Is there any existing obfuscation scheme that makes cipher text indistinguishable from plain text? Suppose a totalitarian government (in the name of anti-terrorism / protection of intellectual property):


has outlawed encryption itself - encryption is only approved for cases where the state has reviewed the design and made sure it can decrypt/inspect the message, and made any unapproved encryption a criminal offense
has total control over anything in and out of the network at ISP-level, as well as anything that passes through web services


How could two citizens Alice and Bob, using approved (and monitored) instant messaging service to set up a secure line of communication, conceal the fact that the communication is encrypted, i.e. to make it indistinguishable from unencrypted data, or at least, make it computationally- or financially-infeasible to distinguish it from plain text?

For example, no one would assume the following message to be encrypted:



  Across the Great Wall, we can reach every corner in the world.



But it would be assumed that the following is:



  WZ2A805Wq3rzpiuzE+ZCulgDrn76pVRW5PVUJ4DDadFQD4P9PsTeegbo5CAkqI4yZrO//p
  sYT+ZQkqZ6IrSGng==


  599D80F34E56AB7AF3A62BB313E642BA
  5803AE7EFAA55456E4F5542780C369D1
  500F83FD3EC4DE7A06E8E42024A88E32
  66B3BFFE9B184FE65092A67A22B4869E



For the purpose of this question, we assume the following technical details:


the IM service is text-only, binary data is not allowed (in an IM setting, sending primarily small binary fragments back and forth would probably raise suspicion anyway)
communication between Alice and the IM service, Bob and the IM service, are both end-to-end encrypted. A government agent Eve has a copy of the decryption key the IM service used
proof that the message is encrypted is not required. I.e. Eve does not need to know the plain text or the algorithm used to produce the cipher text. She only needs to tell, with a reasonably-low false-positive rate, if a message is the result of an encryption
the endpoint is secure, no backdoor or malware on the computer/router, etc.


I'd like to know if there are any reliable research on this, is it feasible or not, and if feasible, any existing protocol or algorithm developed for this?

Eve, in case you are watching, I'm asking this for academic purposes only.
As was mentioned, what you're asking for is a form of steganography,which may or may not use encrypted content.

The classic approach derives from talking around the subject (Crimes and Spies) as in: 

"The Apple crates are Golden Delicious. There are 15 crates."

A more technical approach I've seen is  Spam Mimmic

Spam Mimmic encode:  Bob, meet me at the secret lair at 1900.

Spam Mimmic decode:


  Dear Friend , We know you are interested in receiving  red-hot news !
  This is a one time mailing there is  no need to request removal if you
  won't want any more  . This mail is being sent in compliance with
  Senate  bill 1626 ; Title 1 , Section 307 ! THIS IS NOT MULTI-LEVEL 
  MARKETING ! Why work for somebody else when you can  become rich
  inside 31 DAYS ! Have you ever noticed  the baby boomers are more
  demanding than their parents  plus how many people you know are on the
  Internet !  Well, now is your chance to capitalize on this . WE  will
  help YOU use credit cards on your website plus  increase customer
  response by 120% ! You can begin  at absolutely no cost to you ! But
  don't believe us  . Mr Anderson who resides in Montana tried us and
  says  "My only problem now is where to park all my cars"  ! We are
  licensed to operate in all states . For the  sake of your family order
  now ! Sign up a friend and  you'll get a discount of 10% . Thanks .
  Dear Internet  user , This letter was specially selected to be sent 
  to you ! If you are not interested in our publications  and wish to be
  removed from our lists, simply do NOT  respond and ignore this mail .
  This mail is being sent  in compliance with Senate bill 1620 ; Title 9
  , Section  303 . This is not a get rich scheme . Why work for 
  somebody else when you can become rich within 92 WEEKS  . Have you
  ever noticed most everyone has a cellphone  plus nearly every
  commercial on television has a .com  on in it ! Well, now is your
  chance to capitalize on  this ! We will help you decrease perceived
  waiting  time by 120% and process your orders within seconds  . You
  can begin at absolutely no cost to you . But  don't believe us . Ms
  Ames of Mississippi tried us  and says "Now I'm rich, Rich, RICH" . We
  are licensed  to operate in all states . We urge you to contact us 
  today for your own future financial well-being . Sign  up a friend and
  your friend will be rich too . God  Bless ! Dear Web surfer ; This
  letter was specially  selected to be sent to you ! If you are not
  interested  in our publications and wish to be removed from our 
  lists, simply do NOT respond and ignore this mail .  This mail is
  being sent in compliance with Senate bill  1619 ; Title 3 ; Section
  301 ! THIS IS NOT MULTI-LEVEL  MARKETING . Why work for somebody else
  when you can  become rich in 41 DAYS ! Have you ever noticed people 
  love convenience plus most everyone has a cellphone  . Well, now is
  your chance to capitalize on this !  We will help you deliver goods
  right to the customer's  doorstep and deliver goods right to the
  customer's  doorstep . You can begin at absolutely no cost to you  .
  But don't believe us . Mrs Simpson of Montana tried  us and says "My
  only problem now is where to park all  my cars" ! This offer is 100%
  legal ! DO NOT DELAY 
  - order today . Sign up a friend and you'll get a discount  of 50% ! Warmest regards !


It's rather wordy and not practical for heavy use, but it gives you an idea. In general auto generating believable text is very difficult, hence the use of SPAM as it tends to blend in with other unbelievable text.