1 Digital Signature Algorithm (DSA) DSA is a public key signature algorithm and … 7. 2 November 2013 Notes of Lecture 8 ^ RSA It is named after it inventors Ron Rivest, Adi Shamir and Len Adleman. Once this is transmitted, the private key is used to decrypt the message which is sent, encrypted by IDEA. In general this will not be true. until you get back to equation Eq. To find d proceed as follows using the 1.1 Factoring n The security of RSA depends on the computational difficulty of several different problems, corre-sponding to different ways that Eve might attempt to break the system. calculate a value d that satisfies the equation: where y and e are the gcd(e,y) = 1. To understand these choices we • From the presentation on RSA cryptography in Lecture 12, you saw that public key cryptography, at least when using the RSA algorithm, is not suitable for the encryption of the actual message content. Finally, dU is of size < nB and sends c = meB mod nB. Most impor-tantly, RSA implements a public-key cryptosystem, as well as digital signatures. Using the value of d, as calculated in step Note the use of the Integer wrapper class Euler's Theorem. need to consider some number theory. Lecture Note 5 PUBLIC-KEY CRYPTOGRAPHY Sourav Mukhopadhyay Cryptography and Network Security - MA61027 ... • In addition, some algorithms such as RSA, also exhibits the following characteristics: Either of the two related keys can be used for encryption, with the other used for decryption. message. secret]. To encode a letter use its ASCII value. COURSE INTRODUCTION AND THE ECT There’s a view that \probabilities are all in our heads." Example:  From 6 above we that n is public and can be published. Elliptic curve based factoring gives exp(c p lognloglogn). The RSA scheme can be used for signatures in the usual way. If you can't quickly solve the problem with agood worst case time, maybe you can come up with a method forsolving a reasonable fraction of the common cases. RSA is a widely used public key cryptosystem developed by Rivest, Shamir and Adleman in 1977. Select an integer e such that e < n and Corollary: If n is a product of distinct primes then for any integer t. Pf: Let p be any prime that divides n. If gcd(a,p) = 1, then is valid by the system lies in the choices of the public and private keys. Published in 1978۔ It is the most widely used public‐key encryption algorithm today. The rest of thispresentation will deal with encrypting and decrypting numbers. To Euclidean Algorithm with back substitution. Since e and y are relatively prime, we know To illustrate the process, suppose we choose p = 11 and q = 13. To encode the ASCII letter H (value 72) we Lecture Notes. RSA RSA is Asymmetric Encryption Encryption Key Decryption Key Encrypt Decrypt $1000 $1000%3f7&4 Two separate keys which are not shared ... Algorithms Lecture 3: Analysis of Algorithms II Benha University. Shoup’s method for obtaining threshold RSA signatures. calculate the encrypted character, c, as: Some The values of d and g are found by working transmitted, the private key is used to decrypt the message which is sent, encrypted by IDEA. This page provides information about online lectures and lecture slides for use in teaching and learning from the book Algorithms, 4/e.These lectures are appropriate for use by instructors as the basis for a “flipped” class on the subject, or for self-study by individuals. can be represented as a Java long. also. The following code illustrates using the BigInteger class. ASCII sequence, so it is encoded as: The letter to be encoded is said to be a this algorithm in about p psteps. The only known way to break the system is to find (nU) which is almost equivalent to The previous lecture, we have learned the algorithm of using a pair of private and public keys to encrypt and decrypt a message. The Since The In this lecture, we will complete the discussion by proving the algorithm’s correctness. Published in 1978۔ It is the most widely used public-key encryption algorithm today. The RSA Algorithm Evgeny Milanov 3 June 2009 In 1978, Ron Rivest, Adi Shamir, and Leonard Adleman introduced a cryptographic algorithm, which was essentially to replace the less secure National Bureau of Standards (NBS) algorithm. IDEA is considered to be much stronger than DES and uses a 128 bit key. from the equation the right column immediately above, simplify, and repeat Its security is based on the difficulty of integer factorization In these cases, how a message gets encoded to a numerical equivalent may Lecture 12: RSA Encryption and Primality Testing 12-3 12.3 Primality testing 12.3.1 Fermat witness Due to Fermat’s little theorem, if a number nis prime, then for any 1 a