Related Randomness Attacks for Public Key Encryption

Abstract. Several recent and high-profile incidents give cause to believe that randomness failures of various kinds are endemic in deployed cryptographic systems. In the face of this, it behoves cryptographic researchers to develop methods to immunise – to the extent that it is possible – cryptographic schemes against such failures. This paper considers the practically-motivated situation where an adversary is able to force a public key encryption scheme to reuse random values, and functions of those values, in encryption computations involving adversarially chosen public keys and messages. It presents a security model appropriate to this situation, along with variants of this model. It also provides necessary conditions on the set of functions used in order to attain this security notation, and demonstrates that these conditions are also sufficient in the Random Oracle Model. Further standard model constructions achieving weaker security notions are also given, with these constructions having interesting connections to other primitives including: pseudo-random functions that are secure in the related key attack setting; Correlated Input Secure hash functions; and public key encryption schemes that are secure in the auxiliary input setting (this being a special type of leakage resilience)

Related Randomness Security for Public Key Encryption, Revisited

Motivated by the history of randomness failures in practical systems, Paterson, Schuldt, and Sibborn (PKC 2014) introduced the notion of related randomness security for public key encryption. In this paper, we firstly show an inherent limitation of this notion: if the family of related randomness functions is sufficiently rich to express the encryption function of the considered scheme, then security cannot be achieved. This suggests that achieving security for function families capable of expressing more complex operations, such as those used in random number generation, might be difficult. The current constructions of related randomness secure encryption in the standard model furthermore reflect this; full security is only achieved for function families with a convenient algebraic structure. We additionally revisit the seemingly optimal random oracle model construction by Paterson et al. and highlight its limitations. To overcome this difficulty, we propose a new notion which we denote related refreshable randomness security. This notion captures a scenario in which an adversary has limited time to attack a system before new entropy is added. More specifically, the number of encryption queries with related randomness the adversary can make before the randomness is refreshed, is bounded, but the adversary is allowed to make an unbounded total number of queries. Furthermore, the adversary is allowed to influence how entropy is added to the system. In this setting, we construct an encryption scheme which remains secure in the standard model for arbitrary function families of size $2^p$ (where $p$ is polynomial in the security parameter) that satisfy certain collision-resistant and output-unpredictability properties. This captures a rich class of functions, which includes, as a special case, circuits of polynomial size. Our scheme makes use of a new construction of a (bounded) related-key attack secure pseudorandom function, which in turn is based on a new flavor of the leftover hash lemma. These technical results might be of independent interest

An Efficient Convertible Undeniable Signature Scheme with Delegatable Verification

Undeniable signatures, introduced by Chaum and van Antwerpen, require a verifier to interact with the signer to verify a signature, and hence allow the signer to control the verifiability of his signatures. Convertible undeniable signatures, introduced by Boyar, Chaum, Damg\aa{}rd, and Pedersen, furthermore allow the signer to convert signatures to publicly verifiable ones by publicizing a verification token, either for individual signatures or for all signatures universally. In addition, the signer is able to delegate the ability to prove validity and convert signatures to a semi-trusted third party by providing a verification key. While the latter functionality is implemented by the early convertible undeniable signature schemes, most recent schemes do not consider this despite its practical appeal. In this paper we present an updated definition and security model for schemes allowing delegation, and highlight a new essential security property, token soundness, which is not formally treated in the previous security models for convertible undeniable signatures. We then propose a new convertible undeniable signature scheme. The scheme allows delegation of verification and is provably secure in the standard model assuming the computational co-Diffie-Hellman problem, a closely related problem, and the decisional linear problem are hard. Our scheme is, to the best of our knowledge, the currently most efficient convertible undeniable signature scheme which provably fulfills all security requirements in the standard model

