Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A key distribution system equivalent to factoring
Journal of Cryptology
A key-exchange system based on imaginary quadratic fields
Journal of Cryptology
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Hash functions based on block ciphers: a synthetic approach
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
On the power of quantum computation
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Logical reversibility of computation
IBM Journal of Research and Development
Non-interactive public-key cryptography
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Testing shift-equivalence of polynomials using quantum machines
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Quantum computation of Fourier transforms over symmetric groups
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Quantum Fourier sampling simplified
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Normal subgroup reconstruction and quantum computation using group representations
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Efficient quantum algorithms for some instances of the non-Abelian hidden subgroup problem
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Quantum algorithms for solvable groups
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Quantum algorithms for some hidden shift problems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Trapped Ion Quantum Computer Research at Los Alamos
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
SOFSEM '99 Proceedings of the 26th Conference on Current Trends in Theory and Practice of Informatics on Theory and Practice of Informatics
Unconditionally Secure Digital Signature Schemes Admitting Transferability
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
One complexity theorist's view of quantum computing
Theoretical Computer Science - Algorithms,automata, complexity and games
Polynomial time quantum algorithm for the computation of the unit group of a number field
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Quantum algorithm for a generalized hidden shift problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
On quantum algorithms for noncommutative hidden subgroups
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Quantum random walks - new method for designing quantum algorithms
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
New developments in quantum algorithms
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Decomposing finite Abelian groups
Quantum Information & Computation
Quantum measurements for hidden subgroup problems with optimal sample complexity
Quantum Information & Computation
How a Clebsch-Gordan transform helps to solve the Heisenberg hidden subgroup problem
Quantum Information & Computation
Efficient quantum algorithm for identifying hidden polynomials
Quantum Information & Computation
On the quantum hardness of solving isomorphism problems as nonabelian hidden shift problems
Quantum Information & Computation
On the uselessness of quantum queries
Theoretical Computer Science
Computational indistinguishability between quantum states and its cryptographic application
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Finding hidden Borel subgroups of the general linear group
Quantum Information & Computation
Reduction from non-injective hidden shift problem to injective hidden shift problem
Quantum Information & Computation
Quantum Information & Computation
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Recently there has been a great deal of interest in the power of "Quantum Computers" [4, 15, 18]. The driving force is the recent beautiful result of Shor that shows that discrete log and factoring are solvable in random quantum polynomial time [15]. We use a method similar to Shor's to obtain a general theorem about quantum polynomial time. We show that any cryptosystem based on what we refer to as a 'hidden linear form' can be broken in quantum polynomial time. Our results imply that the discrete log problem is doable in quantum polynomial time over any group including Galois fields and elliptic curves. Finally, we introduce the notion of 'junk bits' which are helpful when performing classical computations that are not injective.