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Random oracles are practical: a paradigm for designing efficient protocols
CCS '93 Proceedings of the 1st ACM conference on Computer and communications security
Improved low-density subset sum algorithms
Computational Complexity
Lattice basis reduction: improved practical algorithms and solving subset sum problems
Mathematical Programming: Series A and B
A course in computational algebraic number theory
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Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
The random oracle methodology, revisited (preliminary version)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Elliptic curves in cryptography
Elliptic curves in cryptography
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Cryptography: Theory and Practice,Second Edition
Cryptography: Theory and Practice,Second Edition
Number Theory for Computing
Making, Breaking Codes: Introduction to Cryptology
Making, Breaking Codes: Introduction to Cryptology
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Handbook of Applied Cryptography
Handbook of Applied Cryptography
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Efficient Identification and Signatures for Smart Cards
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Chosen Ciphertext Attacks Against Protocols Based on the RSA Encryption Standard PKCS #1
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
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
NTRU: A Ring-Based Public Key Cryptosystem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Malicious Cryptography: Exposing Cryptovirology
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The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions
Multi-signatures in the plain public-Key model and a general forking lemma
Proceedings of the 13th ACM conference on Computer and communications security
To Solve the High Degree Congruence
CIS '07 Proceedings of the 2007 International Conference on Computational Intelligence and Security
A polynomial time algorithm for breaking the basic Merkle-Hellman cryptosystem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Fast LLL-type lattice reduction
Information and Computation
Security proofs for signature schemes
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
The exact security of digital signatures-how to sign with RSA and Rabin
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
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EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Cryptanalysis of short RSA secret exponents
IEEE Transactions on Information Theory
New directions in cryptography
IEEE Transactions on Information Theory
Hiding information and signatures in trapdoor knapsacks
IEEE Transactions on Information Theory
A public key cryptosystem and a signature scheme based on discrete logarithms
IEEE Transactions on Information Theory
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In this paper, the authors give the definitions of a coprime sequence and a lever function, and describe the five algorithms and six characteristics of a prototypal public key cryptosystem which is used for encryption and signature, and is based on three new problems and one existent problem: the multivariate permutation problem (MPP), the anomalous subset product problem (ASPP), the transcendental logarithm problem (TLP), and the polynomial root finding problem (PRFP). Prove by reduction that MPP, ASPP, and TLP are computationally at least equivalent to the discrete logarithm problem (DLP) in the same prime field, and meanwhile find some evidence which inclines people to believe that the new problems are harder than DLP each, namely unsolvable in DLP subexponential time. Demonstrate the correctness of the decryption and the verification, deduce the probability of a plaintext solution being nonunique is nearly zero, and analyze the exact securities of the cryptosystem against recovering a plaintext from a ciphertext, extracting a private key from a public key or a signature, and forging a signature through known signatures, public keys, and messages on the assumption that IFP, DLP, and LSSP can be solved. Studies manifest that the running times of effectual attack tasks are greater than or equal to O(2^n) so far when n=80, 96, 112, or 128 with lgM~696, 864, 1030, or 1216. As viewed from utility, it should be researched further how to decrease the length of a modulus and to increase the speed of the decryption.