantiation of the Naor-Yung paradigm for IND-CCA2 security than in earlier proofs of plaintext equalities for JL ciphertexts. As a result of independent interest, we show that applying the Naor-Yung technique to similar-looking schemes is non-trivial when the soundness of the NIZK proof of plaintext equality relies on an assumption that directly relates to the infeasibility of recovering the secret key from the public key in the underlying IND-CPA scheme.

Proving the validity of ballots is a central element of verifiable elections. Such proofs can however create challenges when one desires to make a protocol receipt-free. We explore the challenges raised by validity proofs in the context of protocols where threshold receipt-freeness is obtained by secret sharing an encryption of a vote between multiple authorities. In such contexts, previous solutions verified the validity of votes by decrypting them after passing them through a mix-net. This approach however creates subtle privacy risks, especially when invalid votes leak structural patterns that threaten receipt-freeness. We propose a different approach of threshold receipt-free voting in which authorities re-randomize ballot shares then jointly compute a ZK proof of ballot validity before letting the ballots enter a (possibly homomorphic) tallying phase. Our approach keeps the voter computational costs limited while offering verifiability and improving the ballot privacy of previous solutions. We present two protocols that enable a group of servers to verify and publicly prove that encrypted votes satisfy some validity properties: , which preserves prior voter-side behavior with minimal overhead, and , which requires voters to submit auxiliary data to facilitate validation over large vote domains. We show how to use our two protocols within a threshold receipt-free voting framework. We provide formal security proofs and efficiency analyses to illustrate trade-offs in our designs.

POLKA is a post-quantum public-key encryption scheme from PKC 2023, designed in order to be efficiently protected against side-channel attacks. Its motivation arises from the acknowledged difficulty of protecting KYBER against such attacks. Concretely, the structure of POLKA aims to allow so-called leveled implementations, so that protecting its long-term key requires strong and expensive countermeasures (like masking) for a part of its operations only. This contrasts with KYBER, for which preventing side-channel attacks requires to uniformly protect all its operations. The good leakage-resilience features of POLKA nevertheless come with performance overheads in an unprotected implementation context. Since no concrete implementations of POLKA were proposed so far, it left the question of the number of shares for which it can become an interesting alternative to KYBER open. We bridge this gap by proposing a leveled software implementation of POLKA and show that, already for two shares, it leads to significant performance gains over the state-of-the-art uniformly masked implementations of KYBER (Bos et al., TCHES 2021, Bronchain and Cassiers, TCHES 2022).

Physical attacks are one of the potent threats to modern cryptography. Symmetric-key primitives are well-explored with respect to passive, active, and more recently combined (i.e., simultaneously leaking and faulting) adversaries. For symmetric key operating modes, there are many proposals for encryption (ENC), Message Authentication Codes (MAC), and Authenticated Encryption (AE) covering passive attacks. However, research on active or combined adversaries is more succinct and, to the best of our knowledge, boils down to combined secure MAC due to Berti et al. (ToSC 2023, issue 1), combined secure ENC due to Dobraunig et al. (CCS’22), and active secure AE named MEM due to Saha et al. (ToSC 2022, issue 4). Our first contribution is a security model to formally reason about the combined security of AE. The model extends the fault-then-leak security of MAC introduced by Berti et al. to AE and can also be seen as a natural extension of state-of-the-art leakage resistant notions in their so-called faulty matrix framework. Armed with this model, we show as a second contribution that all the leakage-resilient, including leakage-resistant, AE constructions and the fault-resilient MEM construction are vulnerable to a single fault injection within the composition of their building blocks. These decoupling attacks remain successful even for combined-secure building blocks. As a result, we finally present LEAF, the first AE construction secure against faultthen- leak adversaries with a single fault injection. In encryption, LEAF makes only one call to a MAC and two calls to an ENC that are combined secure.

