Cryptography: Difference between revisions

Latest revision as of 09:37, 6 July 2025

Cryptography is the practice and study of techniques for securing communication and information from adversaries. It encompasses various methods for encoding, transmitting, and decoding information, ensuring data integrity, confidentiality, and authentication. The field of cryptography has evolved significantly since its inception, transitioning from simple techniques such as substitution ciphers to complex algorithms and protocols used in modern computing and telecommunications.

History

Cryptography dates back to ancient civilizations. The earliest known example is the Egyptian hieroglyphs, which included non-standard symbols that may have served a protective purpose. The use of classical ciphers emerged prominently in ancient Greece, where the Greek historian Herodotus documented the use of the scytale for secret communication among the Spartans.

Classical Cryptography

In the medieval period, cryptography was primarily used in diplomatic correspondence. The development of ciphers like the Caesar cipher, named after Julius Caesar, who famously used it for military communication, laid the foundation for later cryptographic techniques. This method involved shifting the letters of the alphabet by a fixed number, a basic yet effective means of obfuscation.

By the Renaissance, cryptography became more sophisticated with the introduction of polyalphabetic ciphers, which allowed for greater complexity in encoding messages. Prominent figures, such as Giovanni Battista Bellaso and Blaise de Vigenère, contributed to this development by inventing various techniques that made it more difficult for eavesdroppers to decode messages without knowledge of the key.

Modern Cryptography

The 20th century witnessed a dramatic transformation in cryptography, particularly with the advent of World War II. Techniques like the Enigma machine, used by Nazi Germany, demonstrated the importance of encryption in military strategy. However, cryptographic breakthroughs, such as the work of mathematicians including Claude Shannon, laid the groundwork for modern cryptographic theory.

The establishment of public-key cryptography in the 1970s represented a revolutionary shift. Pioneered by Whitfield Diffie and Martin Hellman in their landmark 1976 paper, this approach allowed for secure communication without the necessity of sharing a private key in advance. The RSA algorithm, developed shortly thereafter by Ron Rivest, Adi Shamir, and Leonard Adleman, provided a practical implementation of public-key cryptography and secured its place as a critical tool in information security.

Types of Cryptography

Cryptography can be broadly classified into several categories based on the techniques employed and the objectives they aim to achieve.

Symmetric Cryptography

Symmetric cryptography, also known as private-key cryptography, involves a single key used for both encryption and decryption. This method is efficient for large data volumes due to its speed but necessitates a secure means of key exchange. Common symmetric algorithms include Advanced Encryption Standard (AES), Data Encryption Standard (DES), and Triple DES (3DES).

The primary challenge of symmetric cryptography lies in the secure distribution of the encryption key. If the key is intercepted during transmission, the security of the entire communication is compromised. Thus, organizations employing symmetric algorithms must implement robust key management protocols to mitigate this risk.

Asymmetric Cryptography

In contrast to symmetric cryptography, asymmetric cryptography utilizes a pair of keys: a public key and a private key. The public key can be distributed widely, allowing anyone to encrypt a message, while only the corresponding private key holder can decrypt it. This approach enables secure communication channels without the need for prior key sharing.

Asymmetric algorithms such as RSA, Diffie-Hellman, and Elliptic Curve Cryptography (ECC) are widely used in various applications, including email encryption and digital signatures. The critical advantage of this method is its ability to securely exchange keys over insecure channels and authenticate users, thereby ensuring integrity and non-repudiation.

Hash Functions

Hash functions, while not strictly classified as cryptographic algorithms, play a vital role in securing data integrity. A hash function transforms input data into a fixed-length string of characters, which appears random. Any modification to the input results in a drastically different output, allowing for the detection of unauthorized changes.

Common hash functions include SHA-256, MD5, and SHA-1, though the latter two are considered obsolete due to vulnerabilities discovered over time. Hash functions are widely used in digital signatures, certificate generation, and secure password storage due to their characteristics of determinism and pre-image resistance.

Implementation and Applications

Cryptography has a wide array of applications in contemporary technology, ranging from securing electronic communications to protecting sensitive data stored within computer systems.

