'Extended euclidean algorithm' diaporamas de présentation

Session 4

Session 4. Asymmetric ciphers. Contents. Definition of asymmetric (public key) ciphers Applications of asymmetric ciphers The public key encipherment procedure The RSA public key cipher system. KEY. KEY. encipher. Ciphertext. decipher. Plaintext. Plaintext. A. B. Cryptanalysis.

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Software Synthesis using Automated Reasoning

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Software Synthesis using Automated Reasoning

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Public Key Encryption

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Summary From the Last Lecture

Summary From the Last Lecture. Stream ciphers Encrypt chars/bits one at a time Assume XOR w the key, need long key to be secure Keystream generators (pseudo-random key) Synchronous and self-synchronizing Linear congruential generators LFSRs Block ciphers

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October 9, 2003

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1. The Euclidean Algorithm 2. The Fundamental Theorem of Arithmetic's

1. The Euclidean Algorithm 2. The Fundamental Theorem of Arithmetic's. Instructor: Hayk Melikyan melikyan@nccu.edu. Proof:. Example: (963, 657). So, (963, 657) = 9. Example: (450, 198)= ?. j r j r j+1 q j+1 r j+2 0 450 198 2 54

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Chapter 31: Euclidean Algorithm

Chapter 31: Euclidean Algorithm. Euclidean Algorithm Extended Euclidean Algorithm Solving ax mod n = 1 Solving ax mod n = b. Overview. Solving modular equations arises in cryptography Euclidean Algorithm From Euclid to solving ax mod n = 1

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RSA Encryption

RSA Encryption. William Lu. RSA Background. Basic technique first discovered in 1973 by Clifford Cocks of CESG (part of British GCHQ) Invented in 1977 by Ron Rivest, Adi Shamir and Len Adleman. RSA Uses. Public key encryption Digital signatures. RSA Algorithm.

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The Accelerated Euclidean Algorithm

The Accelerated Euclidean Algorithm. Sidi Mohamed Sedjelmaci Proceedings of the EACA, (2004) 283-287 EACA : Encuentro de Algebra Computational y Aplicaciones. Outline. Algorithm ILE Algorithm Example Algorithm AEA Algorithm Example Complexity. Algorithm ILE.

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Cryptanalysis of the Affine Cipher

Cryptanalysis of the Affine Cipher. Ciphertext-only attack: Brute-force (try possible keys) Frequency analysis Any other ideas ? Suppose we know two symbols and what they map to. Example: 0 ? 3 7 ? 10. Cryptanalysis of the Affine Cipher. More challenging examples: 4 ? 17

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