Traceable Receipt-free Encryption (TREnc) is a verifiable public-key encryption primitive introduced at Asiacrypt 2022. A TREnc allows randomizing ciphertexts in transit in order to remove any subliminal information up to a public trace that ensures the non-malleability of the underlying plaintext. A remarkable property of TREnc is the indistingui-shability of the randomization of chosen ciphertexts against traceable chosen-ciphertext attacks (TCCA). This property can support applications like voting, and it was shown that receipt-free non-interactive voting, where voters are unable to convince any third party of the content of their vote, can be generically built from a TREnc. While being a very promising primitive, the few existing TREnc mechanisms either require a secret coin CRS or are fairly demanding in time and space requirements. Their security proofs also come with a linear security degradation in the number of challenge ciphertexts. We address these limitations and offer two efficient public coin TREnc mechanisms tailored for the two common tallying approaches in elections: homomorphic and mixnet-based. The TCCA security of our mechanisms also enjoys an almost-tight reduction to SXDH, based on a new randomizable technique of independent interest in the random oracle model. A Rust implementation of our TREnc mechanisms demonstrates that we can verifiably encrypt 64 bits in less than a second, and full group elements in around 30 ms., which is sufficient for most real-world applications. While comparing with other solutions, we show that our approaches lead to the most efficient non-interactive receipt-free voting system to date.

This paper explores the interaction between receipt- freeness and cast-as-intended verifiability, a property that has been overlooked until now or assumed to be granted through procedural means in the context of receipt-free voting protocols.We first demonstrate that it is impossible to obtain a receipt-free voting protocol with cast-as-intended verifiability if the voting process is non-interactive, unless a trusted authority is available. We also demonstrate that, if a trusted voter registration authority is available, then cast-as-intended verifiability and receipt-freeness can be obtained.Furthermore, after extending standard receipt-freeness security definitions to an interactive voting (and corruption) setting, we demonstrate that the same security properties can be obtained using an interactive voting process.Finally, we discuss the performance of our protocols based on a prototype implementation.

In 2001, Hirt proposed a receipt-free voting scheme, which prevents malicious voters from proving to anybody how they voted, under the assumption of the availability of a helping server that is trusted for receipt-freeness, and only for that property. This appealing design led to a number of subsequent works that made this approach non-interactive and more efficient. Still, in all of these works, receipt-freeness depends on the honesty of one single server. In order to remove this single point of failure, we design a new model in which multiple helping servers are available and propose a new security definition called threshold receipt-freeness. Our definition requires that receipt-freeness should be guaranteed even if some of the helping servers happen to be fully malicious and ensures that voters can express their votes even if the corrupted servers choose the content of their local view of the ballots. Eventually, we propose a generic construction of a single-pass verifiable voting system achieving threshold receipt freenes with a mixnet-based tallying process. Our ballot submission process relies on the recently designed traceable receipt-free encryption primitive.

We design new encryption mechanisms that enable the design of the first universally verifiable voting schemes, supporting both receipt-freeness and everlasting privacy without assuming the existence of an anonymous channel. Our schemes support the two most traditional election tallying methods: One is additively homomorphic, supporting elections in which votes simply need to be added, but decryption is only efficient for a message space of polylogarithmic size. The other is randomizable, is compatible with traditional mixnet-based tallying methods, and supports efficient message encoding, which makes it compatible with virtually any election type. Our approach builds on the recently proposed traceable receipt-free encryption (TREnc) primitive to support the design of a perfectly private audit trail. In particular, we propose two TREnc that are secure under SXDH and rely on a public coin CRS (or on the random oracle model). This improves on previous TREnc mechanisms that required a structured CRS and is of independent interest. A prototype implementation of our mechanisms is proposed, which shows that ballot preparation and verification can be executed in less than a second.

