Fakultät für Informatik und Mathematik
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Cryptography is the scientific study of techniques for securing information and communication against adversaries. It is about designing and analyzing encryption schemes and protocols that protect data from unauthorized reading. However, in our modern information-driven society with highly complex and interconnected information systems, encryption alone is no longer enough as it makes the data unintelligible, preventing any meaningful computation without decryption. On the one hand, data owners want to maintain control over their sensitive data. On the other hand, there is a high business incentive for collaborating with an untrusted external party.
Modern cryptography encompasses different techniques, such as secure multiparty computation, homomorphic encryption or order-preserving encryption, that enable cloud users to encrypt their data before outsourcing it to the cloud while still being able to process and search on the outsourced and encrypted data without decrypting it. In this thesis, we rely on these cryptographic techniques for computing on encrypted data to propose efficient multiparty protocols for order-preserving encryption, decision tree evaluation and kth-ranked element computation.
We start with Order-preserving encryption (OPE) which allows encrypting data, while still enabling efficient range queries on the encrypted data. However, OPE is symmetric limiting, the use case to one client and one server. Imagine a scenario where a Data Owner (DO) outsources encrypted data to the Cloud Service Provider (CSP) and a Data Analyst (DA) wants to execute private range queries on this data. Then either the DO must reveal its encryption key or the DA must reveal the private queries. We overcome this limitation by allowing the equivalent of a public-key OPE.
Decision trees are common and very popular classifiers because they are explainable. The problem of evaluating a private decision tree on private data consists of a server holding a private decision tree and a client holding a private attribute vector. The goal is to classify the client’s input using the server’s model such that the client learns only the result of the classification, and the server learns nothing. In a first approach, we represent the tree as an array and execute only d interactive comparisons (instead of 2 d as in existing solutions), where d denotes the depth of the tree. In a second approach, we delegate the complete tree evaluation to the server using somewhat or fully homomorphic encryption where the ciphertexts are encrypted under the client’s public key.
A generalization of a decision tree is a random forest that consists of many decision trees. A classification with a random forest evaluates each decision tree in the forest and outputs the classification label which occurs most often. Hence, the classification labels are ranked by their number of occurrences and the final result is the best ranked one. The best ranked element is a special case of the kth-ranked element. In this thesis, we consider the secure computation of the kth-ranked element in a distributed setting with applications in benchmarking and auctions. We propose different approaches for privately computing the kth-ranked element in a star network, using either garbled circuits or threshold homomorphic encryption.
This doctoral thesis is dedicated to improve a linear algebra attack on the so-called braid group-based Diffie-Hellman conjugacy problem (BDHCP). The general procedure of the attack is to transform a BDHCP to the problem of solving several simultaneous matrix equations. A first improvement is achieved by reducing the solution space of the matrix equations to matrices that have a specific structure, which we call here the left braid structure. Using the left braid structure the number of matrix equations to be solved reduces to one. Based on the left braid structure we are further able to formulate a structure-based attack on the BDHCP. That is to transform the matrix equation to a system of linear equations and exploiting the structure of the corresponding extended coefficient matrix, which is induced by the left braid structure of the solution space. The structure-based attack then has an empirically high probability to solve the BDHCP with significantly less arithmetic operations than the original attack. A third improvement of the original linear algebra attack is to use an algorithm that combines Gaussian elimination with integer polynomial interpolation and the Chinese remainder theorem (CRT), instead of fast matrix multiplication as suggested by others. The major idea here is to distribute the task of solving a system of linear equations over a giant finite field to several much smaller finite fields. Based on our empirically measured bounds for the degree of the polynomials to be interpolated and the bit size of the coefficients and integers to be recovered via the CRT, we conclude an improvement of the run time complexity of the original algorithm by a factor of n^8 bit operations in the best case, and still n^6 in the worst case.
This doctoral thesis is dedicated to the analysis and the design of
symmetric cryptographic algorithms.
In the first part of the dissertation, we deal with fault-based attacks
on cryptographic circuits which belong to the field of active implementation
attacks and aim to retrieve secret keys stored on such chips. Our main focus
lies on the cryptanalytic aspects of those attacks. In particular, we target
block ciphers with a lightweight and (often) non-bijective key schedule where
the derived subkeys are (almost) independent from each other. An attacker who is
able to reconstruct one of the subkeys is thus not necessarily able to directly
retrieve other subkeys or even the secret master key by simply reversing the key
schedule. We introduce a framework based on differential fault analysis that
allows to attack block ciphers with an arbitrary number of independent subkeys
and which rely on a substitution-permutation network. These methods are then
applied to the lightweight block ciphers LED and PRINCE and we show in both
cases how to recover the secret master key requiring only a small number of
fault injections. Moreover, we investigate approaches that utilize algebraic
instead of differential techniques for the fault analysis and discuss advantages
and drawbacks. At the end of the first part of the dissertation, we explore
fault-based attacks on the block cipher Bel-T which also has a lightweight key
schedule but is not based on a substitution-permutation network but instead on
the so-called Lai-Massey scheme. The framework mentioned above is thus not
usable against Bel-T. Nevertheless, we also present techniques for the case of
Bel-T that enable full recovery of the secret key in a very efficient way using
differential fault analysis.
In the second part of the thesis, we focus on authenticated encryption
schemes. While regular ciphers only protect privacy of processed data,
authenticated encryption schemes also secure its authenticity and integrity.
Many of these ciphers are additionally able to protect authenticity and
integrity of so-called associated data. This type of data is transmitted
unencrypted but nevertheless must be protected from being tampered with during
transmission. Authenticated encryption is nowadays the standard technique to
protect in-transit data. However, most of the currently deployed schemes have
deficits and there are many leverage points for improvements. With NORX we
introduce a novel authenticated encryption scheme supporting associated data.
This algorithm was designed with high security, efficiency in both hardware and
software, simplicity, and robustness against side-channel attacks in mind. Next
to its specification, we present special features, security goals,
implementation details, extensive performance measurements and discuss
advantages over currently deployed standards. Finally, we describe our
preliminary security analysis where we investigate differential and rotational
properties of NORX. Noteworthy are in particular the newly developed
techniques for differential cryptanalysis of NORX which exploit the power of
SAT- and SMT-solvers and have the potential to be easily adaptable to other
encryption schemes as well.