Doctor of Philosophy (Ph.D.)
Significant links exist between cryptography and computational learning theory. Cryptographic functions are the usual method of demonstrating significant intractability results in computational learning theory as they can demonstrate that certain problems are hard in a representation independent sense. On the other hand, hard learning problems have been used to create efficient cryptographic protocols such as authentication schemes, pseudo-random permutations and functions, and even public key encryption schemes.;Learning theory / coding theory also impacts cryptography in that it enables cryptographic primitives to deal with the issues of noise or bias in their inputs. Several different constructions of "fuzzy" primitives exist, a fuzzy primitive being a primitive which functions correctly even in the presence of "noisy", or non-uniform inputs. Some examples of these primitives include error-correcting blockciphers, fuzzy identity based cryptosystems, fuzzy extractors and fuzzy sketches. Error correcting blockciphers combine both encryption and error correction in a single function which results in increased efficiency. Fuzzy identity based encryption allows the decryption of any ciphertext that was encrypted under a "close enough" identity. Fuzzy extractors and sketches are methods of reliably (re)-producing a uniformly random secret key given an imperfectly reproducible string from a biased source, through a public string that is called the "sketch".;While hard learning problems have many qualities which make them useful in constructing cryptographic protocols, such as their inherent error tolerance and simple algebraic structure, it is often difficult to utilize them to construct very secure protocols due to assumptions they make on the learning algorithm. Due to these assumptions, the resulting protocols often do not have security against various types of "adaptive" adversaries. to help deal with this issue, we further examine the inter-relationships between cryptography and learning theory by introducing the concept of "adaptive learning". Adaptive learning is a rather weak form of learning in which the learner is not expected to closely approximate the concept function in its entirety, rather it is only expected to answer a query of the learner's choice about the target. Adaptive learning allows for a much weaker learner than in the standard model, while maintaining the the positive properties of many learning problems in the standard model, a fact which we feel makes problems that are hard to adaptively learn more useful than standard model learning problems in the design of cryptographic protocols. We argue that learning parity with noise is hard to do adaptively and use that assumption to construct a related key secure, efficient MAC as well as an efficient authentication scheme. In addition we examine the security properties of fuzzy sketches and extractors and demonstrate how these properties can be combined by using our related key secure MAC. We go on to demonstrate that our extractor can allow a form of related-key "hardening" for protocols in that, by affecting how the key for a primitive is stored it renders that protocol immune to related key attacks.
© The Author
Goldenberg, David, "Adaptive learning and cryptography" (2010). Dissertations, Theses, and Masters Projects. Paper 1539623564.