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Privacy in blockchain

1. Understanding Ring Signatures Anonymity and Security in Digital Signatures

2.   DEVELOPMENT PROGRAM FOR ARTIFICIAL INTELLIGENCE, DATA SCIENCE AND BLOCKCHAIN An Initiative by Prime minister of Pakistan M. Shahbaz Sharif

3. Team Members Dr Shahzaib Tahir Dr Sadiqa Arshad Major Ammar Major Bilal Miss Aimen Sultan M. Najaf Military College of Signals (NUST ) Colleges Islamabad Model Colleges for Girls, F-7/4 Islamabad Model Colleges for Girls F-10/2 Islamabad Model Colleges for Girls F-10/3 Islamabad Model Colleges for Girls I-8/3 Islamabad Model Colleges for Girls, Humak

4. Introduction to Ring Signatures Ring signatures provide a way to sign a message anonymously within a group. It allows someone to prove that a message was created by one of the members of a group without revealing which member specifically. Developed by Ron Rivest, Adi Shamir, and Yael Tauman in 2001, ring signatures ensure anonymity, unforgeability, and resistance to collusion. The signature scheme convinces a verifier that a document has been signed by one of n independent signers

5. 5 History:Ring Signature The scheme was first introduced in Japan. http://www.nihonkoenmura.jp/theme3/takarabito07.htm In 1756, a signature was generated as a proof of solidarity when farmers in a certain village resisted their ruler. A purpose of the shape of this signature is to hide their leader

6. 6 Derivation The signature scheme is called “KARAKASARENPAN”. Because the shape of the signature looks like Japanese traditional umbrella. An umbrella Joint signatures KARAKASA RENPAN

7. 7 Reason for a shape of ring Members sequentially signed like a ring, try to hide the order of signers. The members who participate in the signature take equal responsibility. If members simply signed, the first signer would be suspected of the leader .

8. 8 A signer can connect the head and tail of the series of values by using own secret key. A verifier computes series of values from the message and members’ public keys, and checks that a signature has a ring structure . Ring Signature : Present Anyone cannot distinguish a part of the signature which is used secret key. Anyone cannot distinguish the actual signer .

9. The White House Leak Dilemma Imagine a scenario where information is leaked from the White House. The president knows the information was leaked by one of his cybersecurity leads, but cannot determine which one

10. The White House Leak Dilemma This scenario illustrates the concept of a ring signature, where the identity of the signer remains hidden, yet the validity of the signature can be verified.

11. Creating the Ring Signature In a ring signature, a group of entities each has their own public/private key pairs ( P 1 , S 1 ), ( P 2 , S 2 ), ..., ( P n , S n ). To sign a message, the signer uses their secret key ( S i ) and the public keys of the other group members ( P 1 , P 2 , ..., P n ). The signature is verified using the public key of the group without revealing the signer's identity.

12. Creating the Ring Signature In a ring signature, a group of entities each has their own public/private key pairs ( P 1 , S 1 ), ( P 2 , S 2 ), ..., ( P n , S n ). To sign a message, the signer uses their secret key ( S i ) and the public keys of the other group members ( P 1 , P 2 , ..., P n ). The signature is verified using the public key of the group without revealing the signer's identity.

13. Basic Method for Ring Signatures Steps involved in creat ing a ring signature: 1. Generate encryption with k = Hash(message). 2. Generate a random value ( u ). 3. Encrypt u to give v = E k ( u ). For each group member (except the signer): a. Calculate e = S i ^{Pi} (mod N i ). b. Calculate v = v ⊕ e. 5. For the signer: a. Calculate S z = (v ⊕ u)^d (mod N z ). b. The result completes the ring signature.

14. Example: Bob Signing a Message Consider a group with Trent, Bob, Eve, and Alice, each having their own public and private keys. Bob wants to sign a message. He generates a random value (v) and random values (xi) for the others. Bob uses his secret key ( S i ) to create a reverse encryption key and then creates a hash (k) of the message. Each ring element is encrypted and linked using an EX-OR function. Bob computes the final ring signature, which can be verified by others without revealing his identity.