How to strengthen any weakly unforgeable signature into a strongly unforgeable signature

Standard signature schemes are usually designed only to achieve weak unforgeability – i.e. preventing forgery of signatures on new messages not previously signed. However, most signature schemes are randomised and allow many possible signatures for a single message. In this case, it may be possible to produce a new signature on a previously signed message. Some applications require that this type of forgery also be prevented – this requirement is called strong unforgeability. At PKC2006, Boneh Shen and Waters presented an efficient transform based on any randomised trapdoor hash function which converts a weakly unforgeable signature into a strongly unforgeable signature and applied it to construct a strongly unforgeable signature based on the CDH problem. However, the transform of Boneh et al only applies to a class of so-called partitioned signatures. Although many schemes fall in this class, some do not, for example the DSA signature. Hence it is natural to ask whether one can obtain a truly generic efficient transform based on any randomised trapdoor hash function which converts any weakly unforgeable signature into a strongly unforgeable one. We answer this question in the positive by presenting a simple modification of the Boneh-Shen-Waters transform. Our modified transform uses two randomised trapdoor hash functions.

Analysis of indirect message injection for MAC generation using stream ciphers

This paper presents a model for generating a MAC tag with a stream cipher using the input message indirectly. Several recent proposals represent instances of this model with slightly different options. We investigate the security of this model for different options, and identify cases which permit forgery attacks. Based on this, we present a new forgery attack on version 1.4 of 128-EIA3. Design recommendations to enhance the security of proposals following this general model are given.

Analysis of stream cipher based authenticated encryption schemes

Authenticated Encryption (AE) is the cryptographic process of providing simultaneous confidentiality and integrity protection to messages. This approach is more efficient than applying a two-step process of providing confidentiality for a message by encrypting the message, and in a separate pass providing integrity protection by generating a Message Authentication Code (MAC). AE using symmetric ciphers can be provided by either stream ciphers with built in authentication mechanisms or block ciphers using appropriate modes of operation. However, stream ciphers have the potential for higher performance and smaller footprint in hardware and/or software than block ciphers. This property makes stream ciphers suitable for resource constrained environments, where storage and computational power are limited. There have been several recent stream cipher proposals that claim to provide AE. These ciphers can be analysed using existing techniques that consider confidentiality or integrity separately; however currently there is no existing framework for the analysis of AE stream ciphers that analyses these two properties simultaneously. This thesis introduces a novel framework for the analysis of AE using stream cipher algorithms. This thesis analyzes the mechanisms for providing confidentiality and for providing integrity in AE algorithms using stream ciphers. There is a greater emphasis on the analysis of the integrity mechanisms, as there is little in the public literature on this, in the context of authenticated encryption. The thesis has four main contributions as follows. The first contribution is the design of a framework that can be used to classify AE stream ciphers based on three characteristics. The first classification applies Bellare and Namprempre's work on the the order in which encryption and authentication processes take place. The second classification is based on the method used for accumulating the input message (either directly or indirectly) into the into the internal states of the cipher to generate a MAC. The third classification is based on whether the sequence that is used to provide encryption and authentication is generated using a single key and initial vector, or two keys and two initial vectors. The second contribution is the application of an existing algebraic method to analyse the confidentiality algorithms of two AE stream ciphers; namely SSS and ZUC. The algebraic method is based on considering the nonlinear filter (NLF) of these ciphers as a combiner with memory. This method enables us to construct equations for the NLF that relate the (inputs, outputs and memory of the combiner) to the output keystream. We show that both of these ciphers are secure from this type of algebraic attack. We conclude that using a keydependent SBox in the NLF twice, and using two different SBoxes in the NLF of ZUC, prevents this type of algebraic attack. The third contribution is a new general matrix based model for MAC generation where the input message is injected directly into the internal state. This model describes the accumulation process when the input message is injected directly into the internal state of a nonlinear filter generator. We show that three recently proposed AE stream ciphers can be considered as instances of this model; namely SSS, NLSv2 and SOBER-128. Our model is more general than a previous investigations into direct injection. Possible forgery attacks against this model are investigated. It is shown that using a nonlinear filter in the accumulation process of the input message when either the input message or the initial states of the register is unknown prevents forgery attacks based on collisions. The last contribution is a new general matrix based model for MAC generation where the input message is injected indirectly into the internal state. This model uses the input message as a controller to accumulate a keystream sequence into an accumulation register. We show that three current AE stream ciphers can be considered as instances of this model; namely ZUC, Grain-128a and Sfinks. We establish the conditions under which the model is susceptible to forgery and side-channel attacks.

Correcting flaws in Mitchell’s analysis of EPBC

Efficient error-Propagating Block Chaining (EPBC) is a block cipher mode intended to simultaneously provide both confidentiality and integrity protection for messages. Mitchell’s analysis pointed out a weakness in the EPBC integrity mechanism that can be used in a forgery attack. This paper identifies and corrects a flaw in Mitchell’s analysis of EPBC, and presents other attacks on the EPBC integrity mechanism.

