A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
The Relationship Between Breaking the Diffie--Hellman Protocol and Computing Discrete Logarithms
SIAM Journal on Computing
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
On the Security of ElGamal Based Encryption
PKC '98 Proceedings of the First International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
The Decision Diffie-Hellman Problem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Number-theoretic constructions of efficient pseudo-random functions
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
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In this paper, we show that curves which are defined over a number field of small degree but have a large torsion group over the number field have considerable cryptographic significance. If those curves exist and the heights of torsions are small, they can serve as a bridge for prime shifting, which results a nonuniform polynomial time algorithm to solve DDH on finite fields and a nonuniform subexpontial time algorithm to solve elliptic curve discrete logarithm problem. At this time we are unable to prove the existence of those curves. To the best of our knowledge, this is the first attempt to apply the ideas related to the Uniform Boundedness Theorem(UBT), formerly known as Uniform Boundedness Conjecture, in cryptography.