Information Theoretic Security Guarantees against More Capable Adversaries

Restricted (Penn State Only)
Author:
Nafea, Mohamed Saeed
Graduate Program:
Electrical Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
August 31, 2018
Committee Members:
  • Aylin Yener, Dissertation Advisor
  • Aylin Yener, Committee Chair
  • David Jonathan Miller, Committee Member
  • Viveck Ramesh Cadambe, Committee Member
  • Jan Severin Reimann, Outside Member
Keywords:
  • Information theoretic security
  • Wiretap channel
  • MIMO wiretap channel
  • Secure degrees of freedom
  • Interference alignment
  • Cooperative jamming
  • Adversarial resource advantage
  • Wiretap Channel II
  • Strong secrecy
  • Concentration of measures
  • Designed adversarial attacks
  • Chosen ciphertext attack
  • Coded caching
  • Secure coded caching
  • Cache tapping
  • Generalized wiretap model
  • Generalized multi-terminal wiretap models
  • Type II adversaries
Abstract:
With the recent growth in network connectivity, the issue of securing information against unauthentic and adversarial parties has become essential. By exploiting the intrinsic noise in physical communication channels, provable --information theoretic-- security guarantees can be provided even against adversaries with unlimited computation capabilities. Earlier approaches in physical layer security typically assume the adversary is weaker than the legitimate terminals, and is a passive entity which does not design attacks. This thesis aims at addressing these issues, with the goal of bringing the information theoretic security vision closer to reality. Our approach includes introducing stronger adversaries in existing models, as well as introducing new adversarial models in emerging communication systems. We begin with considering the multiple antenna Gaussian wiretap channel. An adversary which has resources to deploy more antennas than the legitimate terminals can deteriorate, or even preclude, secure communication. Enlisting a multiantenna terminal with the specific goal of diminishing the adversary's reception can re-enable secure communication. Towards that end, we characterize the secrecy capacity pre-log factor, i.e., the secure degrees of freedom (s.d.o.f.), of the multiple antenna wiretap channel with a multiantenna cooperative jammer, for all possible antenna configurations. Achievability is established by developing a variety of signaling, beamforming, and alignment schemes which vary according to the relative number of antennas at each terminal. Among these schemes, we devise a projection and cancellation decoding scheme that is optimal for certain antenna configurations. Our results show that positive s.d.o.f. is attainable as long as the combined number of transmit antennas is greater than the number of the adversary's antennas. We next turn our focus to the wiretap II channel, introduced back in 1984. The wiretap II channel provides an adversary model that is well received mainly due to its elegance in featuring a designed attack. Additionally, the model has an impact on several problems such as secure network coding, linear codes for secrecy, and adversarial erasure channels. The original communication theoretic version of the model has remained linked to the noiseless legitimate channel assumption for almost three decades. We introduce a noisy, i.e., discrete memoryless, legitimate channel to the model, and derive inner and outer bounds on its capacity-equivocation region, which match for certain cases. The achievability relies on combining random coding and random partitioning. Subsequently, we introduce a generalized wiretap channel model which subsumes both the classical wiretap and wiretap II with a noisy main channel models as special cases. In this model, the adversary chooses a subset of the codeword symbols to tap into, while observing the remainder through a noisy channel. We identify the strong secrecy capacity of the model, and show that it is identical to the secrecy capacity when the subset is randomly chosen by nature. Achievability is established by utilizing source-channel duality, and concentration of measures to prove a super-exponential convergence rate for the security measure, which dominates the exponentially many possible strategies for the adversary. Converse is derived by using Sanov's theorem in method of types. Next, we investigate several multi-terminal extensions of our generalized wiretap model, including the multiple access and broadcast wiretap channels, and the interference and broadcast channels with confidential messages. These extensions require non trivial generalizations of the tool set we develop for the single user case. Our results for the generalized wiretap model and its multiterminal extensions demonstrate the robustness of stochastic wiretap encoding against a powerful adversary which chooses where to tap. Finally, we introduce a new model, namely the notion of cache tapping into the information theoretic models of coded caching, in which the adversary taps into a subset of symbols of its choice either from the cache placement, delivery, or both phases. The legitimate parties know neither the relative fractions of tapped symbols in each phase, nor their positions. We identify the strong secrecy capacity for the instance of two users and two library files. We derive lower and upper bounds on the strong secrecy file rate for a library size of three or larger. Achievability is established by a code design which integrates wiretap coding, security embedding codes, one-time pad keys, and coded caching techniques. Our results establish that strong information theoretic security is possible against a powerful adversary which optimizes its chosen attack over both phases of communication in a cache-aided system.