= 26 292 671 Superposition The mystery of How can a particle be a wave? Well, last week, Dark Reading[1], ... or how it works, as it’s the security of the keys that matters. Suppose Alice wants to send a message to Bob and in an encrypted way. Figure 16.3.1. This diagram shows the basic setup of computers and who says what. It's kind of clear at this point that we need to use some kind of encryption to make sure that the message is readable for Alice and Bob, but complete gibberish for Charlie. Using Bob's public key, Alice can compute a shared secret key. 6. Alice encrypted message with Bob’s Public Key . And then it would use for the AES128 for symmetric encryption. For example 3%2 is 3/2, where the remainder is 1). Now, Alice can send the message encrypting the message with Bob’s public key. Then, Alice and Bob can use symmetric cipher and … Public and private keys are two extremely large numbers, chosen such that there's a mathematical relation between them, and yet it's extremely hard (i.e. AES128 Encryption / Decryption. Meanwhile Bob has also chosen a secret number x = 15, performed the DH algorithm: g x modulo p = (5 15 modulo 23) = 19 (Y) and sent the new number 19 (Y) to Alice. The RSA Encryption Scheme Suppose Alice wants her friends to encrypt email messages before sending them to her. { _ } Kab means symmetric key encryption A Simple Protoco l An Example of Asymmetric Encryption in Action. - Because Bob knows k, he can efficiently recover m from F(k,m). Before sending a message to Bob, Alice would encrypt it with a secret key, turning plaintext into ciphertext; even if Eve intercepted the ciphertext, she could make no sense of it. For example, one may wish to encrypt files on a hard disk to prevent an intruder from reading them. X = 5 ^4 % 29 = 625 % 29 = 16 The receiver of the message (Alice) sends his public key to a sender (Bob). They're the basis of asymmetric cryptography. Alice takes Bob’s public key and uses it to encrypt the session key. E(A) → B : “I’m Alice” “I’m Alice” Elvis A Simple Protoco l Alice Bob {“I’m Alice”} Kab A → B : {“I’m Alice”} Kab If Alice and Bob share a key “Kab”, then Alice an encrypt her message. Some additional viewing Simon Singh's video gives a good explanation of key distribution. Since computers can use very complicated math to encrypt things, this stops people from trying a brute force attack to guess the numbers until it … What does this have to do with Alice, Eve and Bob – a security blog? Since Alice encrypts the message using Bob's public key, Bob is the only one who can decrypt it as only Bob has the private key. The best example to explain this is that of “Alice and Bob”. The example that you have stated provides confidentiality. 5. Alice and Bob agree on a public key algorithm. The message that Alice wants to send Bob is the number 1275. Bob wants to encrypt and send Alice his age – 42. Computers represent text as long numbers (01 for \A", 02 for \B" and so on), so an email message is just a very big number. Asymmetric encryption, often called "public key" encryption, allows Alice to send Bob an encrypted message without a shared secret key; there is a secret key, but only Bob knows what it is, and he does not share it with anyone, including Alice. Alice B “The Attacker” can pretend to be anyone. ? By using both private key and public key, the shared secret key would be generated. Using public-key authenticated encryption, Bob can encrypt a confidential message specifically for Alice, using Alice's public key. So, what are Alice and Bob to do? The sender (Bob) encrypts his message with the public key of the receiver (Alice). Since only Alice and Bob know their private numbers, this is a good way of sending secure information if the numbers are very big and the calculations are difficult. sent for future decryption by Bob. For example, take two users Alice and Bob. would take many billions of years) to derive the private key from the public key. Similarly, Alice has a key pair. If she wanted So, the the last three letters shift to the ﬁrst three. Notice that this protocol does not require any prior arrangements (such as agreeing on a key) for Alice and Bob to communicate securely. Notice they did the same calculation, though it may not look like it at first. Background . The message receiver (Alice) generates a private key and a public key. The public key is distributed to anyone who wants it, but the private key is kept only by the owner. Bob takes Alice's public result and raises it to the power of his private number resulting in the same shared secret. Eve obtains F(k,m), but since she doesn't know k, she cannot efficiently recover m (she can at best perform a brute-force attack). The breakthrough was the realisation that you could make a system that used different keys for encoding and decoding. Network and Communications Security (IN3210/IN4210) Diffie Hellman Key exchange Alice and Bob agree on (public parameters): − Large prime number p − Generator g (i.e. In 1978, Alice and Bob were introduced in the paper “A Method for Obtaining Digital Signatures and Public-key Cryptosystems,” which described a way to encrypt and authenticate data. They have written lots of papers that use Alice and Bob as examples (Alice / Bob fanfic, if you will). The receiver (Alice) decrypts the sender’s message (Bob) using her private key. Systems like this are call symmetric encryption, because Alice and Bob both need an identical copy of the key. Decoding Alice and Bob. The amazing thing is that, using prime numbers and modular arithmetic, Alice and Bob can share their secret, right under Eve's nose! This encrypted symmetric key is sent across the wire to Alice. We will look further at this in the next section. - Alice wants to send message m; she computes F(k,m) and sends it over the public network to Bob. For example: Suppose Alice wants to send a message to Bob and uses an encryption method. Bob starts by randomly generating a Symmetric Secret Key. We assume that the message \(m\) that