Can you give me a summary of cryptographic hardness assumptions? Until recently, I had a link to a website which summarizes up-to-date cryptographic hardness assumptions.
But, unfortunately I cannot find it.

The webpage is categorized well problems such as, DL problem, Factorization, Finite field, DH problems.
More importantly, such problems are very well organized.
For example, DH problem and most of its variants are listed with problem definition, introduced source (authors, paper name, etc.), and its applications.

What I had was not pdf file nor book chapter, just a webpage.
As I remember, its web structure is similar to http://hyperelliptic.org/ECRYPTII/vampire/

I think such a summary would be very helpful.
One of the links in the comments points to this paper, which has a very extensive list of various hardness assumptions used in cryptography. At the end of this post is an addendum that includes problems not found in the mentioned paper. The following is basically the table of contents from the paper:

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 $g^a, g^b ∈G$ to compute $g^{ab}$.

Reductions:


CDH $≤_{p}$ DLP
DLP $≤_{subexp}$ 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 $g_0,g_0^a,g_0^b ∈G$ to compute $g_0^{ab}$. This is $\equiv_{p}$ 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 Problem
AGCD: Approximate Greatest Common Divisor
SIP: Small Inverse Problem


Subset Sum/Knapsack problem


Subset Sum problem 


$(0, 1)$ knapsack problem (The standard version of the problem)

Bounded knapsack problem
Unbounded knapsack problem
RMSS: 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.