Factoring multivariate polynomials over algebraic number fields
SIAM Journal on Computing
Algorithmic number theory
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Generating a Large Prime Factor of p4 ± p2 + 1 in Polynomial Time
OTM '08 Proceedings of the OTM 2008 Confederated International Conferences, CoopIS, DOA, GADA, IS, and ODBASE 2008. Part II on On the Move to Meaningful Internet Systems
On Generating Elements of Orders Dividing p2k±pk + 1
IWSEC '08 Proceedings of the 3rd International Workshop on Security: Advances in Information and Computer Security
Generating elements of orders dividing p6 ± p5 + p4 ± p3 + p2 + p ± 1
Annales UMCS, Informatica - Cryptography and data protection
Practical cryptography in high dimensional tori
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Public-key cryptosystems based on cubic finite field extensions
IEEE Transactions on Information Theory
Factoring Polynomials over Special Finite Fields
Finite Fields and Their Applications
Algorithm for Generating Primes p and q Such that q Divides p4 ± p3 + p2 ± p + 1
Fundamenta Informaticae - Cryptology in Progress: 10th Central European Conference on Cryptology, Będlewo Poland, 2010
A Complete Generalization of Atkin's Square Root Algorithm
Fundamenta Informaticae
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We present a general method of generating primes p and q such that q divides Φnp, where n 2 is a fixed number. In particular, we present the deterministic method of finding a primitive nth roots of unity modulo q. We estimate the computational complexity of our methods.