Secure Communication

One of the primary applications of cryptography is to secure communication over the internet. Protocols such as Transport Layer Security (TLS) and its predecessor, Secure Sockets Layer (SSL), employ cryptographic algorithms to establish secure channels between web browsers and servers. This is indicated by the presence of "https://" in web addresses, which signifies that data transmitted between the user and the site is encrypted.

Email encryption protocols, such as Pretty Good Privacy (PGP) and S/MIME, utilize cryptography to ensure that email contents remain confidential and are only readable by intended recipients. These protocols employ both symmetric and asymmetric techniques to secure emails, allowing for both confidentiality and authentication.

Data Protection

Cryptography is crucial in data protection, particularly in scenarios involving sensitive personal and financial information. Data at rest, such as files stored on disks or cloud storage, can be encrypted using symmetric algorithms to prevent unauthorized access. Implementations such as full disk encryption and file-level encryption serve to protect sensitive information from theft or compromise.

Organizations must adhere to regulatory frameworks like the General Data Protection Regulation (GDPR) and the Health Insurance Portability and Accountability Act (HIPAA), which mandate that personal and medical information be protected through encryption. As such, cryptographic measures are often deployed in compliance with these laws, ensuring data confidentiality and integrity.

Digital Signatures and Authentication

Digital signatures, created through asymmetric cryptography, provide non-repudiation and authentication in digital transactions. By using a private key to sign a message or document, the sender can ensure that the recipient can verify the signature with the corresponding public key. This verification process guarantees the integrity of the message, as even a slight change in the content would invalidate the signature.

Use cases for digital signatures include software distribution, financial transactions, and legal contracts. They serve to assure parties involved that the signatures are genuine and have not been altered since they were signed. Platforms like blockchain technology have also leveraged cryptographic principles to create secure and immutable records of transactions.

Challenges and Limitations

Despite its critical importance, cryptography is not without its challenges and limitations. As computational power increases and new vulnerabilities are discovered, the effectiveness of cryptographic techniques can diminish over time.

Key Management

Key management remains one of the most significant challenges in cryptography. The secure generation, distribution, storage, and revocation of cryptographic keys are essential to maintaining the integrity of a secure system. Ineffective key management practices can lead to data breaches, making it imperative for organizations to implement stringent key lifecycle management protocols.

Vulnerability to Attacks

Cryptographic systems are continuously subjected to various attack vectors, including brute-force attacks, man-in-the-middle attacks, and side-channel attacks. As computing technology evolves, so do the methods employed by attackers. For instance, quantum computing poses a potential threat to traditional cryptographic systems, prompting researchers to explore post-quantum cryptography as a robust solution.

Additionally, implementation flaws, such as weak random number generation or flawed algorithms, can also introduce vulnerabilities, emphasizing the need for rigorous testing and validation of cryptographic systems before deployment.

Legal and Ethical Considerations

The increasing reliance on cryptography has led to various legal and ethical considerations. Governments around the world grapple with the need for secure communications while also seeking to monitor potential threats. This has sparked debates over the use of backdoors in encryption systems, which could potentially compromise user security, privacy, and trust.

The balance between national security and individual privacy remains a contentious issue in various jurisdictions. Cryptography advocates argue for the necessity of strong encryption for personal security, while law enforcement agencies contend that access to encrypted data is crucial for public safety.

Future of Cryptography

The ongoing developments in computing and cybersecurity suggest that the field of cryptography will continue to evolve. With the rise of quantum computing, cryptographic approaches will likely undergo significant transformations to counteract the new threats posed by advanced computational capabilities.

Post-Quantum Cryptography

As quantum computers become more viable, traditional public-key cryptographic algorithms may become vulnerable to quantum attacks. Post-quantum cryptography aims to develop new algorithms that are secure against adversaries equipped with quantum computing power. Researchers are actively reviewing and standardizing these algorithms, with the National Institute of Standards and Technology (NIST) leading the initiative.

Blockchain and Cryptographic Advancements

Blockchain technology has emerged as a transformative application of cryptography, enabling decentralized systems with enhanced security. The cryptographic principles underlying blockchain, including hash functions and digital signatures, facilitate secure and transparent transactions. As industries adopt blockchain for various applications, including supply chain management and finance, the role of cryptography will continue to expand.

