On the Security of the PKCS#1 v1.5 Signature Scheme

The RSA PKCS#1 v1.5 signature algorithm is the most widely used digital signature scheme in practice. Its two main strengths are its extreme simplicity, which makes it very easy to implement, and that verification of signatures is significantly faster than for DSA or ECDSA. Despite the huge practical importance of RSA PKCS#1 v1.5 signatures, providing formal evidence for their security based on plausible cryptographic hardness assumptions has turned out to be very difficult. Therefore the most recent version of PKCS#1 (RFC 8017) even recommends a replacement the more complex and less efficient scheme RSA-PSS, as it is provably secure and therefore considered more robust. The main obstacle is that RSA PKCS#1 v1.5 signatures use a deterministic padding scheme, which makes standard proof techniques not applicable. We introduce a new technique that enables the first security proof for RSA-PKCS#1 v1.5 signatures. We prove full existential unforgeability against adaptive chosen-message attacks (EUF-CMA) under the standard RSA assumption. Furthermore, we give a tight proof under the Phi-Hiding assumption. These proofs are in the random oracle model and the parameters deviate slightly from the standard use, because we require a larger output length of the hash function. However, we also show how RSA-PKCS#1 v1.5 signatures can be instantiated in practice such that our security proofs apply. In order to draw a more complete picture of the precise security of RSA PKCS#1 v1.5 signatures, we also give security proofs in the standard model, but with respect to weaker attacker models (key-only attacks) and based on known complexity assumptions. The main conclusion of our work is that from a provable security perspective RSA PKCS#1 v1.5 can be safely used, if the output length of the hash function is chosen appropriately

Ring Signature from Bonsai Tree: How to Preserve the Long-Term Anonymity

Signer-anonymity is the central feature of ring signatures, which enable a user to sign messages on behalf of an arbitrary set of users, called the ring, without revealing exactly which member of the ring actually generated the signature. Strong and long-term signer-anonymity is a reassuring guarantee for users who are hesitant to leak a secret, especially if the consequences of identification are dire in certain scenarios such as whistleblowing. The notion of \textit{unconditional anonymity}, which protects signer-anonymity even against an infinitely powerful adversary, is considered for ring signatures that aim to achieve long-term signer-anonymity. However, the existing lattice-based works that consider the unconditional anonymity notion did not strictly capture the security requirements imposed in practice, this leads to a realistic attack on signer-anonymity. In this paper, we present a realistic attack on the unconditional anonymity of ring signatures, and formalize the unconditional anonymity model to strictly capture it. We then propose a lattice-based ring signature construction with unconditional anonymity by leveraging bonsai tree mechanism. Finally, we prove the security in the standard model and demonstrate the unconditional anonymity through both theoretical proof and practical experiments

Toward RSA-OAEP without Random Oracles

We show new partial and full instantiation results under chosen-ciphertext security for the widely implemented and standardized RSA-OAEP encryption scheme of Bellare and Rogaway (EUROCRYPT 1994) and two variants. Prior work on such instantiations either showed negative results or settled for ``passive\u27\u27 security notions like IND-CPA. More precisely, recall that RSA-OAEP adds redundancy and randomness to a message before composing two rounds of an underlying Feistel transform, whose round functions are modeled as random oracles (ROs), with RSA. Our main results are: \begin{itemize} \item Either of the two oracles (while still modeling the other as a RO) can be instantiated in RSA-OAEP under IND-CCA2 using mild standard-model assumptions on the round functions and generalizations of algebraic properties of RSA shown by Barthe, Pointcheval, and Báguelin (CCS 2012). The algebraic properties are only shown to hold at practical parameters for small encryption exponent ($e=3$), but we argue they have value for larger $e$ as well. \item Both oracles can be instantiated simultaneously for two variants of RSA-OAEP, called ``$t$-clear\u27\u27 and ``$s$-clear\u27\u27 RSA-OAEP. For this we use extractability-style assumptions in the sense of Canetti and Dakdouk (TCC 2010) on the round functions, as well as novel yet plausible ``XOR-type\u27\u27 assumptions on RSA. While admittedly strong, such assumptions may nevertheless be necessary at this point to make positive progress. \end{itemize} In particular, our full instantiations evade impossibility results of Shoup (J.~Cryptology 2002), Kiltz and Pietrzak (EUROCRYPT 2009), and Bitansky et al. (STOC 2014). Moreover, our results for $s$-clear RSA-OAEP yield the most efficient RSA-based encryption scheme proven IND-CCA2 in the standard model (using bold assumptions on cryptographic hashing) to date

