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Abstract:
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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 . |