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Understanding Digital Signatures: RSA vs. Elgamal Schemes

Explore the concepts and differences between RSA and Elgamal digital signature algorithms, their advantages, scope, and applications. Learn how these schemes ensure data integrity, authentication, non-repudiation, confidentiality, and timestamping.

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Understanding Digital Signatures: RSA vs. Elgamal Schemes

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  1. Digital Signatures Ajaykumar Poondla CSC 692

  2. Objective • The goal is to present the idea of digital signatures and the two commonly used digital signature algorithms • RSA Signature scheme • Elgamal Signature scheme

  3. Digital Signatures • Digital signature is a way of signing an electronic document in much the similar way that we sign conventional documents today.

  4. Advantages • Data Integrity. • Authentication. • Non-Repudiation. • Date-Time stamping.  • Confidentiality.

  5. Digital signature Schemes • RSA signature scheme. • Elgamal signature scheme.

  6. RSA signature scheme • R.L.Rivest, A.Shamir and L.Adleman proposed this method. • Bob computes C = Me mod n. • Bob sends C,M to Alice • Alice computes Cdmod n. • e.d = 1 mod(ø(n)).

  7. Scope of RSA signature Scheme • Used in VISA and Master cards. • Can be broken using the iteration attack. • The difficulty of breaking RSA signature scheme depends on solving the factorization of a large integer into two large prime factors.

  8. Proposed in 1985. • Non-Deterministic scheme. • Based on Discrete Logarithms. Elgamal signature scheme

  9. Details of the Elgamal Scheme • Calculate y = gx mod p • public key is (p, g, y), and the private key is x. • To sign a message, M choose k, such that k is relatively prime to p-1. • Compute a = gkmod p. • Find b in the following equation M = (xa + kb)mod(p –1). To verify the signature, confirm that Yaabmod p = gMmod p.

  10. Scope of Elgamal scheme • The difficulty of breaking Elgamal signature scheme depends on solving the discrete logarithm problem.

  11. References • An Introduction to cryptography and digital signatures. • R.L.Rivest, A.Shamir and L.Adleman A method for obtaining digital signatures and public-key cryptosystem. • ElGamal, T. A Public Key Cryptosystem and a Signature Scheme based on Discrete Logarithms IEEE Transactions on Information Theory, Vol.31, Nr.4, July 1985. • Md5 algorithm. http://rfc.sunsite.dk/rfc/rfc1321.html

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