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I have spent some time studying the "Mental Poker" protocol (sometimes called SRA), initially proposed by Shamir, Rivest, and Adleman -- http://people.csail.mit.edu/~rivest/ShamirRivestAdleman-MentalPoker.pdf

Much of the current literature surrounding SRA deals with implementations, most of which seek to address specific problems like handling of the virtual card deck, player dropouts, and so on. I understand these to be protocol problems, not algorithmic problems or problems specific to the cryptosystem (algorithm + key generation and management). I'm interested in finding flaws or weaknesses within the cryptosystem.

So far I've noted:

  • Information leakage via quadratic residues / non-residues with a prime modulus (Legendre symbol)
  • Unpadded or poorly padded "plaintext" numerical values
  • Potentially novel approaches to the discrete logarithm problem (such as http://link.springer.com/chapter/10.1007%2F978-3-642-55220-5_1)
  • Short key lengths (similar to RSA key-pair bit lengths)
  • Use of a composite modulus rather than a prime
  • Weak Pseudo-Random Number Generator

Assuming one can sufficiently address known performance issues (like Crepeau's 8-hour-long card deal), does SRA have additional known weaknesses or drawbacks? Would some RSA caveats apply here too?

I noted the answer to What is the theoretical and practical status of mental poker?. This was an excellent reply but I did not notice mention of specific publications such as Don Coppersmith's "Cheating at Mental Poker".

I appreciate your comments.

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