New attacks on PKCS#1 v1.5 encryption

Abstract. This paper introduces two new attacks on pkcs#1 v1.5, an rsa-based encryption standard proposed by RSA Laboratories. As opposed to Bleichenbacher's attack, our attacks are chosen-plaintext only, i.e. they do not make use of a decryption oracle. The first attack applies to small public exponents and shows that a plaintext ending by sufficiently many zeroes can be recovered efficiently when two or more ciphertexts corresponding to the same plaintext are available. We believe the technique we employ to be of independent interest, as it extends Coppersmith's low-exponent attack to certain length parameters. Our second attack is applicable to arbitrary public exponents, provided that most message bits are zeroes. It seems to constitute the first chosen-plaintext attack on an rsa-based encryption standard that yields to practical results for any public exponent

On The Broadcast and Validity-Checking Security of PKCS #1 v1.5 Encryption

(article recompensé par le "Best Student Paper Award")International audienceThis paper describes new attacks on PKCS #1 v1.5, a deprecated but still widely used RSA encryption standard. The first cryptanalysis is a broadcast attack, allowing the opponent to reveal an identical plaintext sent to different recipients. This is nontrivial because different randomizers are used for different encryptions (in other words, plaintexts coincide only partially). The second attack predicts, using a single query to a validity checking oracle, which of two chosen plaintexts corresponds to a challenge ciphertext. The attack's success odds are very high. The two new attacks rely on different mathematical tools and underline the need to accelerate the phase out of PKCS #1 v1.5

Stacco: Differentially Analyzing Side-Channel Traces for Detecting SSL/TLS Vulnerabilities in Secure Enclaves

Intel Software Guard Extension (SGX) offers software applications enclave to protect their confidentiality and integrity from malicious operating systems. The SSL/TLS protocol, which is the de facto standard for protecting transport-layer network communications, has been broadly deployed for a secure communication channel. However, in this paper, we show that the marriage between SGX and SSL may not be smooth sailing. Particularly, we consider a category of side-channel attacks against SSL/TLS implementations in secure enclaves, which we call the control-flow inference attacks. In these attacks, the malicious operating system kernel may perform a powerful man-in-the-kernel attack to collect execution traces of the enclave programs at page, cacheline, or branch level, while positioning itself in the middle of the two communicating parties. At the center of our work is a differential analysis framework, dubbed Stacco, to dynamically analyze the SSL/TLS implementations and detect vulnerabilities that can be exploited as decryption oracles. Surprisingly, we found exploitable vulnerabilities in the latest versions of all the SSL/TLS libraries we have examined. To validate the detected vulnerabilities, we developed a man-in-the-kernel adversary to demonstrate Bleichenbacher attacks against the latest OpenSSL library running in the SGX enclave (with the help of Graphene) and completely broke the PreMasterSecret encrypted by a 4096-bit RSA public key with only 57286 queries. We also conducted CBC padding oracle attacks against the latest GnuTLS running in Graphene-SGX and an open-source SGX-implementation of mbedTLS (i.e., mbedTLS-SGX) that runs directly inside the enclave, and showed that it only needs 48388 and 25717 queries, respectively, to break one block of AES ciphertext. Empirical evaluation suggests these man-in-the-kernel attacks can be completed within 1 or 2 hours.Comment: CCS 17, October 30-November 3, 2017, Dallas, TX, US

Statistical Properties of Short RSA Distribution and Their Cryptographic Applications

International audienceIn this paper, we study some computational security assump-tions involve in two cryptographic applications related to the RSA cryp-tosystem. To this end, we use exponential sums to bound the statistical distances between these distributions and the uniform distribution. We are interesting studying the k least (or most) significant bits of x e mod N , where N is a RSA modulus when x is restricted to a small part of [0, N). First of all, we provide the first rigorous evidence that the cryptographic pseudo-random generator proposed by Micali and Schnorr is based on firm foundations. This proof is missing in the original paper and do not cover the parameters chosen by the authors. Consequently, we extend the proof to get a new result closer to the parameters using a recent work of Wooley on exponential sums and we show some limitations of our technique. Finally, we look at the semantic security of the RSA padding scheme called PKCS#1 v1.5 which is still used a lot in practice. We show that parts of the ciphertexts are indistinguisable from uniform bitstrings

