This work describes an existential signature forgery vulnerability of the current CMS and PKCS#7 signature standards. The vulnerability results from an ambiguity of how to process the signed message in the signature verification process. Specifically, the absence or presence of the so called SignedAttributes field determines whether the signature message digest receives as input the message directly or the SignedAttributes, a DER-encoded structure which contains a digest of the message. If...

Cryptographic libraries have become an integral part of every digital device. Studies have shown that these systems are not only vulnerable due to bugs in cryptographic libraries, but also due to misuse of these libraries. In this paper, we focus on vulnerabilities introduced by the application developer. We performed a survey on the potential misusage of well-known libraries such as PKCS #11. We introduced a generic tool CRYScanner, to identify such misuses during and post-development. It...

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...

Being the most widely used and comprehensive standard for hardware security modules, cryptographic tokens and smart cards, PKCS#11 has been the subject of academic study for years. PKCS#11 provides a key store that is separate from the application, so that, ideally, an application never sees a key in the clear. Again and again, researchers have pointed out the need for an import/export mechanism that ensures the integrity of the permissions associated to a key. With version 2.40, for the...

At CRYPTO’98, Bleichenbacher published his seminal paper which described a padding oracle attack against RSA implementations that follow the PKCS #1 v1.5 standard. Over the last twenty years researchers and implementors had spent a huge amount of effort in developing and deploying numerous mitigation techniques which were supposed to plug all the possible sources of Bleichenbacher-like leakages. However, as we show in this paper most implementations are still vulnerable to several novel...

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...

PBKDF2 [27] is a well-known password-based key derivation function. In order to slow attackers down, PBKDF2 introduces CPU-intensive operations based on an iterated pseudorandom function (in our case HMAC-SHA-1). If we are able to speed up a SHA-1 or an HMAC implementation, we are able to speed up PBKDF2-HMAC-SHA-1. This means that a performance improvement might be exploited by regular users and attackers. Interestingly, FIPS 198-1 [31] suggests that it is possible to precompute first...

Many web hosts are still vulnerable to one of the oldest attacks against RSA in TLS. We show that Bleichenbacher’s RSA vulnerability from 1998 is still very prevalent in the Internet and affects almost a third of the top 100 domains in the Alexa Top 1 Million list, among them Facebook and Paypal. We identified vulnerable products from at least eight different vendors and open source projects, among them F5, Citrix, Radware, Cisco, Erlang, Bouncy Castle, and WolfSSL. Further we have...

Cryptographic APIs like PKCS#11 are interfaces to trusted hardware where keys are stored; the secret keys should never leave the trusted hardware in plaintext. In PKCS#11 it is possible to give keys conflicting roles, leading to a number of key-recovery attacks. To prevent these attacks, one can authenticate the attributes of keys when wrapping, but this is not standard in PKCS#11. Alternatively, one can configure PKCS#11 to place additional restrictions on the commands permitted by the...

We present an analysis of key wrapping APIs with generic policies. We prove that certain minimal conditions on policies are sufficient for keys to be indistinguishable from random in any execution of an API. Our result captures a large class of API policies, including both the hierarchies on keys that are common in the scientific literature and the non-linear dependencies on keys used in PKCS#11. Indeed, we use our result to propose a secure refinement of PKCS#11, assuming that the...

Solving a system of multivariate quadratic equations (MQ) is an NP-complete problem whose complexity estimates are relevant to many cryptographic scenarios. In some cases it is required in the best known attack; sometimes it is a generic attack (such as for the multivariate PKCs), and sometimes it determines a provable level of security (such as for the QUAD stream ciphers). Under reasonable assumptions, the best way to solve generic MQ systems is the XL algorithm implemented with a sparse...

Password-based key derivation functions are of particular interest in cryptography because they (a) input a password/passphrase (which usually is short and lacks enough entropy) and derive a cryptographic key; (b) slow down brute force and dictionary attacks as much as possible. In PKCS#5 [17], RSA Laboratories described a password based key derivation function called PBKDF2 that has been widely adopted in many security related applications [6, 7, 11]. In order to slow down brute force...

This paper focuses on a surprising class of cryptanalysis results for symmetric-key primitives: when the number of rounds of the primitive is increased, the complexity of the cryptanalysis result decreases. Our primary target will be primitives that consist of identical round functions, such as PBKDF1, the Unix password hashing algorithm, and the Chaskey MAC function. However, some of our results also apply to constructions with non-identical rounds, such as the PRIDE block cipher. First, we...

PKCS\#11 is a very popular cryptographic API: it is the standard used by many Hardware Security Modules, smartcards and software cryptographic tokens. Several attacks have been uncovered against PKCS\#11 at different levels: intrinsic logical flaws, cryptographic vulnerabilities or severe compliance issues. Since affected hardware remains widespread in computer infrastructures, we propose a user-centric and pragmatic approach for secure usage of vulnerable devices. We introduce \textit{Caml...