Authenticated Encryption (AE) modes of operation based on Tweakable Block Ciphers (TBC) usually measure efficiency in the number of calls to the underlying primitive per message block. On the one hand, many existing solutions reach a primitive-rate of 1, meaning that each n-bit block of message asymptotically needs a single call to the TBC with output length n. On the other hand, while these modes look optimal in a blackbox setting, they become less attractive when leakage comes into play, since all these calls must then be equally well protected to maintain security. Leakage-resistant modes improve this situation, by generating ephemeral keys every constant number of calls. However, rekeying is inherently suboptimal in primitive-rate, since a TBC call can only be used either to refresh a key or to encrypt a block. Even worse, existing solutions achieving almost n bits of security for n-bit secret keys have at most a primitive-rate 2/3. Hence the question: Can we design a highly-secure TBC-based rekeying mode with “nearly optimal” primitive-rate? We answer this question positively with Multiplex, a new mode that has primitive-rate d/(d + 1) given a TBC with a dn-bit tweak. Multiplex achieves n − log2(dn) bits of security for both (i) misuse-resilience CCA confidentiality security in the blackbox setting and (ii) Ciphertext Integrity with Misuse-resistant and unbounded Leakage in encryption and decryption (CIML2). It also provides (iii) confidentiality with leakage up to the birthday bound. Furthermore, Multiplex can run d + 1 calls in parallel in each iteration. The combination of these features gives a mode of operation that inherits most of the good implementation features and flexibility of a sponge construction – therefore paving the way towards sound comparisons between TBC-based and permutation-based AE.

As for any cryptographic algorithm, the deployment of post-quantum CCA-secure public key encryption schemes may come with the need to be protected against side-channel attacks. For existing post-quantum schemes that have not been developed with leakage in mind, recent results showed that the cost of these protections can make their implementations more expensive by orders of magnitude. In this paper, we describe a new design, coined POLKA, that is specifically tailored to reduce this cost. It leverages various ingredients in order to enable efficient side-channel protected implementations such as: (i) the rigidity property (which intuitively means that the de-randomized encryption and decryption are injective functions) to avoid the very leaky re-encryption step of the Fujisaki-Okamoto transform, (ii) the randomization of the decryption thanks to the incorporation of a dummy ciphertext, removing the adversary's control of its intermediate computations and making these computations ephemeral, (iii) key-homomorphic computations that can be masked against side-channel attacks with overheads that scale linearly in the number of shares, (iv) hard physical learning problems to argue about the security of some critical unmasked operations. Furthermore, we use an explicit rejection mechanism (returning an error symbol for invalid ciphertexts) to avoid the additional leakage caused by implicit rejection. As a result, the operations of POLKA can be protected against leakage in a cheaper way than state-of-the-art designs, opening the way towards schemes that are both quantum-safe and leakage-resistant.

CCA-like game-based security definitions capture confidentiality by asking an adversary to distinguish between honestly computed encryptions of chosen plaintexts. In the context of voting systems, such guarantees have been shown to be sufficient to prove ballot privacy (Asiacrypt'12). In this paper, we observe that they fall short when one seeks to obtain receipt-freeness, that is, when corrupted voters who submit chosen ciphertexts encrypting their vote must be prevented from proving how they voted to a third party. Since no known encryption security notion can lead to a receipt-free ballot submission process, we address this challenge by proposing a novel publicly verifiable encryption primitive coined Traceable Receipt-free Encryption (TREnc) and a new notion of traceable CCA security filling the definitional gap underlined above. We propose two TREnc instances, one generic achieving stronger guarantees for the purpose of relating it to existing building blocks, and a dedicated one based on SXDH. Both support the encryption of group elements in the standard model, while previously proposed encryption schemes aiming at offering receipt-freeness only support a polynomialsize message space, or security in the generic group model. Eventually, we demonstrate how a TREnc can be used to build receiptfree protocols, by following a standard blueprint.

Security against side-channels and faults is a must for the deployment of embedded cryptography. A wide body of research has investigated solutions to secure implementations against these attacks at different abstraction levels. Yet, to a large extent, current solutions focus on one or the other threat. In this paper, we initiate a mode-level study of cryptographic primitives that can ensure security in a (new and practically-motivated) adversarial model combining leakage and faults. Our goal is to identify constructions that do not require a uniform protection of all their operations against both attack vectors. For this purpose, we first introduce a versatile and intuitive model to capture leakage and faults. We then show that a MAC from Asiacrypt 2021 natively enables a leveled implementation for fault resilience where only its underlying tweakable block cipher must be protected, if only the tag verification can be faulted. We finally describe two approaches to amplify security for fault resilience when also the tag generation can be faulted. One is based on iteration and requires the adversary to inject increasingly large faults to succeed. The other is based on randomness and allows provable security against differential faults.