Weakened Random Oracle Models with Target Prefix

Weakened random oracle models (WROMs) are variants of the random oracle model (ROM). The WROMs have the random oracle and the additional oracle which breaks some property of a hash function. Analyzing the security of cryptographic schemes in WROMs, we can specify the property of a hash function on which the security of cryptographic schemes depends. Liskov (SAC 2006) proposed WROMs and later Numayama et al. (PKC 2008) formalized them as CT-ROM, SPT-ROM, and FPT-ROM. In each model, there is the additional oracle to break collision resistance, second preimage resistance, preimage resistance respectively. Tan and Wong (ACISP 2012) proposed the generalized FPT-ROM (GFPT-ROM) which intended to capture the chosen prefix collision attack suggested by Stevens et al. (EUROCRYPT 2007). In this paper, in order to analyze the security of cryptographic schemes more precisely, we formalize GFPT-ROM and propose additional three WROMs which capture the chosen prefix collision attack and its variants. In particular, we focus on signature schemes such as RSA-FDH, its variants, and DSA, in order to understand essential roles of WROMs in their security proofs

Practical Padding Oracle Attacks on RSA

We revise attacks on the RSA cipher based on side-channels that leak partial information about the plaintext. We show how to compute a plaintext when only its parity is leaked. We then describe PKCS#1 v1.5 padding for RSA and we show that the simple leakage of padding errors is enough to recover the whole plaintext, even when it is unpadded or padded under another scheme. This vulnerability is well-known since 1998 but the flawed PKCS#1 v1.5 padding is still broadly in use. We discuss recent optimizations of this padding oracle attack that make it effective on commercially available cryptographic devices

Unpicking PLAID: a cryptographic analysis of an ISO-standards-track authentication protocol

The Protocol for Lightweight Authentication of Identity (PLAID) aims at secure and private authentication between a smart card and a terminal. Originally developed by a unit of the Australian Department of Human Services for physical and logical access control, PLAID has now been standardized as an Australian standard AS-5185-2010 and is currently in the fast track standardization process for ISO/IEC 25182-1.2. We present a cryptographic evaluation of PLAID. As well as reporting a number of undesirable cryptographic features of the protocol, we show that the privacy properties of PLAID are significantly weaker than claimed: using a variety of techniques we can fingerprint and then later identify cards. These techniques involve a novel application of standard statistical and data analysi

Everlasting ROBOT: the Marvin Attack

In this paper we show that Bleichenbacher-style attacks on RSA decryption are not only still possible, but also that vulnerable implementations are common. We have successfully attacked multiple implementations using only timing of decryption operation and shown that many others are vulnerable. To perform the attack we used more statistically rigorous techniques like the sign test, Wilcoxon signed-rank test, and bootstrapping of median of pairwise differences. We publish a set of tools for testing libraries that perform RSA decryption against timing side-channel attacks, including one that can test arbitrary TLS servers with no need to write a test harnesses. Finally, we propose a set of workarounds that implementations can employ if they can\u27t avoid the use of RSA

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

Efficient Padding Oracle Attacks on Cryptographic Hardware

We show how to exploit the encrypted key import functions of a variety of different cryptographic devices to reveal the imported key. The attacks are padding oracle attacks, where error messages resulting from incorrectly padded plaintexts are used as a side channel. In the asymmetric encryption case, we modify and improve Bleichenbacher’s attack on RSA PKCS#1v1.5 padding, giving new cryptanalysis that allows us to carry out the ‘million message attack’ in a mean of 49 000 and median of 14 500 oracle calls in the case of cracking an unknown valid ciphertext under a 1024 bit key (the original algorithm takes a mean of 215 000 and a median of 163 000 in the same case). We show how implementation details of certain devices admit an attack that requires only 9 400 operations on average (3 800 median). For the symmetric case, we adapt Vaudenay’s CBC attack, which is already highly efficient. We demonstrate the vulnerabilities on a number of commercially available cryptographic devices, including security tokens, smartcards and the Estonian electronic ID card. The attacks are efficient enough to be practical: we give timing details for all the devices found to be vulnerable, showing how our optimisations make a qualitative difference to the practicality of the attack. We give mathematical analysis of the effectiveness of the attacks, extensive empirical results, and a discussion of countermeasures and manufacturer reaction