Statistical Attacks on Cookie Masking for RC4

Levillain et al. (AsiaCCS 2015) proposed two cookie masking methods, TLS Scramble and MCookies, to counter a class of attacks on SSL/TLS in which the attacker is able to exploit its ability to obtain many encryptions of a target HTTP cookie. In particular, the masking methods potentially make it viable to continue to use the RC4 algorithm in SSL/TLS. In this paper, we provide a detailed analysis of TLS Scramble and MCookies when used in conjunction with RC4 in SSL/TLS. We show that, in fact, both are vulnerable to variants of the known attacks against RC4 in SSL/TLS exploiting the Mantin biases (Mantin, EUROCRYPT 2005): * For the TLS Scramble mechanism, we provide a detailed statistical analysis coupled with extensive simulations that show that about $2^{37}$ encryptions of the cookie are sufficient to enable its recovery. * For the MCookies mechanism, our analysis is made more complex by the presence of a Base64 encoding step in the mechanism, which (unintentionally) acts like a classical block cipher S-box in the masking process. Despite this, we are able to develop a maximum likelihood analysis which provides a rigorous statistical procedure for estimating the unknown cookie. Based on simulations, we estimate that $2^{45}$ encryptions of the cookie are sufficient to enable its recovery. Taken together, our analyses show that the cookie masking mechanisms as proposed by Levillain et al. only moderately increase the security of RC4 in SSL/TLS

Spritz---a spongy RC4-like stream cipher and hash function.

This paper reconsiders the design of the stream cipher RC4, and proposes an improved variant, which we call ``Spritz\u27\u27 (since the output comes in fine drops rather than big blocks.) Our work leverages the considerable cryptanalytic work done on the original RC4 and its proposed variants. It also uses simulations extensively to search for biases and to guide the selection of intermediate expressions. We estimate that Spritz can produce output with about 24 cycles/byte of computation. Furthermore, our statistical tests suggest that about $2^{81}$ bytes of output are needed before one can reasonably distinguish Spritz output from random output; this is a marked improvement over RC4. [Footnote: However, see Appendix F for references to more recent work that suggest that our estimates of the work required to break Spritz may be optimistic.] In addition, we formulate Spritz as a ``sponge (or sponge-like) function,\u27\u27 (see Bertoni et al.), which can ``Absorb\u27\u27 new data at any time, and from which one can ``Squeeze\u27\u27 pseudorandom output sequences of arbitrary length. Spritz can thus be easily adapted for use as a cryptographic hash function, an encryption algorithm, or a message-authentication code generator. (However, in hash-function mode, Spritz is rather slow.

Forward-Secure Public Key Encryption without Key Update from Proof-of-Stake Blockchain

A forward-secure public-key encryption (PKE) scheme prevents eavesdroppers from decrypting past ciphertexts in order to mitigate the damage caused by a potential secret key compromise. In prior works, forward security in a non-interactive setting, such as forward-secure PKE, is achieved by constantly updating (secret) keys. In this paper, we formalize the notion of blockchain-based forward-secure PKE and show the feasibility of constructing a forward-secure PKE scheme without key update (i.e. both the public key and the secret key are immutable), assuming the existence of a proof-of-stake blockchain with the distinguishable forking property introduced by Goyal, et al. (TCC 2017). Our construction uses the proof-of-stake blockchain as an immutable decryption log and witness encryption by Garg, et al. (STOC 2013) to ensure that the same ciphertext cannot be decrypted twice, thereby rendering a compromised secret key useless with respect to decryption of past ciphertext the legitimate user has already decrypted

Plaintext Recovery Attacks Against WPA/TKIP

We conduct an analysis of the RC4 algorithm as it is used in the IEEE WPA/TKIP wireless standard. In that standard, RC4 keys are computed on a per-frame basis, with specific key bytes being set to known values that depend on 2 bytes of the WPA frame counter (called the TSC). We observe very large, TSC-dependent biases in the RC4 keystream when the algorithm is keyed according to the WPA specification. These biases permit us to mount an effective statistical, plaintext-recovering attack in the situation where the same plaintext is encrypted in many different frames (the so-called ``broadcast attack\u27\u27 setting). We assess the practical impact of these attacks on WPA/TKIP

On the Security of the Schnorr Signature Scheme and DSA against Related-Key Attacks