Range proofs allow a sender to convince a verifier that committed integers belong to an interval without revealing anything else. So far, all known non-interactive range proofs in the standard model rely on groups endowed with a bilinear map. Moreover, they either require the group order to be larger than the range of any proven statement or they suffer from a wasteful rate. Recently (Eurocrypt'21), Couteau et al. introduced a new approach to efficiently prove range membership by encoding integers as a modular ratio between small integers. We show that their technique can be transposed in the standard model under the Composite Residuosity (DCR) assumption. Interestingly, with this modification, the size of ranges is not a priori restricted by the common reference string. It also gives a constant ratio between the size of ranges and proofs. Moreover, we show that their technique of encoding messages as bounded rationals provides a secure standard model instantiation of the Naor-Yung CCA2 encryption paradigm under the DCR assumption.

The standard model security of the Fiat-Shamir transform has been an active research area for many years. In breakthrough results, Canetti et al. (STOC’19) and Peikert-Shiehian (Crypto’19) showed that, under the Learning-With-Errors ( 𝖫𝖶𝖤_ ) assumption, it provides soundness by applying correlation-intractable (CI) hash functions to so-called trapdoor -protocols. In order to be compatible with CI hash functions based on standard 𝖫𝖶𝖤_ assumptions with polynomial approximation factors, all known such protocols have been obtained via parallel repetitions of a basic protocol with binary challenges. In this paper, we consider languages related to Paillier’s composite residuosity assumption ( 𝖣𝖢𝖱 ) for which we give the first trapdoor -protocols providing soundness in one shot, via exponentially large challenge spaces. This improvement is analogous to the one enabled by Schnorr over the original Fiat-Shamir protocol in the random oracle model. Using the correlation-intractable hash function paradigm, we then obtain simulation-sound NIZK arguments showing that an element of ℤ_N^2^* is a composite residue, which opens the door to space-efficient applications in the standard model. As a concrete example, we build logarithmic-size ring signatures (assuming a common reference string) with the shortest signature length among schemes based on standard assumptions in the standard model. We prove security under the 𝖣𝖢𝖱 and 𝖫𝖶𝖤_ assumptions, while keeping the signature size comparable with that of random-oracle-based schemes.

The verifiable encryption of bits is the main computational step that is needed to prepare ballots in many practical voting protocols. Its computational load can also be a practical bottleneck, preventing the deployment of some protocols or requiring the use of computing clusters. We investigate the question of producing many verifiably encrypted bits in an efficient and portable way, using as a baseline the protocol that is in use in essentially all modern voting systems and libraries supporting homomorphic voting, including ElectionGuard, a state-of-the-art open source voting SDK deployed in government elections. Combining fixed base exponentiation techniques and new encryption and ZK proof mechanisms, we obtain speed-ups by more than one order of magnitude against standard implementations. Our exploration requires balancing conflicting optimization strategies, and the use of asymptotically less efficient protocols that turn out to be very effective in practice. Several of our proposed improvements are now on the ElectionGuard roadmap.

This paper introduces and analyzes Triplex, a leakage-resistant mode of operation based on Tweakable Block Ciphers (TBCs) with 2n-bit tweaks. Triplex enjoys beyond-birthday ciphertext integrity in the presence of encryption and decryption leakage in a liberal model where all intermediate computations are leaked in full and only two TBC calls operating a long-term secret are protected with implementationlevel countermeasures. It provides beyond-birthday confidentiality guarantees without leakage, and standard confidentiality guarantees with leakage for a single-pass mode embedding a re-keying process for the bulk of its computations (i.e., birthday confidentiality with encryption leakage under a bounded leakage assumption). Triplex improves leakage-resistant modes of operation relying on TBCs with n-bit tweaks when instantiated with large-tweak TBCs like Deoxys-TBC (a CAESAR competition laureate) or Skinny (used by the Romulus finalist of the NIST lightweight crypto competition). Its security guarantees are maintained in the multi-user setting.