Additionally, innovations in cryptographic techniques, such as homomorphic encryption and zero-knowledge proofs, are being explored to address specific challenges, including data privacy in cloud computing and secure multi-party computations. These advancements could reshape the landscape of secure computing, offering novel solutions to existing limitations.

References

@@ Line 1: / Line 1: @@
-= Cryptography =
+'''Cryptography''' is the practice and study of techniques for securing communication and information from adversaries. It encompasses various methods for encoding, transmitting, and decoding information, ensuring data integrity, confidentiality, and authentication. The field of cryptography has evolved significantly since its inception, transitioning from simple techniques such as substitution ciphers to complex algorithms and protocols used in modern computing and telecommunications.
-== Introduction ==
+== History ==
-Cryptography is the practice and study of techniques for securing communication and information from adversarial interference. It encompasses a wide range of methods that provide confidentiality, integrity, authentication, and non-repudiation in data exchange. At its core, cryptography converts original information (plaintext) into an unreadable format (ciphertext) and vice versa through a predefined process involving algorithms and keys. The significance of cryptography in the digital age cannot be overstated, as it underpins the security of nearly all electronic communications, from emails to online banking transactions.
+Cryptography dates back to ancient civilizations. The earliest known example is the Egyptian hieroglyphs, which included non-standard symbols that may have served a protective purpose. The use of classical ciphers emerged prominently in ancient Greece, where the Greek historian Herodotus documented the use of the ''scytale'' for secret communication among the Spartans.
-== History ==
+=== Classical Cryptography ===
-The origins of cryptography can be traced back to ancient civilizations where secret writing was used for military and diplomatic purposes. Early forms of cryptography included simple substitutions and transpositions, such as the Caesar cipher attributed to Julius Caesar, who used it to secure military communications. As societies evolved, so did the complexity of cryptographic methods.
+In the medieval period, cryptography was primarily used in diplomatic correspondence. The development of ciphers like the Caesar cipher, named after Julius Caesar, who famously used it for military communication, laid the foundation for later cryptographic techniques. This method involved shifting the letters of the alphabet by a fixed number, a basic yet effective means of obfuscation.
-In the Middle Ages, cryptography became more sophisticated with the introduction of polyalphabetic ciphers, notably the Vigenère cipher. During the Renaissance, the development of printing technology allowed for the widespread dissemination of cryptographic literature, leading to advancements in code-making and code-breaking.
+By the Renaissance, cryptography became more sophisticated with the introduction of polyalphabetic ciphers, which allowed for greater complexity in encoding messages. Prominent figures, such as Giovanni Battista Bellaso and Blaise de Vigenère, contributed to this development by inventing various techniques that made it more difficult for eavesdroppers to decode messages without knowledge of the key.
-The 20th century witnessed significant milestones in cryptography, particularly during both World Wars, where cryptographic systems played pivotal roles in securing military communications. The development of the Enigma machine by the Germans and its subsequent decryption by Allied cryptanalysts, most notably at Bletchley Park, is one of the most famous episodes in cryptographic history.
+=== Modern Cryptography ===
+The 20th century witnessed a dramatic transformation in cryptography, particularly with the advent of World War II. Techniques like the Enigma machine, used by Nazi Germany, demonstrated the importance of encryption in military strategy. However, cryptographic breakthroughs, such as the work of mathematicians including Claude Shannon, laid the groundwork for modern cryptographic theory.
-With the advent of computers, cryptography underwent a transformation. The introduction of public-key cryptography in the 1970s by Whitfield Diffie and Martin Hellman marked a watershed moment, allowing for secure communication without the need for a shared secret key. The RSA algorithm, developed by Ron Rivest, Adi Shamir, and Leonard Adleman, further established the foundation for modern cryptographic practices.
+The establishment of public-key cryptography in the 1970s represented a revolutionary shift. Pioneered by Whitfield Diffie and Martin Hellman in their landmark 1976 paper, this approach allowed for secure communication without the necessity of sharing a private key in advance. The RSA algorithm, developed shortly thereafter by Ron Rivest, Adi Shamir, and Leonard Adleman, provided a practical implementation of public-key cryptography and secured its place as a critical tool in information security.
-== Design and Architecture ==
+== Types of Cryptography ==
