A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
An Efficient Digital Signature Scheme Based on an Elliptic Curve Over the Ring Zn
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Fast RSA-Type Cryptosystem Modulo pkq
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Finding Small Roots of Univariate Modular Equations Revisited
Proceedings of the 6th IMA International Conference on Cryptography and Coding
Riemann's Hypothesis and tests for primality
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Deterministic Polynomial-Time Equivalence of Computing the RSA Secret Key and Factoring
Journal of Cryptology
Deterministic Polynomial Time Equivalence between Factoring and Key-Recovery Attack on Takagi's RSA
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
A tool kit for finding small roots of bivariate polynomials over the integers
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Deterministic Polynomial Time Equivalence between Factoring and Key-Recovery Attack on Takagi's RSA
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
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For RSA, May showed a deterministic polynomial time equivalence of computing d to factoring N(= pq). On the other hand, Takagi showed a variant of RSA such that the decryption algorithm is faster than the standard RSA, where N = prq while ed = 1 mod (p-1)(q-1). In this paper, we show that a deterministic polynomial time equivalence also holds in this variant. The coefficient matrix T to which LLL algorithm is applied is no longer lower triangular, and hence we develop a new technique to overcome this problem.