Lightweight Public Key Encryption in Post-Quantum Computing Era

Confidentiality in our digital world is based on the security of cryptographic algorithms. These are usually executed transparently in the background, with people often relying on them without further knowledge. In the course of technological progress with quantum computers, the protective function of common encryption algorithms is threatened. This particularly affects public-key methods such as RSA and DH based on discrete logarithms and prime factorization. Our concept describes the transformation of a classical asymmetric encryption method to a modern complexity class. Thereby the approach of Cramer-Shoup is put on the new basis of elliptic curves. The system is provable cryptographically strong, especially against adaptive chosen-ciphertext attacks. In addition, the new method features small key lengths, making it suitable for Internet-of-Things. It represents an intermediate step towards an encryption scheme based on isogeny elliptic curves. This approach shows a way to a secure encryption scheme for the post-quantum computing era

The zheng-seberry public key cryptosystem and signcryption

In 1993 Zheng-Seberry presented a public key cryptosystem that was considered efficient and secure in the sense of indistinguishability of encryptions (IND) against an adaptively chosen ciphertext adversary (CCA2). This thesis shows the Zheng-Seberry scheme is not secure as a CCA2 adversary can break the scheme in the sense of IND. In 1998 Cramer-Shoup presented a scheme that was secure against an IND-CCA2 adversary and whose proof relied only on standard assumptions. This thesis modifies this proof and applies it to a modified version of the El-Gamal scheme. This resulted in a provably secure scheme relying on the Random Oracle (RO) model, which is more efficient than the original Cramer-Shoup scheme. Although the RO model assumption is needed for security of this new El-Gamal variant, it only relies on it in a minimal way

Design and Analysis of Opaque Signatures

Digital signatures were introduced to guarantee the authenticity and integrity of the underlying messages. A digital signature scheme comprises the key generation, the signature, and the verification algorithms. The key generation algorithm creates the signing and the verifying keys, called also the signer’s private and public keys respectively. The signature algorithm, which is run by the signer, produces a signature on the input message. Finally, the verification algorithm, run by anyone who knows the signer’s public key, checks whether a purported signature on some message is valid or not. The last property, namely the universal verification of digital signatures is undesirable in situations where the signed data is commercially or personally sensitive. Therefore, mechanisms which share most properties with digital signatures except for the universal verification were invented to respond to the aforementioned need; we call such mechanisms “opaque signatures”. In this thesis, we study the signatures where the verification cannot be achieved without the cooperation of a specific entity, namely the signer in case of undeniable signatures, or the confirmer in case of confirmer signatures; we make three main contributions. We first study the relationship between two security properties important for public key encryption, namely data privacy and key privacy. Our study is motivated by the fact that opaque signatures involve always an encryption layer that ensures their opacity. The properties required for this encryption vary according to whether we want to protect the identity (i.e. the key) of the signer or hide the validity of the signature. Therefore, it would be convenient to use existing work about the encryption scheme in order to derive one notion from the other. Next, we delve into the generic constructions of confirmer signatures from basic cryptographic primitives, e.g. digital signatures, encryption, or commitment schemes. In fact, generic constructions give easy-to-understand and easy-to-prove schemes, however, this convenience is often achieved at the expense of efficiency. In this contribution, which constitutes the core of this thesis, we first analyze the already existing constructions; our study concludes that the popular generic constructions of confirmer signatures necessitate strong security assumptions on the building blocks, which impacts negatively the efficiency of the resulting signatures. Next, we show that a small change in these constructionsmakes these assumptions drop drastically, allowing as a result constructions with instantiations that compete with the dedicated realizations of these signatures. Finally, we revisit two early undeniable signatures which were proposed with a conjectural security. We disprove the claimed security of the first scheme, and we provide a fix to it in order to achieve strong security properties. Next, we upgrade the second scheme so that it supports a iii desirable feature, and we provide a formal security treatment of the new scheme: we prove that it is secure assuming new reasonable assumptions on the underlying constituents

Programmable hash functions and their applications

We introduce a new combinatorial primitive called *programmable hash functions* (PHFs). PHFs can be used to *program* the output of a hash function such that it contains solved or unsolved discrete logarithm instances with a certain probability. This is a technique originally used for security proofs in the random oracle model. We give a variety of *standard model* realizations of PHFs (with different parameters). The programmability makes PHFs a suitable tool to obtain black-box proofs of cryptographic protocols when considering adaptive attacks. We propose generic digital signature schemes from the strong RSA problem and from some hardness assumption on bilinear maps that can be instantiated with any PHF. Our schemes offer various improvements over known constructions. In particular, for a reasonable choice of parameters, we obtain short standard model digital signatures over bilinear maps

A Novel Mathematical Formal Proof in Unreliability Protocol with XOR in Two\u27s Complement System

Exclusive OR (XOR), a common Boolean logical operation, is an operation on two factors where the result is true if and only if one operand is true and the other is false. A simple way to state this is ``one or the other, but not both\u27\u27. Using this logical operation, a text string can be encrypted by applying the XOR operator to every character using a ``key\u27\u27. If you want to decrypt the output, simply reapply the key and the resulting output will be the original message

Tightly-Secure Signatures from Chameleon Hash Functions

We give a new framework for obtaining signatures with a tight security reduction from standard hardness assumptions. Concretely, we show that any Chameleon Hash function can be transformed into a (binary) tree-based signature scheme with tight security. The transformation is in the standard model, i.e., it does not make use of any random oracle. For specific assumptions (such as RSA, Diffie-Hellman and Short Integer Solution (SIS)) we further manage to obtain a more efficient flat-tree construction. Our framework explains and generalizes most of the existing schemes as well as providing a generic means for constructing tight signature schemes based on arbitrary assumptions, which improves the standard Merkle tree transformation. Moreover, we obtain the first tightly secure signature scheme from the SIS assumption and several schemes based on Diffie-Hellman in the standard model. Some of our signature schemes can (using known techniques) be combined with Groth-Sahai proof methodology to yield tightly secure and efficient simulation-sound NIZK proofs of knowledge and CCA-secure encryption in the multi-user/-challenge setting under classical assumptions

Group Signatures with Message-Dependent Opening: Formal Definitions and Constructions

This paper introduces a new capability for group signatures called message-dependent opening. It is intended to weaken the high trust placed on the opener; i.e., no anonymity against the opener is provided by an ordinary group signature scheme. In a group signature scheme with message-dependent opening (GS-MDO), in addition to the opener, we set up an admitter that is not able to extract any user’s identity but admits the opener to open signatures by specifying messages where signatures on the specified messages will be opened by the opener. The opener cannot extract the signer’s identity from any signature whose corresponding message is not specified by the admitter. This paper presents formal definitions of GS-MDO and proposes a generic construction of it from identity-based encryption and adaptive non-interactive zero-knowledge proofs. Moreover, we propose two specific constructions, one in the standard model and one in the random oracle model. Our scheme in the standard model is an instantiation of our generic construction but the message-dependent opening property is bounded. In contrast, our scheme in the random oracle model is not a direct instantiation of our generic construction but is optimized to increase efficiency and achieves the unbounded message-dependent opening property. Furthermore, we also demonstrate that GS-MDO implies identity-based encryption, thus implying that identity-based encryption is essential for designing GS-MDO schemes