-The design of cryptographic systems primarily revolves around mathematical algorithms and protocols that ensure secure communications. Broadly, cryptography can be classified into two categories: symmetric and asymmetric cryptography.
+Cryptography can be broadly classified into several categories based on the techniques employed and the objectives they aim to achieve.
 === Symmetric Cryptography ===
-In symmetric cryptography, also known as secret key cryptography, the same key is used for both encryption and decryption. The security of symmetric systems relies heavily on the key's secrecy and the complexity of the algorithm. Notable symmetric encryption algorithms include the Data Encryption Standard (DES), which has since been superseded by the Advanced Encryption Standard (AES) due to vulnerabilities in its key length.
+Symmetric cryptography, also known as private-key cryptography, involves a single key used for both encryption and decryption. This method is efficient for large data volumes due to its speed but necessitates a secure means of key exchange. Common symmetric algorithms include Advanced Encryption Standard (AES), Data Encryption Standard (DES), and Triple DES (3DES).
+The primary challenge of symmetric cryptography lies in the secure distribution of the encryption key. If the key is intercepted during transmission, the security of the entire communication is compromised. Thus, organizations employing symmetric algorithms must implement robust key management protocols to mitigate this risk.
 === Asymmetric Cryptography ===
-Asymmetric cryptography employs a pair of keys: a public key, which can be shared openly, and a private key, which is kept secret. This paradigm allows for secure key exchange and digital signatures, improving authentication processes. Prominent asymmetric algorithms include RSA, Diffie-Hellman, and Elliptic Curve Cryptography (ECC).
+In contrast to symmetric cryptography, asymmetric cryptography utilizes a pair of keys: a public key and a private key. The public key can be distributed widely, allowing anyone to encrypt a message, while only the corresponding private key holder can decrypt it. This approach enables secure communication channels without the need for prior key sharing.
+Asymmetric algorithms such as RSA, Diffie-Hellman, and Elliptic Curve Cryptography (ECC) are widely used in various applications, including email encryption and digital signatures. The critical advantage of this method is its ability to securely exchange keys over insecure channels and authenticate users, thereby ensuring integrity and non-repudiation.
 === Hash Functions ===
-Hash functions are also vital components of cryptographic systems, providing data integrity by transforming input data into a fixed-length string of characters. Cryptographic hash functions, such as SHA-256, serve various purposes including secure password storage and digital signatures. Unlike encryption, hash functions are one-way processes, meaning that the original data cannot be easily reconstructed from the hash output.
+Hash functions, while not strictly classified as cryptographic algorithms, play a vital role in securing data integrity. A hash function transforms input data into a fixed-length string of characters, which appears random. Any modification to the input results in a drastically different output, allowing for the detection of unauthorized changes.
-=== Protocols ===
+Common hash functions include SHA-256, MD5, and SHA-1, though the latter two are considered obsolete due to vulnerabilities discovered over time. Hash functions are widely used in digital signatures, certificate generation, and secure password storage due to their characteristics of determinism and pre-image resistance.
-Cryptographic protocols establish rules for secure communication. Notable examples include the Transport Layer Security (TLS) protocol, which secures communications over computer networks, and the Pretty Good Privacy (PGP) protocol, which provides cryptographic privacy and authentication for email communications.
-== Usage and Implementation ==
+== Implementation and Applications ==
-Cryptography is employed across various domains, primarily driven by the need for data protection in an increasingly interconnected world. Major areas of application include:
+Cryptography has a wide array of applications in contemporary technology, ranging from securing electronic communications to protecting sensitive data stored within computer systems.
 === Secure Communication ===
-Cryptography secures voice, video, and text communications through end-to-end encryption, ensuring only intended recipients can decode the data. Messaging applications such as Signal and WhatsApp use advanced cryptographic techniques to protect users' privacy.
+One of the primary applications of cryptography is to secure communication over the internet. Protocols such as Transport Layer Security (TLS) and its predecessor, Secure Sockets Layer (SSL), employ cryptographic algorithms to establish secure channels between web browsers and servers. This is indicated by the presence of "https://" in web addresses, which signifies that data transmitted between the user and the site is encrypted.
