A public key cryptosystem based on block upper triangular matrices

We propose a public key cryptosystem based on block upper triangular matrices. This system is a variant of the Discrete Logarithm Problem with elements in a finite group, capable of increasing the difficulty of the problem while maintaining the key size. We also propose a key exchange protocol that guarantees that both parties share a secret element of this group and a digital signature scheme that provides data authenticity and integrity.

Public key cryptography and error correcting codes as Ising models

We employ the methods of statistical physics to study the performance of Gallager type error-correcting codes. In this approach, the transmitted codeword comprises Boolean sums of the original message bits selected by two randomly-constructed sparse matrices. We show that a broad range of these codes potentially saturate Shannon's bound but are limited due to the decoding dynamics used. Other codes show sub-optimal performance but are not restricted by the decoding dynamics. We show how these codes may also be employed as a practical public-key cryptosystem and are of competitive performance to modern cyptographical methods.

Security and reliability of LPDC based public-key cryptosystems

Security and reliability of LDPC based public-key cryptosystems are discussed and analysed. We study attacks on the cryptosystem when partial knowledge of one or more of the private key components and/or of the plaintext have been acquired.

Analysis of common attacks in public-key cryptosystems based on low-density parity-check codes

The security and reliability of a class of public-key cryptosystems against attacks by unauthorized parties, who had acquired partial knowledge of one or more of the private key components and/or of the message, were discussed. The standard statistical mechanical methods of dealing with diluted spin systems with replica symmetric considerations were analyzed. The dynamical transition which defined decryption success in practical situation was studied. The phase diagrams which showed the dynamical threshold as a function of the partial acquired knowledge of the private key were also presented.

Homomorphic encryption and database query privacy

Homomorphic encryption is a particular type of encryption method that enables computing over encrypted data. This has a wide range of real world ramifications such as being able to blindly compute a search result sent to a remote server without revealing its content. In the first part of this thesis, we discuss how database search queries can be made secure using a homomorphic encryption scheme based on the ideas of Gahi et al. Gahi’s method is based on the integer-based fully homomorphic encryption scheme proposed by Dijk et al. We propose a new database search scheme called the Homomorphic Query Processing Scheme, which can be used with the ring-based fully homomorphic encryption scheme proposed by Braserski. In the second part of this thesis, we discuss the cybersecurity of the smart electric grid. Specifically, we use the Homomorphic Query Processing scheme to construct a keyword search technique in the smart grid. Our work is based on the Public Key Encryption with Keyword Search (PEKS) method introduced by Boneh et al. and a Multi-Key Homomorphic Encryption scheme proposed by L´opez-Alt et al. A summary of the results of this thesis (specifically the Homomorphic Query Processing Scheme) is published at the 14th Canadian Workshop on Information Theory (CWIT).

Cryptographic techniques for managing computational effort

Availability has become a primary goal of information security and is as significant as other goals, in particular, confidentiality and integrity. Maintaining availability of essential services on the public Internet is an increasingly difficult task in the presence of sophisticated attackers. Attackers may abuse limited computational resources of a service provider and thus managing computational costs is a key strategy for achieving the goal of availability. In this thesis we focus on cryptographic approaches for managing computational costs, in particular computational effort. We focus on two cryptographic techniques: computational puzzles in cryptographic protocols and secure outsourcing of cryptographic computations. This thesis contributes to the area of cryptographic protocols in the following ways. First we propose the most efficient puzzle scheme based on modular exponentiations which, unlike previous schemes of the same type, involves only a few modular multiplications for solution verification; our scheme is provably secure. We then introduce a new efficient gradual authentication protocol by integrating a puzzle into a specific signature scheme. Our software implementation results for the new authentication protocol show that our approach is more efficient and effective than the traditional RSA signature-based one and improves the DoSresilience of Secure Socket Layer (SSL) protocol, the most widely used security protocol on the Internet. Our next contributions are related to capturing a specific property that enables secure outsourcing of cryptographic tasks in partial-decryption. We formally define the property of (non-trivial) public verifiability for general encryption schemes, key encapsulation mechanisms (KEMs), and hybrid encryption schemes, encompassing public-key, identity-based, and tag-based encryption avors. We show that some generic transformations and concrete constructions enjoy this property and then present a new public-key encryption (PKE) scheme having this property and proof of security under the standard assumptions. Finally, we combine puzzles with PKE schemes for enabling delayed decryption in applications such as e-auctions and e-voting. For this we first introduce the notion of effort-release PKE (ER-PKE), encompassing the well-known timedrelease encryption and encapsulated key escrow techniques. We then present a security model for ER-PKE and a generic construction of ER-PKE complying with our security notion.

