That's not really the point. With SHA1/MD5 etc you may only ensure integrity against random non-malicious errors. But think of a malicious attacker targeting existential forgery using chosen message attack where she may change both the message and the hash.
Don't think I'm missing your idea to secure only the hash distribution, but you simply delay the same problem one step ahead. So you decouple the hashes [h{1}, h{2}, ... h{n}] from the contents (or messages) they are derived from. [m{1}, m{2}.. m{n}) and you think you may ensure the secure distribution of the hashes without their "messages". Now in recursion your new "content" are now those hashes which require their own confidentiality and integrity check which may better be done using an authenticated encryption with mac. Ultimately an attacker may simply forge hashes and provide contents for them.
Think of 10K of linux distro files with hashes being the target of a malicious government who wants to install modified versions of those files. Only SHAx etc won't help you to achieve "integrity". At some point you need secure hashes or macs (which are hashes secured with keys).
That's not really the point. With SHA1/MD5 etc you may only ensure integrity against random non-malicious errors. But think of a malicious attacker targeting existential forgery using chosen message attack where she may change both the message and the hash.
Don't think I'm missing your idea to secure only the hash distribution, but you simply delay the same problem one step ahead. So you decouple the hashes [h{1}, h{2}, ... h{n}] from the contents (or messages) they are derived from. [m{1}, m{2}.. m{n}) and you think you may ensure the secure distribution of the hashes without their "messages". Now in recursion your new "content" are now those hashes which require their own confidentiality and integrity check which may better be done using an authenticated encryption with mac. Ultimately an attacker may simply forge hashes and provide contents for them.
Think of 10K of linux distro files with hashes being the target of a malicious government who wants to install modified versions of those files. Only SHAx etc won't help you to achieve "integrity". At some point you need secure hashes or macs (which are hashes secured with keys).