Seminars

 11.00 AM, Seminar Hall Finding quadratic non-residue over finite fields Rajat Mittal IIT Kanpur. 01-12-16 Abstract It is known that finding square roots is equivalent to solving quadratic equations over finite fields. By Tonelli-Shanks algorithm, finding square roots is equivalent to finding an element in the finite field which does not have a square root (called a quadratic non-residue). We will show that given an irreducible polynomial of even degree over \$\mathbb{F}_p\$, we can find quadratic non-residues in any finite field of characteristic \$p\$. If time permits, we will show that this can be generalized to \$r\$th non-residues. This is joint work with Vishwas Bhargava and Nitin Saxena.