There are many recommended modes of operation for block ciphers as described by NIST here, e.g. for DES and AES.

However, I am struggling to find any for lightweight ciphers. I am particularly interested in modes of operation for PRESENT, Clefia and other standardised lightweight ciphers, and why they are suggested.

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    $\begingroup$ I'm not directly an expert on this, but common sense says to me that it mainly depends on the block size. The key size and internal structure of the block cipher has preciously little influence on the mode of operation: the block cipher just needs to be secure. PRESENT seems to have a block size of 64 bit, making the use of PRESENT in CTR mode and most authenticated modes of security a rather tricky endeavor (you could say that 64 bit block size is a rather big drawback in general, and you might want to consider lightweight stream ciphers as well). $\endgroup$ – Maarten Bodewes Oct 24 '18 at 11:50
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    $\begingroup$ There is only one I found A MAC Mode for Lightweight Block Ciphers $\endgroup$ – kelalaka Oct 24 '18 at 12:46
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    $\begingroup$ According to this slide NIST research idaed; New dedicated proposals,... new modes of operations $\endgroup$ – kelalaka Oct 24 '18 at 13:54

When using lightweight ciphers, the block size can make a huge difference to security. Fortunately, there has been a lot of work in recent years on tight bounds for modes of operations, and methods for going beyond the birthday bound. These modes are not stated as being especially for lightweight ciphers, so don't search for that. However, there is no doubt that when using lightweight ciphers with block sizes smaller than 128, then different modes of operation are needed (of course, depending on how much you want to encrypt). Here are three examples of work to look at (and the references therein):

  1. CENC is Optimally Secure
  2. New Blockcipher Modes of Operation with Beyond the Birthday Bound Security
  3. Better Bounds for Block Cipher Modes of Operation via Nonce-Based Key Derivation

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