+Email encryption protocols, such as Pretty Good Privacy (PGP) and S/MIME, utilize cryptography to ensure that email contents remain confidential and are only readable by intended recipients. These protocols employ both symmetric and asymmetric techniques to secure emails, allowing for both confidentiality and authentication.
 === Data Protection ===
-In enterprise environments, cryptography protects sensitive data stored on disks and during transmission over networks. Technologies like full disk encryption and secure file transfer protocols ensure that unauthorized access to data is prevented.
+Cryptography is crucial in data protection, particularly in scenarios involving sensitive personal and financial information. Data at rest, such as files stored on disks or cloud storage, can be encrypted using symmetric algorithms to prevent unauthorized access. Implementations such as full disk encryption and file-level encryption serve to protect sensitive information from theft or compromise.
-=== Digital Signatures ===
-Digital signatures are used to validate the authenticity and integrity of electronic documents. They involve a combination of hashing and asymmetric encryption, ensuring that a document has not been altered and that it was signed by a known entity.
-=== Electronic Payments ===
-Cryptography is crucial in facilitating secure electronic transactions, including online banking and e-commerce. Protocols like Secure Socket Layer (SSL) and TLS encrypt transaction data, safeguarding against interception and fraud.
-=== Blockchain Technology ===
+Organizations must adhere to regulatory frameworks like the General Data Protection Regulation (GDPR) and the Health Insurance Portability and Accountability Act (HIPAA), which mandate that personal and medical information be protected through encryption. As such, cryptographic measures are often deployed in compliance with these laws, ensuring data confidentiality and integrity.
-The rise of cryptocurrencies has further highlighted the role of cryptography. Blockchain technology, which underlies cryptocurrencies like Bitcoin, utilizes cryptographic hashing to secure transactions and maintain a tamper-proof ledger of activity.
-== Real-World Examples ==
+=== Digital Signatures and Authentication ===
-Several high-profile instances exemplify the practical implementation of cryptography:
+Digital signatures, created through asymmetric cryptography, provide non-repudiation and authentication in digital transactions. By using a private key to sign a message or document, the sender can ensure that the recipient can verify the signature with the corresponding public key. This verification process guarantees the integrity of the message, as even a slight change in the content would invalidate the signature.
-=== The Enigma Machine ===
+Use cases for digital signatures include software distribution, financial transactions, and legal contracts. They serve to assure parties involved that the signatures are genuine and have not been altered since they were signed. Platforms like blockchain technology have also leveraged cryptographic principles to create secure and immutable records of transactions.
-The Enigma machine was employed by the German military in World War II to encrypt communications. Its complexity made it seem unbreakable until cryptanalysts, including Alan Turing and his team, successfully deciphered its codes, significantly contributing to the Allied victory.
-=== SSL/TLS Encryption ===
+== Challenges and Limitations ==
-Secure Socket Layer (SSL) and its successor, Transport Layer Security (TLS), are widely used protocols that safeguard the privacy of online communications. Websites employing HTTPS use SSL/TLS to encrypt data between users and servers, helping mitigate risks associated with eavesdropping.
+Despite its critical importance, cryptography is not without its challenges and limitations. As computational power increases and new vulnerabilities are discovered, the effectiveness of cryptographic techniques can diminish over time.
-=== Ransomware Attacks ===
+=== Key Management ===
-Ransomware attacks provide a compelling example of both the benefits and risks associated with cryptography. Attackers often encrypt victims' data, rendering it inaccessible until a ransom is paid, illustrating the potential weaponization of cryptographic techniques.
+Key management remains one of the most significant challenges in cryptography. The secure generation, distribution, storage, and revocation of cryptographic keys are essential to maintaining the integrity of a secure system. Ineffective key management practices can lead to data breaches, making it imperative for organizations to implement stringent key lifecycle management protocols.
-== Criticism and Controversies ==
+=== Vulnerability to Attacks ===
-Despite its many advantages, cryptography also faces criticism and controversy:
+Cryptographic systems are continuously subjected to various attack vectors, including brute-force attacks, man-in-the-middle attacks, and side-channel attacks. As computing technology evolves, so do the methods employed by attackers. For instance, quantum computing poses a potential threat to traditional cryptographic systems, prompting researchers to explore post-quantum cryptography as a robust solution.
-=== Government Surveillance ===
+Additionally, implementation flaws, such as weak random number generation or flawed algorithms, can also introduce vulnerabilities, emphasizing the need for rigorous testing and validation of cryptographic systems before deployment.
