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Practical implementation and analysis of hyper-encryption

Jason K Juang

Published Jan 1, 2009• 4 citations
OpenAlex

Abstract

The security of modern cryptographic schemes relies on limits on computational power and assumptions about the difficulty of certain mathematical problems, such as integer factorization. This thesis describes hyper-encryption in the limited access model, a system that provides perfect secrecy and authentication against an adversary who possesses unbounded computational power, but who is limited in the ability to eavesdrop on more than a fraction of computers in a large network, such as the Internet.

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The security of modern cryptographic schemes relies on limits on computational power and assumptions about the difficulty of certain mathematical problems, such as integer factorization. This thesis describes hyper-encryption in the limited access model, a system that provides perfect secrecy and authentication against an adversary who possesses unbounded computational power, but who is limited in the ability to eavesdrop on more than a fraction of computers in a large network, such as the Internet.
Traditional modern cryptography relies on unproven complexity assumptions that certain problems, such as integer factorization, are computationally hard, and the adversary is bounded in computing power. However, advances in algorithms and computing technology may render current cryptosystems insecure, and lead to the decryption of past secret messages. On the other hand, Shannon's pessimistic negative result essentially implies that if the adversary is all-powerful and has complete access to the communication line, then efficient practical solutions for information-theoretic security do not exist. This thesis is a study of cryptography in the bounded storage model, where provable everlasting security can be achieved efficiently without any complexity assumption. It first presents an efficient scheme for encryption and authentication that is provably secure against strong adaptive attacks, by an adversary who is computationally unbounded and only storage-bounded. A major new result is that the shared secret key employed by the sender and the receiver can be re-used to send an exponential number of messages. Our encryption scheme further enjoys the surprising property that even if the secret key is captured by the adversary after the transmission of the ciphertext, the secrecy of the message is assured. The above is joint work with Michael Rabin. Oblivious transfer is a cryptographic protocol that can serve as a basic primitive for all of cryptography. This thesis presents an implementation of oblivious transfer in the bounded storage model, which is again provably secure without complexity assumption.
Motivation The ability to guarantee security and privacy in communication are critical factors in encouraging people to accept and trust new tools and methods for today's information-based society (e.g. in eCommerce or eHealth) and for future services (e.g. eGovernment, eVoting). Cybercrime already hinders these new possibilities by creating widespread mistrust in these new services. Another problem is that a (perhaps unpublicized) break-through in mathematics or computer science could completely compromise current state-of-the-art encryption methods overnight, even those which are the basis of all existing internet banking transactions. This is because the security of cutting-edge public-key cryptography (conventional cryptography) relies on the computational difficulty of certain mathematical tasks, meaning that conventional cryptography alone can neither provide any evidence of eavesdropping nor guarantee strong security. The trend towards faster electronics provides the ability to handle longer keys, thus providing better security, but also increases the possibility to break keys. This also has another worrying effect: even using today's most advanced available security technology to protect data during communication with best practice and without making any mistakes, the ongoing improvements in technology (which hence require longer key lengths to ensure security) mean that today's transmitted data will not be secure for more than a few years. Thus, while encrypted data might be safe today, it can still be stored by the adversary now and then broken later on once the future technology has caught up with today's encryption. Alternatively, modern quantum cryptography has created a new paradigm for cryptographic communication, which provides strong, long-term security and incontrovertible evidence of any attempted eavesdropping which is based on theoretically and experimentally proven laws of nature.
The fast growing of personal wireless communications, and the spreading of new services like Internet banking on mobile phones, has made the preventing unauthorized extraction of information a key problem for wireless systems. However, all the ciphering algorithms developed since now can be broken under an attack with unlimited computational resource. Consequently, the final goal of the cryptography is the developing of an unconditionally secure cryptographic system able to resist to any cryptanalytic attack, no matter how much computation power is available.
Quantum Computers are designed to be sufficiently large to be able to efficiently solve specific problems that would take an impractical amount of time to solve using classical computers. The most widely discussed application of quantum computing technology is more powerful algorithms, which efficiently solves all instances of integer factorization—a number theoretic problem that is the foundation of the most of the existing public-key encryption schemes. This means that all public-key cryptographic systems commonly used on the Internet for security will become as insecure as an open communication channel, easy to eavesdrop on or to tamper with. Moreover, traffic passes through numerous fixed, mobile and personal sensors connected to the Internet. This extremely large amount of data becomes the “air” of IoT and only a small part of it will be automatically analysed for a specific purpose. Nevertheless, an important part of the immense amount of data exchanged across the network is sensitive. Presently, these data communication and storage are protected by encryption, but that means of protection will be lost to a future quantum adversary. Because of these urgent necessities, products implementing quantum-resistant security solutions can be built and put into operation in a “post-quantum world”. This must be done now because cryptography research is currently inventing and standardizing new cryptographic algorithms. Once the new algorithms are widely and publicly agreed upon, systems with old encryption will remain vulnerable. This topic is motivated by the above.