We provide new bounds on how close to regular the map x |--> x^e is on arithmetic progressions in Z_N, assuming e | Phi(N) and N is composite. We use these bounds to analyze the security of natural cryptographic problems related to RSA, based on the well-studied Phi-Hiding assumption. For example, under this assumption, we show that RSA PKCS #1 v1.5 is secure against chosen-plaintext attacks for messages of length roughly (log N)/4 bits, whereas the previous analysis, due to Lewko et al...

The TLS Internet Standard features a mixed bag of cryptographic algorithms and constructions, letting clients and servers negotiate their use for each run of the handshake. Although many ciphersuites are now well-understood in isolation, their composition remains problematic, and yet it is critical to obtain practical security guarantees for TLS. We experimentally confirm that all mainstream implementations of TLS share key materials between different algorithms, some of them of dubious...

TLS is one of the most widely deployed cryptographic protocols on the Internet; it is used to protect the confidentiality and integrity of transmitted data in various client-server protocols. Its non-standard use of cryptographic primitives, however, makes it hard to formally assess its security. It is in fact difficult to use traditional (well-understood) security notions for the key-exchange (here: handshake) and the encryption/authentication (here: record layer) parts of the protocol due...

At Eurocrypt 2013, Joye and Libert proposed a method for constructing public key cryptosystems (PKCs) and lossy trapdoor functions (LTDFs) from $(2^\alpha)^{th}$-power residue symbols. Their work can be viewed as non-trivial extensions of the well-known PKC scheme due to Goldwasser and Micali, and the LTDF scheme due to Freeman et al., respectively. In this paper, we will demonstrate that this kind of work can be extended \emph{more generally}: all related constructions can work for any...

At Eurocrypt 2013, Joye and Libert proposed a method for constructing public key cryptosystems (PKCs) and lossy trapdoor functions (LTDFs) from $(2^\alpha)^{th}$-power residue symbols. Their work can be viewed as non-trivial extensions of the well-known PKC scheme due to Goldwasser and Micali, and the LTDF scheme due to Freeman et al., respectively. In this paper, we will demonstrate that this kind of work can be extended \emph{more generally}: all related constructions can work for any...

TLS is the most widely-used cryptographic protocol on the Internet. It comprises the TLS Handshake Protocol, responsible for authentication and key establishment, and the TLS Record Protocol, which takes care of subsequent use of those keys to protect bulk data. TLS has proved remarkably stubborn to analysis using the tools of modern cryptography. This is due in part to its complexity and its flexibility. In this paper, we present the most complete analysis to date of the TLS Handshake...

We present a computer-aided framework for proving concrete security bounds for cryptographic machine code implementations. The front-end of the framework is an interactive verification tool that extends the EasyCrypt framework to reason about relational properties of C-like programs extended with idealised probabilistic operations in the style of code-based security proofs. The framework also incorporates an extension of the CompCert certified compiler to support trusted libraries providing...

In the past few years, cryptographic key management APIs have been shown to be subject to tricky attacks based on the improper use of cryptographic keys. In fact, real APIs provide mechanisms to declare the intended use of keys but they are not strong enough to provide key security. In this paper, we propose a simple imperative programming language for specifying strongly-typed APIs for the management of symmetric, asymmetric and signing keys. The language requires that type information is...

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...

This paper develops a theory of multi-instance (mi) security and applies it to provide the first proof-based support for the classical practice of salting in password-based cryptography. Mi-security comes into play in settings (like password-based cryptography) where it is computationally feasible to compromise a single instance, and provides a second line of defense, aiming to ensure (in the case of passwords, via salting) that the effort to compromise all of some large number $m$ of...

We show that the widely deployed RSA-OAEP encryption scheme of Bellare and Rogaway (Eurocrypt 1994), which combines RSA with two rounds of an underlying Feistel network whose hash ({\em i.e.}, round) functions are modeled as random oracles, meets indistinguishability under chosen-plaintext attack (IND-CPA) in the {\em standard model} based on simple, non-interactive, and non-interdependent assumptions on RSA and the hash functions. To prove this, we first give a result on a more general...

Group signature allows a group member to sign messages anonymously on the behalf of a group. In the case of a dispute, the designated group manager can open the signature to reveal the identity of its originator. As far as we know, most of the group signatures are based on traditional cryptography, such as RSA and discrete logarithm. Unfortunately these schemes would be broken if quantum computers emerge. The $\mathcal{MQ}$-problem based Multivariate Public-Key Cryptosystem (MPKC) is an...

This 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...

Since the Merkle-Damgård (MD) type hash functions are differentiable from ROs even when compression functions are modeled by ideal primitives, there is no guarantee as to the security of cryptosystems when ROs are instantiated with structural hash functions. In this paper, we study the security of the instantiated cryptosystems whereas the hash functions have the well known structure of Merkle-Damgård construction with Stam's type-II compression function (denoted MD-TypeII) in the Ideal...

We show that Multivariate Public Key Cryptosystems (MPKCs) over fields of small odd prime characteristic, say 31, can be highly efficient. Indeed, at the same design security of $2^{80}$ under the best known attacks, odd-char MPKC is generally faster than prior MPKCs over \GF{2^k}, which are in turn faster than ``traditional'' alternatives. This seemingly counter-intuitive feat is accomplished by exploiting the comparative over-abundance of small integer arithmetic resources in commodity...

