Efficient, provably secure code constructions



Journal Title

Journal ISSN

Volume Title



The importance of constructing reliable and efficient methods for securing digital information in the modern world cannot be overstated. The urgency of this need is reflected in mainstream media--newspapers and websites are full of news about critical user information, be it credit card numbers, medical data, or social security information, being compromised and used illegitimately. According to news reports, hackers probe government computer networks millions of times a day, about 9 million Americans have their identities stolen each year and cybercrime costs large American businesses 3.8 million dollars a year. More than 1 trillion worth of intellectual property has already been stolen from American businesses. It is this evergrowing problem of securing valuable information that our thesis attempts to address (in part). In this thesis, we study methods to secure information that are fast, convenient and reliable. Our overall contribution has four distinct threads. First, we construct efficient, "expressive" Public Key Encryption systems (specifically, Identity Based Encryption systems) based on the hardness of lattice problems. In Identity Based Encryption (IBE), any arbitrary string such as the user's email address or name can be her public key. IBE systems are powerful and address several problems faced by the deployment of Public Key Encryption. Our constructions are secure in the standard model. Next, we study secure communication over the two-user interference channel with an eavesdropper. We show that using lattice codes helps enhance the secrecy rate of this channel in the presence of an eavesdropper. Thirdly, we analyze the security requirements of network coding. Network Coding is an elegant method of data transmission which not only helps achieve capacity in several networks, but also has a host of other benefits. However, network coding is vulnerable to "pollution attacks" when there are malicious users in the system. We design mechanisms to prevent pollution attacks. In this setting, we provide two constructions -- a homomorphic Message Authentication Code (HMAC) and a Digital Signature, to secure information that is transmitted over such networks. Finally, we study the benefits of using Compressive Sensing for secure communication over the Wyner wiretap channel. Compressive Sensing has seen an explosion of interest in the last few years with its elegant mathematics and plethora of applications. So far however, Compressive Sensing had not found application in the domain of secrecy. Given its inherent assymetry, we ask (and answer in the affirmative) the question of whether it can be deployed to enable secure communication. Our results allow linear encoding and efficient decoding (via LASSO) at the legitimate receiver, along with infeasibility of message recovery (via an information theoretic analysis) at the eavesdropper, regardless of decoding strategy.