Unconditionally Secure Cryptography

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Unconditionally secure cryptographic protocols refer to protocols that can be proven secure mathematically without the need for any assumptions regarding the intractability of underlying computational problems. The first example of an unconditionally secure cryptosystem was the one-time pad, which was proven secure by Shannon. There are by now many examples of many such schemes. Examples include certain types of authentication codes, secret sharing schemes, key predistribution schemes, commitment schemes, tracing schemes, broadcast encryption, and even some schemes that are most often studied in the public-key setting, such as signature schemes.***There has been increasing interest in post-quantum cryptography over the last 10-15 years, as an insurance policy in case a practical quantum computer is built. Indeed, the NSA announced in August 2015 that it intends to transition to quantum-resistant cryptography in its "Suite B'' of standardized cryptosystems. ***Most work in post-quantum cryptography involves constructing systems based on computational problems that are apparently hard to solve, even by quantum computers (e.g., lattice-based cryptography). Unconditionally secure cryptography can be regarded as the strongest form of post-quantum cryptography, since these protocols are by their very nature immune to attacks by (hypothetical) quantum computers.***Security proofs in unconditionally secure cryptography ultimately rely on considerations from information theory and probability. Roughly speaking, a security proof establishes that an adversary does not have sufficient information to be able to compute some specified secret information or to successfully carry out a specified attack. The construction of unconditionally secure cryptographic schemes typically involve methods and techniques from various branches of mathematics, including combinatorics, coding theory, finite fields, group theory, number theory, etc.***My objective is to continue to study various long-term research problems in unconditionally secure cryptography, as well as to initiate the study of new problems. Some specific research problems I plan to undertake include the following:***1. Construct new types of fingerprinting codes for tracing pirated content. ***2. Give new constructions for unconditionally secure proof-of-retrievability schemes, especially in the (distributed) setting which employs multiple servers.***3. Give new constructions and necessary conditions for algebraic manipulation detection codes and investigate connections with related mathematical structures and cryptographic primitives.***4. Give new constructions and necessary conditions for generalized all-or-nothing transforms. ***Research in these specific areas (and others) will lead to new unconditionally secure cryptographic techniques that will be valuable in securing the internet in a post-quantum setting.*** **