On the Security of RSA-PSS in the Wild

The RSA Probabilistic Signature Scheme (RSA-PSS) due to Bellare and Rogaway (EUROCRYPT 1996) is a widely deployed signature scheme. In particular it is a suggested replacement for the deterministic RSA Full Domain Hash (RSA-FDH) by Bellare and Rogaway (ACM CCS 1993) and PKCS#1 v1.5 (RFC 2313), as it can provide stronger security guarantees. It has since been shown by Kakvi and Kiltz (EUROCRYPT 2012, Journal of Cryptology 2018) that RSA-FDH provides similar security to that of RSA-PSS, also in the case when RSA-PSS is not randomized. Recently, Jager, Kakvi and May (ACM CCS 2018) showed that PKCS#1 v1.5 provides comparable security to both RSA-FDH and RSA-PSS. However, all these proofs consider each signature scheme in isolation, where in practice this is not the case. The most interesting case is that in TLS 1.3, PKCS#1 v1.5 signatures are still included for reasons of backwards compatibility, meaning both RSA-PSS and PKCS#1 v1.5 signatures are implemented. To save space, the key material is shared between the two schemes, which means the aforementioned security proofs no longer apply. We investigate the security of this joint usage of key material in the context of Sibling Signatures, which were introduced by Camenisch, Drijvers, and Dubovitskaya (ACM CCS 2017). It must be noted that we consider the standardised version of RSA-PSS (IEEE Standard P1363-2000), which deviates from the original scheme considered in all previous papers. We are able to show that this joint usage is indeed secure, and achieves a security level that closely matches that of PKCS#1 v1.5 signatures and that both schemes can be safely used, if the output lengths of the hash functions are chosen appropriately

A Note on the Instantiability of the Quantum Random Oracle

In a highly influential paper from fifteen years ago, Canetti, Goldreich, and Halevi showed a fundamental separation between the Random Oracle Model (ROM) and the Standard Model. They constructed a signature scheme which can be shown to be secure in the ROM, but is insecure when instantiated with any hash function (and thus insecure in the standard model). In 2011, Boneh et al. defined the notion of the Quantum Random Oracle Model (QROM), where queries to the random oracle may be made in quantum superposition. Because the QROM generalizes the ROM, a proof of security in the QROM is stronger than one in the ROM. This leaves open the possibility that security in the QROM could imply security in the standard model. In this work, we show that this is not the case, and that security in the QROM cannot imply standard model security. We do this by showing that the original schemes that show a separation between the standard model and the ROM are also secure in the QROM. We consider two schemes that establish such a separation, one with length-restricted messages, and one without, and show both to be secure in the QROM. Our results give further understanding to the landscape of proofs in the ROM versus the QROM or standard model, and point towards the QROM and ROM being much closer to each other than either is to standard model security

On the Real-World Instantiability of Admissible Hash Functions and Efficient Verifiable Random Functions

Verifiable random functions (VRFs) are essentially digital signatures with additional properties, namely verifiable uniqueness and pseudorandomness, which make VRFs a useful tool, e.g., to prevent enumeration in DNSSEC Authenticated Denial of Existence and the CONIKS key management system, or in the random committee selection of the Algorand blockchain. Most standard-model VRFs rely on admissible hash functions (AHFs) to achieve security against adaptive attacks in the standard model. Known AHF constructions are based on error-correcting codes, which yield asymptotically efficient constructions. However, previous works do not clarify how the code should be instantiated concretely in the real world. The rate and the minimal distance of the selected code have significant impact on the efficiency of the resulting cryptosystem, therefore it is unclear if and how the aforementioned constructions can be used in practice. First, we explain inherent limitations of code-based AHFs. Concretely, we show that even if we were given codes that achieve the well-known Gilbert-Varshamov or McEliece-Rodemich-Rumsey-Welch bounds, existing AHF-based constructions of VRFs can only be instantiated quite inefficiently. Then we introduce and construct computational AHFs (cAHFs). While classical AHFs are information-theoretic, and therefore work even in presence of computationally unbounded adversaries, cAHFs provide only security against computationally bounded adversaries. However, we show that cAHFs can be instantiated significantly more efficiently. Finally, we present a new VRF scheme using cAHFs and show that it is currently the most efficient verifiable random function with full adaptive security in the standard model

