This is a cryptography question from the book Introduction to Modern Cryptograph
ID: 3816701 • Letter: T
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This is a cryptography question from the book Introduction to Modern Cryptography by Katz and Lindell. If needed, please refer to the textbook's online pdf ( https://www.politicalavenue.com/libraryebooks/cryptology-and-cryptography/Introduction%20to%20Modern%20Cryptography.pdf ) (Exercise 10.17) to answer the question.
Consider the following protocol for two parties A and B to flip a fair coin coin. 1. A trusted party T publishes her public key A pk; 2. Then A chooses a uniform bit bA, encrypts it using pk, an announces the ciphertext CA to B and T 3. Next, B acts symmetrically and announces a ciphertext cB CA; 4. T decrypts both CA and CB, and the parties XOR the results to obtain the value of the coin. Argue that even if A is dishonest (but B is honest), the final value of the coin is uniformly distributed. Assume the parties use EI Gamal encryption (where the bit b is encoded as the group element g before being encrypted note that efficient decryption is still possible Show how a dishonest B can bias the coin to any values he likes. Suggest what type of encryption scheme would be appropriate to use here. Can you define an appropriate notion of security for a fair coin flipping and prove that the above coin flipping protocol achieves this definition when using an appropriate encryption scheme?Explanation / Answer
a)
if A is dishonest then it will not effect the result because it is given in 3 point that b is dong symmetrical but cb is not equal to ca hence A's dishonesty will not effect the uniformity of result
if it will use private key cryptography then it wll be more efficient for the encryption and decryption
As this the pubblic key cryptography it uses the key publicly where chances of dishonesty are more rather than using private key cryptography
hence private key crypto graphy is much more efficient then this
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