Quadratic Residues and Applications in Cryptography

The theory of quadratic residues (QR), a field of great importance in mathematics, has fully proved its usefulness in computer science as well. Thus, in 1992, S. Goldwasser and S. Micali introduced the concept of semantic security and exemplified it on a quadratic residuosity based cipher. In 2001, C. Cocks proposed, almost simultaneously with D. Boneh and M. Franklin, the first IBE scheme that lies its fundament on the theory of quadratic residuosity.Cocks' success in using QR to construct IBE schemes did little more than drive research toward the accentuated exploitation of this mathematical field in cryptography. As was the case, things went in two directions: algorithmization of purely mathematical properties of QR and their application in cryptography either.The doctoral work "Quadratic Residues and Applications in Cryptography" proposed by Anca-Maria Nica reaches both directions elegantly and brings contributions to them. In the first direction, the thesis focuses on the distribution of residues and non-residues in sets of integers of various types. In the second direction, the thesis brings contributions to the identity-based cryptography.Prof. Dr. Ferucio Laurenţiu Ţiplea