If you know the first hash value and the hash algorithm, then you can iteratively derive the entire hash chain.

I was asking for example; there is a chain

Hash1.....Hash2.....Hash3.....Hash4......Hash5......Hash6......Hash7

an adversary delete "Hash3.....Hash4......Hash5......Hash6" can we recover the the chain by any mean?

short answer: If the hash algorithm is a cryptographic secure function (which it should be in general) it shall not be possible to revert even one hashing step.

Albeit an adversary deletes some of your hash values, you should know your own hash function and be able to recover them.

long answer:

a hash function will always return the same output for a given input. The (bit-)length of the output marks the number of different outputs possible; i.e. sha256 returns 2 power 255 different outputs. Obviously it is therefore possible, that two inputs passed through the hash function generate the same output (so called collisions). Cryptographic secure hash functions have proved to distribute the outcome over the possible output number space and produce a very low numbers of collisions while generating big differences in outcome even with small differences between the input.

Reverting a hash function is hard because of the before mentioned distribution and furthermore because you can not guess the number of input-bits from the output (fixed length).

Since the input-output relation in a known hash function is constant, reverting the input from output is possible, if the number of input-bits is known ( i.e. 8 Byte passwords) and you have a collection of all the in-out results (i.e. md5 rainbow tables for 8 Byte inputs).

This said, Günter Fahrnberger is right to claim that restoring the hash sequence in your example is possible if 1. the first input is known and 2. all hash functions are known.

Anyway, using hash functions in a sequence like you described h1-h2-..-h7 does make very very little sense if always the same hash function is used - it does not improve hash security in any way and may even decrease it.

Usually it is better by all means to choose one cryptographic secure hash function with an appropriate output space: i.e. 512bit from sha512 or blake2s .

Under certain circumstances you might need to preserve a weak hash (i.e. md5) to not break an older software while improving it's security. In general chaining hash functions is weaker than hashing a mix-concat of two different hash functions:

I -> h1 (i.e. old md5 password hash)

                                     mix/concat h1xh2 -> h3 (i.e. blake2s) --> store for pw check

I -> h2 (i.e. sha512 password hash)

Answering the question regarding the example "Hash1.....Hash2.....Hash3.....Hash4......Hash5......Hash6......Hash7". As Günter Fahrnberger mentioned it, it can be reconstructed, since in your example you still have Hash1 and thus you just have to iteratively compute the hash to reconstruct the chain and you do not have to be able revert it.

A comment on the statement:

"Anyway, using hash functions in a sequence like you described h1-h2-..-h7 does make very very little sense if always the same hash function is used"

Hash chains have meaningful applications in cryptography, for a survey see (Thomas Page's PhD thesis "The application of hash chains and hash

structures to cryptography" 2009) and for a specific example the TESLA authentication protocol (Adrian Perrig, Ran Canetti, J.D. Tygar, and Dawn Xiaodong Song. Efficient authentication and signing of multicast

streams over lossy channels. In IEEE Symposium on Security and Privacy, May 2000) 

@ Janos Follat

thanks for pointing at Thomas Page's PhD thesis "The application of hash chains and hash structures to cryptography" 2009. Interesting reading. Obviously there are indeed useful applications of combining hashes in various ways.

My comment about hash chains was directed at the fact that hash chaining reduces the input length of h2...hx from 'unlimited' to the length of h1'th output.

If you chain for example FNV32 Hash functions (please note that the original question did not mention cryptographic secure algorithms) the input length from h2..h7 is 32 bits only. Thus when chaining hash functions with an output length smaller than the first original input, distribution width within a chain will decrease in relation to the original variability.

Furthermore the collision probability of the total chain h1->h2->...hx might increase. Thomas Page referred to this at p.43 & p.44 (3.1.4.3 ff.). If simply chaining hash functions like h1->h2->h2...->hx  security might decrease therefore in relation to their onetime usage.

thanks @Andreas Briese and @ Janos Follat for the fruitfull discussion on hash. my question was not to revert the hash value. what I meant is, For Instance there is chain:

1. User1, password1, C1=H(password1)

2. User2, password2, C2=H(password2)||C1

3. User3, password3, C3=H(password3)||C2

4. User4, password4, C4=H(password4)||C3

5. User5, password5, C5=H(password5)||C4

6. User6, password6, C6=H(password6)||C5

An adversary deletes some records i.e 2,3,4 and 5 as a result the chain becomes:

1. User1, password1, C1=H(password1)

6. User6, password6, C6=H(password6)||C5.

Can we by any mean reconstruct the chain? and how ?

You can use the (t,n) threshold mechanism to construct a hash chain,  t/n is close to the packet loss probability

@Indrees Ahmed

what does the "||" in the expression C6=H(password6)||C5 mean ? 

@andreas Briese

'||' =concatanation

@Indrees Ahmed

if it means concatenation, then h7 would have 7 times the length of h1 ? 

if yes, cut h7 into 7 pieces of length h1, assign the pieces to h1… h7 and you have all seven hashes recovered.

if instead h7 has the same length as h1, the expression h7 = hash(pw7)||h6 is incorrect and is h7 = hash(pw7||h6) instead. In that case, you would need to revert the hash functions backward to recover the deleted hashes h2..h6. Then my first answer from two days ago would apply and i doubt you can recover the information without having the password2 … password6 which means the full information of about who attended in each conversation.

(i might add, that you may also assign the problem to a developer experienced with this type of sec problems like my bureau to get your problem solved.)

Another simple (and well-known) possibility is to use binary linking schemes, i.e., to link each node with the previous one and a well-chosen other node. Depending on concrete circumstances you can design such a scheme to satisfy various security requirements, including resistance to deletion. 

googling "time-stamping" "binary linking scheme" might help.