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Discrete logarithm problem
DLP: discrete logarithm problem CDH: computational Diffie-Hellman problem SDH:…参考网址(科学上网) 密码学问题常见困难问题,需要点击参考网址进行查找 其困难问题的介绍非常友好请根据目录快速找到相关资料
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Discrete logarithm problem
DLP: discrete logarithm problem CDH: computational Diffie-Hellman problem SDH: static Diffie-Hellman problem gap-CDH: Gap Diffie-Hellman problem DDH: decision Diffie-Hellman problem Strong-DDH: strong decision Diffie-Hellman problem sDDH: skewed decision Diffie-Hellman problem PDDH: parallel decision Diffie-Hellman problem Square-DH: Square Diffie-Hellman problem l-DHI: l-Diffie-Hellman inversion problem l-DDHI: l-Decisional Diffie-Hellman inversion problem REPRESENTATION: Representation problem LRSW: LRSW Problem Linear: Linear problem D-Linear1: Decision Linear problem (version 1) l-SDH: l-Strong Diffie-Hellman problem c-DLSE: Discrete Logarithm with Short Exponents CONF: (conference-key sharing scheme) 3PASS: 3-Pass Message Transmission Scheme LUCAS: Lucas Problem XLP: x-Logarithm Problem MDHP: Matching Diffie-Hellman Problem DDLP: Double Discrete Logarithm Problem rootDLP: Root of Discrete Logarithm Problem n-M-DDH: Multiple Decision Diffie-Hellman Problem l-HENSEL-DLP: l-Hensel Discrete Logarithm Problem DLP(Inn(G)): Discrete Logarithm Problem over Inner Automorphism Group IE: Inverse Exponent TDH: The Twin Diffie-Hellman Assumption XTR-DL: XTR discrete logarithm problem XTR-DH: XTR Diffie-Hellman problem XTR-DHD: XTR decision Diffie-Hellman problem CL-DLP: discrete logarithms in class groups of imaginary quadratic orders TV-DDH: Tzeng Variant Decision Diffie-Hellman problem n-DHE: n-Diffie-Hellman Exponent problem
Factoring
FACTORING: integer factorisation problem SQRT: square roots modulo a composite CHARACTERd: character problem MOVAd: character problem CYCLOFACTd: factorisation in Z[θ] FERMATd: factorisation in Z[θ] RSAP: RSA problem Strong-RSAP: strong RSA problem Difference-RSAP: Difference RSA problem Partial-DL-ZN2P: Partial Discrete Logarithm problem in Z∗n DDH-ZN2P: Decision Diffie-Hellman problem over Z∗n Lift-DH-ZN2P: Lift Diffie-Hellman problem over Z∗n EPHP: Election Privacy Homomorphism problem AERP: Approximate e-th root problem l-HENSEL-RSAP: l-Hensel RSA DSeRP: Decisional Small e-Residues in Z∗n2 DS2eRP: Decisional Small 2e-Residues in Z∗n2 DSmallRSAKP: Decisional Reciprocal RSA-Paillier in Z∗n2 HRP: Higher Residuosity Problem ECSQRT: Square roots in elliptic curve groups over Z/nZ RFP: Root Finding Problem phiA: PHI-Assumption C-DRSA: Computational Dependent-RSA problem D-DRSA: Decisional Dependent-RSA problem E-DRSA: Extraction Dependent-RSA problem DCR: Decisional Composite Residuosity problem CRC: Composite Residuosity Class problem DCRC: Decisional Composite Residuosity Class problem GenBBS: generalised Blum-Blum-Shub assumption
Product groups
co-CDH: co-Computational Diffie-Hellman Problem PG-CDH: Computational Diffie-Hellman Problem for Product Groups XDDH: External Decision Diffie-Hellman Problem D-Linear2: Decision Linear Problem (version 2) PG-DLIN: Decision Linear Problem for Product Groups FSDH: Flexible Square Diffie-Hellman Problem KSW1: Assumption 1 of Katz-Sahai-Waters
Pairings
BDHP: Bilinear Diffie-Hellman Problem DBDH: Decision Bilinear Diffie-Hellman Problem B-DLIN: Bilinear Decision-Linear Problem l-BDHI: l-Bilinear Diffie-Hellman Inversion Problem l-DBDHI: l-Bilinear Decision Diffie-Hellman Inversion Problem l-wBDHI: l-weak Bilinear Diffie-Hellman Inversion Problem l-wDBDHI: l-weak Decisional Bilinear Diffie-Hellman Inversion Problem KSW2: Assumption 2 of Katz-Sahai-Waters MSEDH: Multi-sequence of Exponents Diffie-Hellman Assumption