Security Analysis of Randomize-Hash-then-Sign Digital Signatures

At CRYPTO 2006, Halevi and Krawczyk proposed two randomized hash function modes and analyzed the security of digital signature algorithms based on these constructions. They showed that the security of signature schemes based on the two randomized hash function modes relies on properties similar to the second preimage resistance rather than on the collision resistance property of the hash functions. One of the randomized hash function modes was named the RMX hash function mode and was recommended for practical purposes. The National Institute of Standards and Technology (NIST), USA standardized a variant of the RMX hash function mode and published this standard in the Special Publication (SP) 800-106. In this article, we first discuss a generic online birthday existential forgery attack of Dang and Perlner on the RMX-hash-then-sign schemes. We show that a variant of this attack can be applied to forge the other randomize-hash-then-sign schemes. We point out practical limitations of the generic forgery attack on the RMX-hash-then-sign schemes. We then show that these limitations can be overcome for the RMX-hash-then-sign schemes if it is easy to find fixed points for the underlying compression functions, such as for the Davies-Meyer construction used in the popular hash functions such as MD5 designed by Rivest and the SHA family of hash functions designed by the National Security Agency (NSA), USA and published by NIST in the Federal Information Processing Standards (FIPS). We show an online birthday forgery attack on this class of signatures by using a variant of Dean’s method of finding fixed point expandable messages for hash functions based on the Davies-Meyer construction. This forgery attack is also applicable to signature schemes based on the variant of RMX standardized by NIST in SP 800-106. We discuss some important applications of our attacks and discuss their applicability on signature schemes based on hash functions with ‘built-in’ randomization. Finally, we compare our attacks on randomize-hash-then-sign schemes with the generic forgery attacks on the standard hash-based message authentication code (HMAC).

On Randomizing Hash Functions to Strengthen the Security of Digital Signatures

Halevi and Krawczyk proposed a message randomization algorithm called RMX as a front-end tool to the hash-then-sign digital signature schemes such as DSS and RSA in order to free their reliance on the collision resistance property of the hash functions. They have shown that to forge a RMX-hash-then-sign signature scheme, one has to solve a cryptanalytical task which is related to finding second preimages for the hash function. In this article, we will show how to use Dean’s method of finding expandable messages for finding a second preimage in the Merkle-Damgård hash function to existentially forge a signature scheme based on a t-bit RMX-hash function which uses the Davies-Meyer compression functions (e.g., MD4, MD5, SHA family) in 2 t/2 chosen messages plus 2 t/2 + 1 off-line operations of the compression function and similar amount of memory. This forgery attack also works on the signature schemes that use Davies-Meyer schemes and a variant of RMX published by NIST in its Draft Special Publication (SP) 800-106. We discuss some important applications of our attack.

Security Analysis of salt||password Hashes

Protection of passwords used to authenticate computer systems and networks is one of the most important application of cryptographic hash functions. Due to the application of precomputed memory look up attacks such as birthday and dictionary attacks on the hash values of passwords to find passwords, it is usually recommended to apply hash function to the combination of both the salt and password, denoted salt||password, to prevent these attacks. In this paper, we present the first security analysis of salt||password hashing application. We show that when hash functions based on the compression functions with easily found fixed points are used to compute the salt||password hashes, these hashes are susceptible to precomputed offline birthday attacks. For example, this attack is applicable to the salt||password hashes computed using the standard hash functions such as MD5, SHA-1, SHA-256 and SHA-512 that are based on the popular Davies-Meyer compression function. This attack exposes a subtle property of this application that although the provision of salt prevents an attacker from finding passwords, salts prefixed to the passwords do not prevent an attacker from doing a precomputed birthday attack to forge an unknown password. In this forgery attack, we demonstrate the possibility of building multiple passwords for an unknown password for the same hash value and salt. Interestingly, password||salt (i.e. salts suffixed to the passwords) hashes computed using Davies-Meyer hash functions are not susceptible to this attack, showing the first security gap between the prefix-salt and suffix-salt methods of hashing passwords.

Analysis of one-pass block cipher based authenticated encryption schemes

This project analyses and evaluates the integrity assurance mechanisms used in four Authenticated Encryption schemes based on symmetric block ciphers. These schemes are all cross chaining block cipher modes that claim to provide both confidentiality and integrity assurance simultaneously, in one pass over the data. The investigations include assessing the validity of an existing forgery attack on certain schemes, applying the attack approach to other schemes and implementing the attacks to verify claimed probabilities of successful forgeries. For these schemes, the theoretical basis of the attack was developed, the attack algorithm implemented and computer simulations performed for experimental verification.

Forgery attacks on ++AE authenticated encryption mode

In this paper, we analyse a block cipher mode of operation submitted in 2014 to the cryptographic competition for authenticated encryption (CAESAR). This mode is designed by Recacha and called ++AE (plus-plus-ae). We propose a chosen plaintext forgery attack on ++AE that requires only a single chosen message query to allow an attacker to construct multiple forged messages. Our attack is deterministic and guaranteed to pass ++AE integrity check. We demonstrate the forgery attack using 128-bit AES as the underlying block cipher. Hence, ++AE is insecure as an authenticated encryption mode of operation.