What is RSA algorithm Rivest Shamir Adleman RSA is a cryptosystem for public key encryption, and is widely used for securing sensitive data, particularly when being sent over an insecure network such as the Internet. By submitting your personal information, you agree that Tech. Target and its partners may contact you regarding relevant content, products and special offers. You also agree that your personal information may be transferred and processed in the United States, and that you have read and agree to the Terms of Use and the Privacy Policy. RSA algorithm is asymmetric cryptography algorithm. Asymmetric actually means that it works on two different keys i. Public Key and Private Key. As the name. Comodo, the leading SSL Provider offers Free Antivirus, Internet Security, Firewall, Endpoint Security and other PC Security software for Windows all OS. NextGeneration Encryption NGE for Secure Connectivity at a Glance. A quick overview of Cisco NGE and how it can be used to help secure your networks. Rsa Encryption Program In C' title='Rsa Encryption Program In C' />RSA was first described in 1. Ron Rivest, Adi Shamir and Leonard Adleman of the Massachusetts Institute of Technology. Public key cryptography, also known as asymmetric cryptography, uses two different but mathematically linked keys, one public and one private. The public key can be shared with everyone, whereas the private key must be kept secret. In RSA cryptography, both the public and the private keys can encrypt a message the opposite key from the one used to encrypt a message is used to decrypt it. This attribute is one reason why RSA has become the most widely used asymmetric algorithm It provides a method of assuring the confidentiality, integrity, authenticity and non reputability of electronic communications and data storage. Many protocols like SSH, Open. PGP, SMIME, and SSLTLS rely on RSA for encryption and digital signature functions. It is also used in software programs browsers are an obvious example, which need to establish a secure connection over an insecure network like the Internet or validate a digital signature. RSA signature verification is one of the most commonly performed operations in IT. Explaining RSAs popularity. RSA derives its security from the difficulty of factoring large integers that are the product of two large prime numbers. Multiplying these two numbers is easy, but determining the original prime numbers from the total factoring is considered infeasible due to the time it would take even using todays super computers. The public and the private key generation algorithm is the most complex part of RSA cryptography. Two large prime numbers, p and q, are generated using the Rabin Miller primality test algorithm. A modulus n is calculated by multiplying p and q. This number is used by both the public and private keys and provides the link between them. Its length, usually expressed in bits, is called the key length. The public key consists of the modulus n, and a public exponent, e, which is  normally set at 6. The e figure  doesnt have to be a secretly selected prime number as the public key is shared with everyone. The private key consists of the modulus n and the private exponent d, which is calculated using the Extended Euclidean algorithm to find the multiplicative inverse with respect to the totient of n. A simple, worked example. Alice generates her RSA keys by selecting two primes p1. The modulus npq1. The totient of n np1xq11. She chooses 7 for her RSA public key e and calculates her RSA private key using the Extended Euclidean Algorithm which gives her 1. Bob wants to send Alice an encrypted message M so he obtains her RSA public key n,e which in this example is 1. His plaintext message is just the number 9 and is encrypted into ciphertext. C as follows Me mod n 9. CWhen Alice receives Bobs message she decrypts it by using her RSA private key d, n as follows Cd mod n 4. MTo use RSA keys to digitally sign a message, Alice would create a hash or message digest of her message to Bob, encrypt the hash value with her RSA private key and add it to the message. Bob can then verify that the message has been sent by Alice and has not been altered by decrypting the hash value with her public key. If this value matches the hash of the original message, then only Alice could have sent it authentication and non repudiation and the message is exactly as she wrote it integrity. Alice could, of course, encrypt her message with Bobs RSA public key confidentiality before sending it to Bob. A digital certificate contains information that identifies the certificates owner and also contains the owners public key. Certificates are signed by the certificate authority that issues them, and can simplify the process of obtaining public keys and verifying the owner. Security of RSAAs discussed, the security of RSA relies on the computational difficulty of factoring large integers. As computing power increases and more efficient factoring algorithms are discovered, the ability to factor larger and larger numbers also increases. Encryption strength is directly tied to key size, and doubling key length delivers an exponential increase in strength, although it does impair performance. RSA keys are typically 1. Barring an unforeseen breakthrough in quantum computing, it should be many years before longer keys are required, but elliptic curve cryptography is gaining favor with many security experts as an alternative to RSA for implementing public key cryptography. It can create faster, smaller and more efficient cryptographic keys. Much of todays hardware and software is ECC ready and its popularity is likely to grow as it can deliver equivalent security with lower computing power and battery resource usage, making it more suitable for mobile apps than RSA. Finally, a team of researchers which included Adi Shamir, a co inventor of RSA, has successfully determined a 4. RSA key using acoustic cryptanalysis, however any encryption algorithm is vulnerable to this type of attack. The inventors of the RSA algorithm founded RSA Data Security in 1. The company was later acquired by Security Dynamics, which was in turn purchased by EMC Corporation in 2. The RSA algorithm was released to the public domain by RSA Security in 2. How the RSA Cipher Works. Preface What is ThisThe RSA cipher is a fascinating example of how some of the most. Few are the mathematicians who study creatures like the prime numbers. But every now and then that is exactly. This text explains the mathematics behind RSA how and why it works. The intended audience is just about anyone who is interested in the. The most important mathematical facts necessary for understanding. RSAs foundations are reviewed near the beginning. Even if you are. familiar with everything covered in these sections, I would recommend. In one