Lattices
Main Lattice Problems
SVPγp: (Approximate) Shortest vector problem CVPpγ: (Approximate) Closest vector problem GapSVPpγ: Decisional shortest vector problem GapCVPpγ: Decisional closest vector problem
Modular Lattice Problems
SISp(n,m,q,β): Short integer solution problem ISISp(n,m,q,β): Inhomogeneous short integer solution problem LWE(n,q,φ): Learning with errors problem
Miscellaneous Lattice Problems
USVPp(n,γ): Approximate unique shortest vector problem SBPp(n,γ): Approximate shortest basis problem SLPp(n,γ): Approximate shortest length problem SIVPp(n,γ): Approximate shortest independent vector problem hermiteSVP: Hermite shortest vector problem CRP: Covering radius problem
Ideal Lattice Problems
Ideal-SVPf,pγ: (Approximate) Ideal shortest vector problem / Shortest polynomial problem Ideal-SISf,p q,m,β: Ideal small integer solution problem
Miscellaneous Problems
KEA1: Knowledge of Exponent assumption MQ: Multivariable Quadratic equations CF: Given-weight codeword finding ConjSP: Braid group conjugacy search problem GenConjSP: Generalised braid group conjugacy search problem ConjDecomP: Braid group conjugacy decomposition problem ConjDP: Braid group conjugacy decision problem DHCP: Braid group decisional Diffie-Hellman-type conjugacy problem ConjSearch: (multiple simlutaneous) Braid group conjugacy search problem SubConjSearch: subgroup restricted Braid group conjugacy search problem LINPOLY : A linear algebra problem on polynomials HFE-DP: Hidden Field Equations Decomposition Problem HFE-SP: Hidden Field Equations Solving Problem MKS: Multiplicative Knapsack BP: Balance Problem AHA: Adaptive Hardness Assumptions SPI: Sparse Polynomial Interpolation SPP: Self-Power Problem VDP: Vector Decomposition Problem 2-DL: 2-generalized Discrete Logarithm Problem
Problem Details
The full paper provides details about each assumption. Here is an example entry:
CDH: computational Diffie-Hellman problem
Definition :
Given ga,gb∈G to compute gab.
Reductions:
CDH ≤p DLPDLP ≤subexp CDH in groups of squarefree order.
Algorithms:
The best known algorithm for CDH is to actually solve the DLP.
Use in cryptography: Diffie-Hellman key exchange and variants, Elgamal encryption and variants, BLS signatures and variants.
History:
Discovered by W. Diffie and M. Hellman.
Remark:
A variant of CDH is: Given g0,ga0,gb0∈G to compute gab0. This is ≡p CDH.
References: W. Diffie and M. E. Hellman, New directions in cryptography, IEEE Transactions on Information Theory, vol. IT-22, No. 6, Nov. 1976, p. 644-654. U.M. Maurer and S. Wolf, Diffie-Hellman Oracles, Proceedings of CRYPTO ’96, p. 268-282. D. Boneh and R.J. Lipton Algorithms for Black-Box Fields and Applications to Cryp- tography, Proceedings of CRYPTO ’96, p. 283-297.
The complete text is far too long to copy paste here, but this provides a pretty good example of how extensive and thorough it is.
Addendum: Unlisted Problem(s)
The following problem(s) were not listed in the above reference:
MIHNP: Modular Inversion Hidden Number ProblemAGCD: Approximate Greatest Common DivisorSIP: Small Inverse Problem
Subset Sum/Knapsack problem
Subset Sum problem (0,1) knapsack problem (The standard version of the problem) Bounded knapsack problemUnbounded knapsack problemRMSS: Random Modular Subset Sum
Note about parameters
Hardness assumptions only hold when parameterized correctly. Inappropriate parameters can lead to easily solved instances of hard problems.