In the ordinary security model for signature schemes, we consider an adversary that may forge a signature on a new message using only his knowledge of other valid message and signature pairs. To take into account side channel attacks such as tampering or fault-injection attacks, Bellare and Kohno (Eurocrypt 2003) formalized related-key attacks (RKA), where stronger adversaries are considered. In RKA for signature schemes, the adversary can also manipulate the signing key and obtain signatures for the modified key. This paper considers RKA security of two established signature schemes: the Schnorr signature scheme and (a well-known variant of) DSA. First, we show that these signature schemes are secure against a weak notion of RKA. Second, we demonstrate that, on the other hand, neither the Schnorr signature scheme nor DSA achieves the standard notion of RKA security, by showing concrete attacks on these. Lastly, we show that a slight modification of both the Schnorr signature scheme and (the considered variant of) DSA yields fully RKA secure schemes

Two-Dimensional Dynamic Fusion for Continuous Authentication

Continuous authentication has been widely studied to provide high security and usability for mobile devices by continuously monitoring and authenticating users. Recent studies adopt multibiometric fusion for continuous authentication to provide high accuracy even when some of captured biometric data are of a low quality. However, existing continuous fusion approaches are resource-heavy as they rely on all classifiers being activated all the time and may not be suitable for mobile devices. In this paper, we propose a new approach to multibiometric continuous authentication: two-dimensional dynamic fusion. Our key insight is that multibiometric continuous authentication calculates two-dimensional matching scores over classifiers and over time. Based on this, we dynamically select a set of classifiers based on the context in which authentication is taking place, and fuse matching scores by multi-classifier fusion and multi-sample fusion. Through experimental evaluation, we show that our approach provides a better balance between resource usage and accuracy than the existing fusion methods. In particular, we show that our approach provides higher accuracy than the existing methods with the same number of score calculations by adopting multi-sample fusion.Comment: Accepted to IJCB'2

Adam in Private: Secure and Fast Training of Deep Neural Networks with Adaptive Moment Estimation

Machine Learning (ML) algorithms, especially deep neural networks (DNN), have proven themselves to be extremely useful tools for data analysis, and are increasingly being deployed in systems operating on sensitive data, such as recommendation systems, banking fraud detection, and healthcare systems. This underscores the need for privacy-preserving ML (PPML) systems, and has inspired a line of research into how such systems can be constructed efficiently. We contribute to this line of research by proposing a framework that allows efficient and secure evaluation of full-fledged state-of-the-art ML algorithms via secure multi-party computation (MPC). This is in contrast to most prior works on PPML, which require advanced ML algorithms to be substituted with approximated variants that are ``MPC-friendly\u27\u27, before MPC techniques are applied to obtain a PPML algorithm. A drawback of the latter approach is that it requires careful fine-tuning of the combined ML and MPC algorithms, and might lead to less efficient algorithms or inferior quality ML (such as lower prediction accuracy). This is an issue for secure training of DNNs in particular, as this involves several arithmetic algorithms that are thought to be ``MPC-unfriendly\u27\u27, namely, integer division, exponentiation, inversion, and square root extraction. In this work, we propose secure and efficient protocols for the above seemingly MPC-unfriendly computations (but which are essential to DNN). Our protocols are three-party protocols in the honest-majority setting, and we propose both passively secure and actively secure with abort variants. A notable feature of our protocols is that they simultaneously provide high accuracy and efficiency. This framework enables us to efficiently and securely compute modern ML algorithms such as Adam (Adaptive moment estimation) and the softmax function ``as is\u27\u27, without resorting to approximations. As a result, we obtain secure DNN training that outperforms state-of-the-art three-party systems; our \textit{full} training is up to $6.7$ times faster than just the \textit{online} phase of the recently proposed FALCON (Wagh et al. at PETS\u2721) on the standard benchmark network for secure training of DNNs. To further demonstrate the scalability of our protocols, we perform measurements on real-world DNNs, AlexNet and VGG16, which are complex networks containing millions of parameters. The performance of our framework for these networks is up to a factor of about $12\sim 14$ faster for AlexNet and $46\sim 48$ faster for VGG16 to achieve an accuracy of $70\%$ and $75\%$, respectively, when compared to FALCON