A NOVEL TECHNIQUE FOR SECURE ENCRYPTED MESSAGES IN MOBILE AND PERVASIVE APPLICATIONS

More than applications rely on the existence of small devices that can exchange information and form communication networks. In a significant portion of such applications, the confidentiality and integrity of the communicated messages are of particular interest. In this work, to propose two novel techniques for authenticating short encrypted messages that are directed to meet the requirements of mobile and pervasive applications. By taking advantage of the fact that the message to be authenticated must also be encrypted, to propose provably secure authentication codes that are more efficient than any message authentication code in the literature. The key idea behind the proposed techniques is to utilize the security that the encryption algorithm can provide to design more efficient authentication mechanisms, as opposed to using standalone authentication primitives

Proficient Authentication Mechanism for Mobile and Pervasive Computing

Mobile Computing is a technology that allows transmission of data, voice and video via a computer or any other wireless enabled device without having to be connected to a fixed physical link. With today’s technology, many applications rely on the existence of small devices that can exchange information and form communication networks. In a significant portion of such applications, the confidentiality and integrity of the communicated messages are of particular interest. In this work, we propose two novel techniques for authenticating short encrypted messages that are directed to meet the requirements of mobile and pervasive applications. By taking advantage of the fact that the message to be authenticated must also be encrypted, we propose provably secure authentication codes that are more efficient than any message authentication code in the literature. The key idea behind the proposed techniques is to utilize the security that the encryption algorithm can provide to design more efficient authentication mechanisms, as opposed to using standalone authentication primitive

Design and Cryptanalysis of a Customizable Authenticated Encryption Algorithm

It is common knowledge that encryption is a useful tool for providing confidentiality. Authentication, however, is often overlooked. Authentication provides data integrity; it helps ensure that any tampering with or corruption of data is detected. It also provides assurance of message origin. Authenticated encryption (AE) algorithms provide both confidentiality and integrity / authenticity by processing plaintext and producing both ciphertext and a Message Authentication Code (MAC). It has been shown too many times throughout history that encryption without authentication is generally insecure. This has recently culminated in a push for new authenticated encryption algorithms. There are several authenticated encryption algorithms in existence already. However, these algorithms are often difficult to use correctly in practice. This is a significant problem because misusing AE constructions can result in reduced security in many cases. Furthermore, many existing algorithms have numerous undesirable features. For example, these algorithms often require two passes of the underlying cryptographic primitive to yield the ciphertext and MAC. This results in a longer runtime. It is clear that new easy-to-use, single-pass, and highly secure AE constructions are needed. Additionally, a new AE algorithm is needed that meets stringent requirements for use in the military and government sectors. This thesis explores the design and cryptanalysis of a novel, easily customizable AE algorithm based on the duplex construction. Emphasis is placed on designing a secure pseudorandom permutation (PRP) for use within the construction. A survey of state of the art cryptanalysis methods is performed and the resistance of our algorithm against such methods is considered. The end result is an algorithm that is believed to be highly secure and that should remain secure if customizations are made within the provided guidelines

On Sigma-Protocols and (packed) Black-Box Secret Sharing Schemes

$\Sigma$-protocols are a widely utilized, relatively simple and well understood type of zero-knowledge proofs. However, the well known Schnorr $\Sigma$-protocol for proving knowledge of discrete logarithm in a cyclic group of known prime order, and similar protocols working over this type of groups, are hard to generalize to dealing with other groups. In particular with hidden order groups, due to the inability of the knowledge extractor to invert elements modulo the order. In this paper, we introduce a universal construction of $\Sigma$-protocols designed to prove knowledge of preimages of group homomorphisms for any abelian finite group. In order to do this, we first establish a general construction of a $\Sigma$-protocol for $\mathfrak{R}$-module homomorphism given only a linear secret sharing scheme over the ring $\mathfrak{R}$, where zero knowledge and special soundness can be related to the privacy and reconstruction properties of the secret sharing scheme. Then, we introduce a new construction of 2-out-of-$n$ packed black-box secret sharing scheme capable of sharing $k$ elements of an arbitrary (abelian, finite) group where each share consists of $k+\log n-3$ group elements. From these two elements we obtain a generic ``batch\u27\u27 $\Sigma$-protocol for proving knowledge of $k$ preimages of elements via the same group homomorphism, which communicates $k+\lambda-3$ elements of the group to achieve $2^{-\lambda}$ knowledge error. For the case of class groups, we show that our $\Sigma$-protocol improves in several aspects on existing proofs for knowledge of discrete logarithm and other related statements that have been used in a number of works. Finally, we extend our constructions from group homomorphisms to the case of ZK-ready functions, introduced by Cramer and Damg\aa rd in Crypto 09, which in particular include the case of proofs of knowledge of plaintext (and randomness) for some linearly homomorphic encryption schemes such as Joye-Libert encryption. However, in the case of Joye-Libert, we show an even better alternative, using Shamir secret sharing over Galois rings, which achieves $2^{-k}$ knowledge soundness by communicating $k$ ciphertexts to prove $k$ statements

Computing Hilbert class polynomials with the Chinese Remainder Theorem

We present a space-efficient algorithm to compute the Hilbert class polynomial H_D(X) modulo a positive integer P, based on an explicit form of the Chinese Remainder Theorem. Under the Generalized Riemann Hypothesis, the algorithm uses O(|D|^(1/2+o(1))log P) space and has an expected running time of O(|D|^(1+o(1)). We describe practical optimizations that allow us to handle larger discriminants than other methods, with |D| as large as 10^13 and h(D) up to 10^6. We apply these results to construct pairing-friendly elliptic curves of prime order, using the CM method.Comment: 37 pages, corrected a typo that misstated the heuristic complexit

Investigating Lattice-Based Cryptography

Cryptography is important for data confidentiality, integrity, and authentication. Public key cryptosystems allow for the encryption and decryption of data using two different keys, one that is public and one that is private. This is beneficial because there is no need to securely distribute a secret key. However, the development of quantum computers implies that many public-key cryptosystems for which security depends on the hardness of solving math problems will no longer be secure. It is important to develop systems that have harder math problems which cannot be solved by a quantum computer. In this project, two public-key cryptosystems which are candidates for quantum-resistance were implemented using Rust. The security of the McEliece system is based on the hardness of decoding a linear code which is an NP-hard problem, and the security of the Regev system is based off of the Learning with Errors problem which is as hard as several worst-case lattice problems [1], [2]. Tests were run to verify the correctness of the implemented systems and experiments were run to analyze the cost of replacing pre-quantum systems with post- quantum systems