Post - Quantum Cryptography Using Complexity Doctoral

In order to cope with new technologies such as quantum computing and the possibility of developing new algorithms, new cryptosystems should be developed based on a diverse set of unrelated complexity assumptions so that one technique will not break more than a handful of systems. As demonstrated by Shor in 1994, quantum algorithms are known to break traditional cryptosystems based on RSA and Diffie-Hellman. Therefore, post-quantum systems are needed to provide security should quantum computers become a reality. In this thesis, we develop two post-quantum cryptographic primitives: a symmetric-key cipher using two new cipher design techniques and a solution to the secure set membership problem. The new techniques in the symmetric-key cipher are polymorphic S-boxes and pseudo-independent subkeys. The secure set membership primitive includes a distributed protocol for set establishment and a proofof-possession protocol to show set membership without revealing the member of the set. The symmetric-key cipher is based on state-of-the-art cipher designs alongwith our new cipher design techniques. This makes its base properties predictable while adding what we believe to be new difficulties for the cryptanalyst. The polymorphic S-box technique may be used with new ciphers while existing ciphers may be retrofitted to use pseudo-independent subkeys. We use a subset of the instances of the 3SAT witness-finding problem in developing a new complexity assumption for the secure set membership primitive. It is risky to base cryptosystems onNP-complete problems, as what is hard in the worst