Alice encrypts and sends to Bob is an integer. In a multi-user setting, encryption allows secure communication over an insecure channel. Map every letter to the letter that is three higher (modulo 26). General Alice’s Setup: Chooses two prime numbers. Using Alice's public key and his secret key, Bob can compute the exact same shared secret key. Alice now computes Y x modulo p = (19 6 modulo 23) = 2. A is 0, B is 1, C is 2, etc, Z is 25. Alice and Bob may use this secret number as their key to a Vigenere cipher, or as their key to some other cipher. For some cryptosystems, Alice and Bob must each hold a copy of the same key, which both encrypts and decrypts. ElGamal Encryption System by Matt Farmer and Stephen Steward. Bob has a pair of keys — public and private. Alice and Bob: Calling an encryption algorithm asymmetric is just a fancy way of saying that you need two different keys: one to encrypt, and one to decrypt. Let’s describe how that works by continuing to use Alice and Bob from above as an example. So her calculation was the same as 3 to the power 13 to the power 15 mod 17. The general scenario is as follows: Alice wishes to send a message to Bob so that no one else besides Bob can read it. The following shows the grouping after adding a bogus character (z) at the end to make the last group the same size as the others. For example, Alice may be writing a will that she wants to keep hidden in her lifetime. two people (Alice and Bob) using a padlocked box. x ? But Bob had the decryption key, so he could recover the plaintext. Example 16.2 Alice needs to send the message “ Enemy attacks tonight ” to Bob. 4) A worked example of RSA public key encryption Let’s suppose that Alice and Bob want to communicate, using RSA technology (It’s always Alice and Bob in the computer science literature.) If Eve gets the key, then she'll be able to read all of Alice and Bob's correspondence effortlessly. We give an introduction to the ElGamal Encryption System and an example in the video in Figure 16.3.1. Consider Alice, the 12 she received from Bob was calculated as 3 to the power 13 mod 17. Only Bob can then decrypt the encrypted session key, because he is the only one who knows the corresponding private key. [That’s not very interesting. Alice and Bob have agreed to divide the text into groups of five characters and then permute the characters in each group. Alice and Bob have wanted to exchange secret messages for the last 4000 years. You can … That is, Alice and Bob have exchanged a key, xab, that can now be used in a conventional cryptosystem to encrypt any messages between Alice and Bob. Alice and Bob in the Quantum Wonderland Two Easy Sums 7873 x 6761 = ? Alice and Bob are not considerably developed characters, but over the years, the convention of using these names has become an effective narrative device. Encrypting information is done by an encryption algorithm, which takes a key (for example a string) and gives back an encrypted value, called ciphertext. As we mentioned earlier in the symmetric encryption example, Bob is an undercover spy agent who’s on a secret mission in a foreign country and Alice is his case manager. Of course, the RSA algorithm deals with sending numbers, but seeing as any text can be converted to digits … Public Key Cryptography is a form of asymmetric encryption; For Bob to send Alice a message, ... Notice that Bob's first instruction (shown at right), for example, is to wait until he hears Alice announce something. For example, if Alice and Bob agree to use a secret key X for exchanging their messages, the same key X cannot be used to exchange messages between Alice and Jane. Both Bob and Alice exchanges their public keys. Let us take an example in which Bob and Alice are trying to communicate using asymmetric encryption. - Alice and Bob agree on a random, large key k, and both agree to keep it secret. Let’s understand this, as you rightly guessed, with the example of Alice and Bob once again. By encrypting it using personal secrets shared with Bob, only he can read it after her death but he does not need to be made aware of it by an explicit key transfer. Alice encrypts her message with Bob's public key and sends it to Bob. g is primitive root mod p) Alice: I did the example on the nRF51 with SDK 12.3. Encryption. One of the earliest techniques for this, called the Caesar Cipher, operates as follows. First imagine all letters as numbers. Encryption in transit: ... A simple example: Alice and Bob. In Chapter 12 we saw how a message can be encoded into integers. Bob decrypts Alice's message with his private key. ... for example, Alice and Bob don’t know each other’s private keys) The public key can be distributed – the idea is that if someone does know the public key, they still can’t decipher the message, so it can be considered as being available to anyone and it doesn’t matter if enemies know it or not . On the next page is the public key crypto widget. The RSA Encryption Scheme is often used to encrypt and then decrypt electronic communications. So A goes to D 1. To give an example: I plan to encrypt a piece of data under the AES algorithm[4], which allows for a particular type of (symmetric) encryption. In this case, the encryption algorithm is an alphabet shift, the letters are being shifted forward and number 2 is the key (shifted by two spaces). For example: Bob and Alice agree on two numbers, a large prime, p = 29, and base g = 5; Now Bob picks a secret number, x (x = 4) and does the following: X = g^x % p (in this case % indicates the remainder. Bob sends Alice his public key. For example, instead of the first letter of the alphabet (“A”) Bob and Alice will use the third letter (“C”), instead of the second (“B”) – the fourth one (“D”), and so on. Asymmetric ciphers are quite slow when compared with the symmetric ones, which is why asymmetric ciphers are used only to securely distribute the key. Bob now computes Y x modulo p = (8 6 modulo 23) = 2. 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