RSA-FDH and many other schemes secure in the Random-Oracle Model (ROM) require a hash function with output size larger than standard sizes. We show that the random-oracle instantiations proposed in the literature for such cases are weaker than a random oracle, including the proposals by Bellare and Rogaway from 1993 and 1996, and the ones implicit in IEEE P1363 and PKCS standards: for instance, there is a practical $2^{30}$ preimage attack on BR93 for 1024-bit digests. Next, we study the...

Formal verification is getting more and more important in computer science. However the state of the art formal verification methods in cryptography are very rudimentary. This paper is one step to provide a tool box allowing the use of formal methods in every aspect of cryptography. In this paper we give a formal specification of the RSA probabilistic signature scheme (RSA-PSS) [4] which is used as algorithm for digital signatures in the PKCS #1 v2.1 standard [7]. Additionally we show the...

Attack is possible upon all three RSA analogue PKCs based on singular cubic curves given by Koyama. While saying so, Seng et al observed that the scheme become insecure if a linear relation is known between two plaintexts. In this case, attacker has to compute greatest common divisor of two polynomials corresponding to those two plaintexts. However, the computation of greatest common divisor of two polynomials is not efficient. For the reason, the degree e of both polynomials, an encryption...

In this paper, we present a new class of public-key cryptosystem (PKC) using algebraic coding on the basis of superimposition and randomness. The proposed PKC is featured by a generator matrix, in a characteristic form, where the generator matrix of an algebraic code is repeatedly used along with the generator matrix of a random code, as sub-matrices. This generator matrix, in the characteristic form, will be referred to as $K$-matrix. We show that the $K$-matrix yields the following...

We herein discuss two modes of attack on multivariate public-key cryptosystems. A 2000 Goubin-Courtois article applied these techniques against a special class of multivariate PKC's called ``Triangular-Plus-Minus'' (TPM), and may explain in part the present dearth of research on ``true'' multivariates -- multivariate PKC's in which the middle map is not really taken in a much larger field. These attacks operate by finding linear combinations of matrices with a given rank. Indeed, we can...

We build several highly-practical and optimized signcryption constructions directly from trapdoor permutations, in the random oracle model. All our constructions share features such as simplicity, efficiency, generality, near-optimal exact security, flexible and ad-hoc key management, key reuse for sending/receiving data, optimally-low message expansion, "backward" use for plain signature/encryption, long message and associated data support, the strongest-known qualitative security...

Vaudenay has shown in [5] that a CBC encryption mode ([2], [9]) combined with the PKCS#5 padding [3] scheme allows an attacker to invert the underlying block cipher, provided she has access to a valid-padding oracle which for each input ciphertext tells her whether the corresponding plaintext has a valid padding or not. Having on mind the countermeasures against this attack, different padding schemes have been studied in [1]. The best one is referred to as the ABYT-PAD. It is designed for...

In this paper we present a practically feasible attack on RSA-based sessions in SSL/TLS protocols. These protocols incorporate the PKCS#1 (v. 1.5) encoding method for the RSA encryption of a premaster-secret value. The premaster-secret is the only secret value that is used for deriving all the particular session keys. Therefore, an attacker who can recover the premaster-secret can decrypt the whole captured SSL/TLS session. We show that incorporating a version number check over PKCS#1...

We present a new, elegant composition method for joint signature and encryption, also referred to as signcryption. The new method, which we call *Padding-based Parallel Signcryption* (PbPS), builds an efficient signcryption scheme from any family of trapdoor permutations, such as RSA. Each user U generates a single public/secret key pair f_U/f^{-1}_U used for both sending and receiving the data. To signcrypt a message m to a recipient with key f_{rcv}, a sender with key f_{snd} efficiently...

This paper contains three parts. In the first part we present a new side channel attack on plaintext encrypted by EME-OAEP PKCS#1 v.2.1. In contrast with Manger´s attack, we attack that part of the plaintext, which is shielded by the OAEP method. In the second part we show that Bleichenbacher’s and Manger’s attack on the RSA encryption scheme PKCS#1 v.1.5 and EME-OAEP PKCS#1 v.2.1 can be converted to an attack on the RSA signature scheme with any message encoding (not only PKCS). This is a...

Vaudenay [1] has presented an attack on the CBC mode of block ciphers, which uses padding according to the PKCS#5 standard. One of the countermeasures, which he has assumed, consisted of the encryption of the message M´= M || padding || hash(M || padding) instead of the original M. This can increase the length of the message by several blocks compared with the present padding. Moreover, Wagner [1] showed a security weakness in this proposal. The next correction, which Vaudenay proposed ("A...

We consider threshold cryptosystems over a composite modulus $N$ where the \emph{factors} of $N$ are shared among the participants as the secret key. This is a new paradigm for threshold cryptosystems based on a composite modulus, differing from the typical treatment of RSA-based systems where a ``decryption exponent'' is shared among the participants. Our approach yields solutions to some open problems in threshold cryptography; in particular, we obtain the following: 1. \emph{Threshold...