JooSeok Song 2007. public-key encryption. Security of a Cryptographic Algorithm should rely. 9.2 The RSA Algorithm sample RSA encryption/decryption is: given message M = 88(nb. ★ n=p.q, where p and q are distinct primes Proposed by Rivest, Shamir, and Adleman in 1977 and a paper was published in The Communications of ACM in 1978 A public-key cryptosystem RSA algorithm is a public key encryption technique and is considered as the most secure way of encryption. 2004/1/15 22 9.2 The RSA Algorithm Computational Aspects: Encryption and Decryption Square and Multiply Algorithm for Exponentiation a fast, efficient algorithm for exponentiation Because of its speed, it may have uses in certain applications. The RSA Algorithm Based on the idea that factorization of integers into their prime factors is hard. RSA is still seen in a range of web browsers, email, VPNs, chat and other communication channels. Algorithm. by the number of decimal digits: RSA-100, . Tue Private-Key Cryptography traditional private/secret/single key cryptography uses one key shared by both sender and receiver if this key is disclosed communications are compromised also is symmetric, parties are equal hence does not protect sender from receiver forging a message & claiming is sent by sender. 4 RSA RSA is a public-key cryptosystem for both encryption and authentication; it was invented in 1977 by Ron Rivest, Adi Shamir, and Leonard Adleman [RSA78]. The RSA Algorithm. 13. IDEA (International Data Encryption Algorithm) Ø Developed at ETH Zurich in Switzerland. 88 <187 ) • encryption: C=88 7mod 187 =11 • decryption: M=11 23 mod 187 =88 Exponentiation • can use the Square and Multiply Algorithm • a fast, efficient algorithm for exponentiation • concept is based on repeatedly squaring base RSA Numbers x x.., RSA-500, RSA-617. RSA: The first and the most popular . RSA Encryption. Public-Key Cryptography and RSA - Abstract We will discuss The concept of public-key cryptography RSA algorithm Attacks on RSA Suggested reading: Sections 4.2, 4.3, 8.1, 8.2, ... | PowerPoint PPT presentation | free to view ONLY on the . ... PowerPoint Presentation Last modified by: vinod Company: It was invented by Rivest, Shamir and Adleman in year 1978 and hence name RSA algorithm. 3. CCLAB Each RSA number is a semiprime. It was traditionally used in TLS and was also the original algorithm used in PGP encryption. 11. Ø Algorithms using 40-bits or less are used in browsers to satisfy export constraints Ø The algorithm is very fast. by the number of bits: RSA-576, 640, 704, 768, 896, , 151024 36, 2048. There are two labeling schemes. ... RSA Encryption Scheme. RSA Example - En/Decryption • sample RSA encryption/decryption is: • given message M=88 (NB. Each station randomly and independently choose two large primes p and q number, and multiplies them to produce n=pq. In the RSA algorithm, one party uses a public key and the other party uses a secret key, known as the private key. S/MIME Cryptographic Algorithms • digital signatures: DSS & RSA • hash functions: SHA‐1 & MD5 • session key encryption: ElGamal & RSA • message encryption: AES, Triple‐DES, RC2/40 and others • MAC: HMAC with SHA‐1 • have process to decide which algs to use S/MIME Messages 88<187) encryption: C = 887 mod 187 = 11 decryption: M = 1123 mod 187 = 88. (A nu mber is semiprime if it is the product of tw o primes.) 12.1 Public-Key Cryptography 3 12.2 The Rivest-Shamir-Adleman (RSA) Algorithm for 8 Public-Key Cryptography — The Basic Idea 12.2.1 The RSA Algorithm — Putting to Use the Basic Idea 12 12.2.2 How to Choose the Modulus for the RSA Algorithm 14 12.2.3 Proof of the RSA Algorithm 17 12.3 Computational Steps for Key Generation in RSA 21 It works as follows: take two large primes 512-bits, RSA1024-bits, p and q, and find their product N=pq and n is called the modulus. 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