or two places, I have specifically targeted an explanation to. I consider to be the average computer programmer, leveraging. Before getting started, I should make some observations on the. For the most part, where notations for the same idea differ between. I have stuck with the mathematicians. This is, after all. However, I have deviated in a few places where. I have used to denote. PQ as shorthand for P Q. Since not all web browsers. I have used to denote exponentiation. This necessitates more parenthesizing than would normally be used. The mathematicians three bar congruency symbol is not available, so I. Variables are always named with a single. Finally, please note that throughout the text I use the word number. Introduction The Idea of a Trapdoor Function. What a mathematician refers to as a function is very similar to a. It is, in essence, an abbreviation. If X happens to be 3, then FX will be 6. So, F3 is shorthand. The same function in a C program might look like. Fint x. return 7 x 4. Of course, in a computer program, functions are used to encapsulate. In mathematics, however, a function is used solely for. And, given a certain number as input, they will. Thus, rand would not qualify as a. Mathematicians often consider how to construct a functions inverse. G6. 4 is equal to 3, and in general, GFX is equal to X. Therefore. G is Fs inverse. Not all functions are invertible, of course. Clearly, the function. Because how could GFX return X when FX is. Usually, when you have a mathematical function for which an inverse. In fact, it is often. Typically, you can just run through the steps backwards. But can it. be done for every invertible function To put the question in terms of programming, imagine that there are. And pretend for the moment that. Suppose. you are told that bar is the inverse of foo. The statement. x barfoox. Now, imagine that you have the source code for foo, but not for. Can you write your own replacement for bar, just by examining. It seems that you ought to be able to. There are no secrets as to what. You can run foo with different inputs as many. You already know that bar exists, somewhere, so. Is it guaranteed that you can. Theoretically speaking, the answer is yes. Given such an function, it. However, if we also throw. There are some special functions that, though what they do is simple. Such a creature is. Anyone can fall through a trapdoor, but only. In 1. 97. 5, Whitfield Diffie, Martin E. Hellman, and Ralph Merkle. Diffie and. Hellman published a paper in 1. And in 1. 97. 7, Ronald. L. Rivest, Adi Shamir, and Leonard Adleman outlined, in an MIT. What follows is a description of that function. Background, Part I How to Calculate with Exponents. Heres a quick refresher on how to combine exponents. Recall that. N2 N N, N3 N N N, N4 N N N N. For example. 27 2 2 2 2 2 2 2 1. If we fiddle with exponents for a bit, we will quickly realize that. So, for example. 27 2 1. Building upon this, we can also see that. But N N can also be written as N2. We can extrapolate from this, and derive a more general rule namely. And, if we repeated this process on the next level up, we would find. These two simple facts are very useful when handling exponent laden. Background, Part II Modulus Arithmetic. Most computer programmers are familiar with modulus as a remainder. For example. Though the idea is the same, the mechanics here are slightly different. In essence. modulus arithmetic consists of taking the infinitely long number line. All the numbers that land on. Thus, the analogue to the above example in modulus. Though note that mathematicians actually use a three barred version. In this case, 1. 2 is the. Likewise. 1. 1 plus 1. Modulus arithmetic is sometimes called clockface arithmetic if. Of course, the analogy is less perfect when the modulus is something. An important feature of modulus arithmetic is that you can replace the. Another example. 9. Even better, this trick also works with multiplication. If our modulus was 1. And, in a sense, a C program does all of its calculations in modulus. Screeching Weasel Television City Dream Reissue Rar there. Since integer calculations in C are permitted to overflow. C program. using 3. As you might imagine, some calculations that are time consuming and. The ability. to reduce values to their remainders before doing the actual. Background, Part III The Fundamental Theorem of Arithmetic. The Fundamental Theorem of Arithmetic states that for every number. It is guaranteed that there is no other way to break 1. And, certainly, any time you take three 2s, two 7s, and a. The Fundamental Theorem of Arithmetic assures us that both. By the way, this is one of the reasons that 1 is not considered to be. Instead, 1 is considered to have no prime factors at all. Put another way, the Fundamental Theorem of Arithmetic states that the. A number is therefore defined by its prime factorization. Background, Part IV Relatively Prime Numbers. The greatest common divisor abbreviated GCD of two numbers is the. For example. GCD1. GCD1. 8, 1. 0 2, GCD2. GCD1. 70, 1. 02 3. Or, another way to look at it is to say that the GCD is the. GCD23 31 72, 22 51 73 22 72, so GCD1. When two numbers have no common factors, their GCD will be 1, and the. For. example, we can see in our list up above that 2. Since a prime number has no factors besides itself, clearly a prime. And the same can be said of the number 1. Okay. Enough background material. Lets get to the good stuff. Eulers Totient Function. Eulers Totient Function is denoted by the Greek letter phi, and is. N how many numbers between 1 and N  1 which are relatively. How To Install Cccam In Dreambox there. Here is the same definition expressed as C code. N i. if gcdi, N 1. By the way, notice that phi1 is specially defined to be 1. It should be easy to see that phiN will be N  1 whenever N is. Somewhat less obvious is the useful fact that phiN is also. N has exactly two different prime factors. P Q P 1 Q 1, if P and Q are prime. The proof of this fact is left as an exercise for the reader. Its. actually not too hard. Thus, for example. The two prime factors cannot be the same number for this to work, and. Eulers Totient Theorem. This theorem is one of the important keys to the RSA algorithm. If GCDT, R  1 and T lt R, then TphiR  1 mod R. If T and R are relatively prime, with T being the smaller number, then. T with itself phiR times and divide the result by. R, the remainder will always be 1. We can test this theorem on some smaller numbers for which we have. Using 5 for T and 6 for R, we get. Using 2 for T and 1. R, we have. phi1. Variations on a Theme. Here again is the equation of Eulers Totient Theorem. T lt R, and T and R are relatively prime. Thanks to. the way that modulus arithmetic works on multiplication, we can easily. TphiR TphiR 1 1 mod R. TphiR phiR 1 1 mod R.