Publicly verifiable ciphertexts

In many applications, where encrypted traffic flows from an open (public) domain to a protected (private) domain, there exists a gateway that bridges the two domains and faithfully forwards the incoming traffic to the receiver. We observe that indistinguishability against (adaptive) chosen-ciphertext attacks (IND-CCA), which is a mandatory goal in face of active attacks in a public domain, can be essentially relaxed to indistinguishability against chosen-plaintext attacks (IND-CPA) for ciphertexts once they pass the gateway that acts as an IND-CCA/CPA filter by first checking the validity of an incoming IND-CCA ciphertext, then transforming it (if valid) into an IND-CPA ciphertext, and forwarding the latter to the recipient in the private domain. “Non-trivial filtering'' can result in reduced decryption costs on the receivers' side. We identify a class of encryption schemes with publicly verifiable ciphertexts that admit generic constructions of (non-trivial) IND-CCA/CPA filters. These schemes are characterized by existence of public algorithms that can distinguish between valid and invalid ciphertexts. To this end, we formally define (non-trivial) public verifiability of ciphertexts for general encryption schemes, key encapsulation mechanisms, and hybrid encryption schemes, encompassing public-key, identity-based, and tag-based encryption flavours. We further analyze the security impact of public verifiability and discuss generic transformations and concrete constructions that enjoy this property.

NTRUCCA : how to strengthen NTRUEncrypt to chosen-ciphertext security in the standard model

NTRUEncrypt is a fast and practical lattice-based public-key encryption scheme, which has been standardized by IEEE, but until recently, its security analysis relied only on heuristic arguments. Recently, Stehlé and Steinfeld showed that a slight variant (that we call pNE) could be proven to be secure under chosen-plaintext attack (IND-CPA), assuming the hardness of worst-case problems in ideal lattices. We present a variant of pNE called NTRUCCA, that is IND-CCA2 secure in the standard model assuming the hardness of worst-case problems in ideal lattices, and only incurs a constant factor overhead in ciphertext and key length over the pNE scheme. To our knowledge, our result gives the first IND-CCA2 secure variant of NTRUEncrypt in the standard model, based on standard cryptographic assumptions. As an intermediate step, we present a construction for an All-But-One (ABO) lossy trapdoor function from pNE, which may be of independent interest. Our scheme uses the lossy trapdoor function framework of Peikert and Waters, which we generalize to the case of (k − 1)-of-k-correlated input distributions.

Lattice-based completely non-malleable PKE in the standard model

This paper presents ongoing work toward constructing efficient completely non-malleable public-key encryption scheme based on lattices in the standard (common reference string) model. An encryption scheme is completely non-malleable if it requires attackers to have negligible advantage, even if they are allowed to transform the public key under which the related message is encrypted. Ventre and Visconti proposed two inefficient constructions of completely non-malleable schemes, one in the common reference string model using non-interactive zero-knowledge proofs, and another using interactive encryption schemes. Recently, two efficient public-key encryption schemes have been proposed, both of them are based on pairing identity-based encryption.

An efficient scheme of common secure indices for conjunctive keyword-based retrieval on encrypted data

We consider the following problem: members in a dynamic group retrieve their encrypted data from an untrusted server based on keywords and without any loss of data confidentiality and member’s privacy. In this paper, we investigate common secure indices for conjunctive keyword-based retrieval over encrypted data, and construct an efficient scheme from Wang et al. dynamic accumulator, Nyberg combinatorial accumulator and Kiayias et al. public-key encryption system. The proposed scheme is trapdoorless and keyword-field free. The security is proved under the random oracle, decisional composite residuosity and extended strong RSA assumptions.

Threshold MACs

The power of sharing computation in a cryptosystem is crucial in several real-life applications of cryptography. Cryptographic primitives and tasks to which threshold cryptosystems have been applied include variants of digital signature, identification, public-key encryption and block ciphers etc. It is desirable to extend the domain of cryptographic primitives which threshold cryptography can be applied to. This paper studies threshold message authentication codes (threshold MACs). Threshold cryptosystems usually use algebraically homomorphic properties of the underlying cryptographic primitives. A typical approach to construct a threshold cryptographic scheme is to combine a (linear) secret sharing scheme with an algebraically homomorphic cryptographic primitive. The lack of algebraic properties of MACs rules out such an approach to share MACs. In this paper, we propose a method of obtaining a threshold MAC using a combinatorial approach. Our method is generic in the sense that it is applicable to any secure conventional MAC by making use of certain combinatorial objects, such as cover-free families and their variants. We discuss the issues of anonymity in threshold cryptography, a subject that has not been addressed previously in the literature in the field, and we show that there are trade-offis between the anonymity and efficiency of threshold MACs.