Stronger Security and Generic Constructions for Adaptor Signatures

Adaptor signatures have seen wide applications in layer-2 and peer-to-peer blockchain ap- plications such as atomic swaps and payment channels. We first identify two shortcomings of previous literature on adaptor signatures. (1) Current aim of “script-less” adaptor signatures restricts instantiability, limiting designs based on BLS or current NIST PQC candidates. (2) We identify gaps in current formulations of security. In particular, we show that current notions do not rule out a class of insecure schemes. Moreover, a natural property concerning the on-chain unlinkability of adaptor signatures has not been formalized. We then address these shortcomings by providing new and stronger security notions, as well as new generic constructions from any signature scheme and hard relation. On definitions: 1. We develop security notions that strictly imply previous notions. 2. We formalize the notion of unlinkability for adaptor signatures. 3. We give modular proof frameworks that facilitate simpler proofs. On constructions: 1. We give a generic construction of adaptor signature from any signature scheme and any hard relation, showing that theoretically, (linkable) adaptor signatures can be constructed from any one-way function. 2. We also give an unlinkable adaptor signature construction from any signature scheme and any strongly random-self reducible relation, which we show instantiations of using DL, RSA, and LWE

New Design and Analysis Techniques for Post-Quantum Cryptography

Due to the threat of scalable quantum computation breaking existing public-key cryptography, interest in post-quantum cryptography has exploded in the past decade. There are two key aspects to the mitigation of the quantum threat. The first is to have a complete understanding of the capabilities of a quantum enabled adversary and be able to predict the impact on the security of protocols. The second is to find suitable replacements for those protocols rendered insecure. In this thesis, we develop new techniques to help address these problems, in order to better prepare for the post-quantum era. Proofs in security models that consider quantum adversaries are notoriously more challenging compared to their classical analogues. The quantum random oracle model abstracts real world hash functions to a black box, but allows for superposition queries. This model is important as it often makes possible the reduction of the security of a protocol to the hardness of an underlying hard problem. We prove several results about the model itself. We provide upper and lower bounds on the ability of the adversary to find collisions in non-uniform functions in this model. We also compare the quantum random oracle model to the classical random oracle model and establish that a key aspect of their relationship to the standard model is unchanged. As well, we develop a way to model a new security property (dubbed quantum annoyingness) that considers the security of classical password-authenticated key exchange schemes in the presence of quantum adversaries, and prove the security of a recently standardized protocol in this model. For the second problem, we show how established post-quantum problems can be used to build protocols beyond key establishment and signing. We look at two protocols, that of key-blinded signatures and updatable public-key encryption, which are variants of signature and key-establishment protocols. We show how these protocols can be instantiated by modifying existing post-quantum signature and key-establishment protocols. Both of these protocols were originally built heavily relying on the structure of the discrete logarithm problem. In instantiating the schemes with post-quantum assumptions, we also highlight how alternative mathematical structures can be adapted to achieve the same results. Finally, we provide proofs, implementations, and performance metrics for these instantiations

Optimal Security Proofs for Signatures from Identification Schemes

We perform a concrete security treatment of digital signature schemes obtained from canonical identification schemes via the Fiat-Shamir transform. If the identification scheme is rerandomizable and satisfies the weakest possible security notion (key-recoverability), then the implied signature scheme is unforgeability against chosen-message attacks in the multi-user setting in the random oracle model. The reduction loses a factor of roughly Qh, the number of hash queries. Previous security reductions incorporated an additional multiplicative loss of N, the number of users in the system. As an important application of our framework, we obtain a concrete security treatment for Schnorr signatures. Our analysis is done in small steps via intermediate security notions, and all our implications have relatively simple proofs. Furthermore, for each step we show the optimality of the given reduction via a meta-reduction