\newcommand{\xx}{\mathtt{\#}} This topic presents a list of the learning outcomes for the module; Symmetric Key Cryptography, from the course: Advanced Diploma in Cryptography. \newcommand{\Th}{\mathtt{h}} Mathematical Underpinnings of Asymmetric Cryptography Abstract The mathematics of the Diffie-Hellman-Merkle key exchange and of RSA are explored. It also uses the same mathematical permutation, known as a key, to decrypt messages. Descriptions of cryptographic protocols are commonly phrased as interactions between Alice, Bob, and Eve. \newcommand{\PP}{\mathbb{P}} \newcommand{\Tv}{\mathtt{v}} \newcommand{\ZZ}{\Z} \newcommand{\lcm}{\mathrm{lcm}} The sender and the recipient should know the secret key that is used to encrypt and decrypt all the messages. In this scenario, the receiver of the message is actively involved in the process as well, instead of just being a passive passenger. Symmetric cryptography was well suited for organizations such as governments, military, and big financial corporations were involved in the classified communication. \newcommand{\Tj}{\mathtt{j}} \newcommand{\blanksp}{\underline{\hspace{.25in}}} An algorithm is a specific formula with a limited number of steps that contains instructions for solving a problem, and a symmetric-key algorithm is a specific formula that often uses the same cryptographic key for both encryption and decryption. \newcommand{\Tb}{\mathtt{b}} \(\newcommand{\longdivision}[2]{#1\big)\!\!\overline{\;#2}} [7] See the ISO/IEC 13888-2 standard. Nearly all modern cryptographic systems still use symmetric-key algorithms internally to encrypt the bulk of the messages, but they eliminate the need for a physically secure channel by using DiffieâHellman key exchange or some other public-key protocol to securely come to agreement on a fresh new secret key for each message (forward secrecy). \newcommand{\Tk}{\mathtt{k}} If the secret key is known to any intruder, he could decrypt the message. \newcommand{\Ts}{\mathtt{s}} \newcommand{\Tm}{\mathtt{m}} \newcommand{\amp}{&} Unlike symmetric key cryptography, we do not find historical use of public-key cryptography. [citation needed]. However, lack of randomness in those generators or in their initialization vectors is disastrous and has led to cryptanalytic breaks in the past. \newcommand{\mlongdivision}[2]{\longdivision{#1}{#2}} The. \newcommand{\fixme}[1]{{\color{red}FIX ME: #1}} The key must not be known to anyone else other than sender and receiver. All early cryptographic systems required one of those people to somehow receive a copy of that secret key over a physically secure channel. This method uses an encryption key with length 56 bits, meaning there are 2 56 possible keys. \newcommand{\Z}{\mathbb{Z}} 7.2.2 Key Length with Symmetric Key Algorithms Among those who are not entirely familiar with the mathematics of cryptography, key length is a topic of continuing confusion. Mathematical Cryptosystems (1 of 2: Symmetric Cryptography) [3][4], Symmetric-key encryption can use either stream ciphers or block ciphers. Alice sends a message to Bob, and the eavesdropper Eve listens in on their conversion and tries to break their encryption (Figure 8.2.1). \newcommand{\ttx}[1]{\texttt{\##1}} Symmetric key cryptography relies on a shared key between two parties. In this module you will develop an understanding of the mathematical and security properties of both symmetric key cipher systems and public key cryptography. 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