-Concerns about government surveillance and the use of cryptographic technologies for mass monitoring have sparked debate in many countries. Advocacy groups argue for privacy rights and against backdoors in encryption systems that could jeopardize users' security.
-=== Cryptography vs. Law Enforcement ===
+=== Legal and Ethical Considerations ===
-Law enforcement agencies often argue that strong encryption hinders their ability to investigate crimes, especially in instances involving child exploitation and terrorism. This tension between promoting privacy and ensuring public safety has led to ongoing discussions about the balance of rights and responsibilities.
+The increasing reliance on cryptography has led to various legal and ethical considerations. Governments around the world grapple with the need for secure communications while also seeking to monitor potential threats. This has sparked debates over the use of backdoors in encryption systems, which could potentially compromise user security, privacy, and trust.
-=== Security vs. Usability ===
+The balance between national security and individual privacy remains a contentious issue in various jurisdictions. Cryptography advocates argue for the necessity of strong encryption for personal security, while law enforcement agencies contend that access to encrypted data is crucial for public safety.
-The complex nature of cryptographic systems can lead to poor implementation, making them vulnerable to attacks. Ensuring both security and usability remains a challenge for developers and organizations, emphasizing the need for user-friendly systems that do not compromise on security standards.
-== Influence and Impact ==
+== Future of Cryptography ==
-The impact of cryptography extends beyond technical applications as it addresses fundamental issues of trust, privacy, and security in a digital society. The growing reliance on cryptographic solutions shapes policies and regulations related to data protection globally.
+The ongoing developments in computing and cybersecurity suggest that the field of cryptography will continue to evolve. With the rise of quantum computing, cryptographic approaches will likely undergo significant transformations to counteract the new threats posed by advanced computational capabilities.
-=== Economic Impact ===
+=== Post-Quantum Cryptography ===
-As businesses increasingly embrace digital transformation, the demand for cryptographic solutions continues to soar. This has prompted advancements in cybersecurity industries, creating new markets and job opportunities focused on protecting information.
+As quantum computers become more viable, traditional public-key cryptographic algorithms may become vulnerable to quantum attacks. Post-quantum cryptography aims to develop new algorithms that are secure against adversaries equipped with quantum computing power. Researchers are actively reviewing and standardizing these algorithms, with the National Institute of Standards and Technology (NIST) leading the initiative.
-=== Social Implications ===
+=== Blockchain and Cryptographic Advancements ===
-Cryptography empowers individuals by enhancing their capacity to control personal data. The rise of privacy-focused technologies has fostered a culture of digital self-determination, encouraging users to prioritize privacy in their online interactions.
+Blockchain technology has emerged as a transformative application of cryptography, enabling decentralized systems with enhanced security. The cryptographic principles underlying blockchain, including hash functions and digital signatures, facilitate secure and transparent transactions. As industries adopt blockchain for various applications, including supply chain management and finance, the role of cryptography will continue to expand.
-=== Future of Cryptography ===
+Additionally, innovations in cryptographic techniques, such as homomorphic encryption and zero-knowledge proofs, are being explored to address specific challenges, including data privacy in cloud computing and secure multi-party computations. These advancements could reshape the landscape of secure computing, offering novel solutions to existing limitations.
-The future of cryptography is being shaped by developments in quantum computing, which poses potential threats to traditional cryptographic techniques. Researchers are actively exploring post-quantum cryptography—new algorithms designed to secure systems against quantum attacks—establishing the next frontier in cryptography.
 == See also ==
-* [[Public-key cryptography]]
+* [[Information security]]
-* [[Symmetric-key cryptography]]
-* [[Cryptographic hash function]]
-* [[Block cipher]]
-* [[Digital signature]]
 * [[Cryptanalysis]]
-* [[Quantum cryptography]]
+* [[Public key infrastructure]]
+* [[Encryption]]
+* [[Hash function]]
 == References ==
-* [https://www.nsa.gov/cryptography/ National Security Agency - Cryptography]
+* [https://www.nsa.gov Cryptography resources by the National Security Agency]
-* [https://www.encryption.com/ Encryption.com - Concept and practices of encryption]
+* [https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.197.pdf FIPS PUB 197: Advanced Encryption Standard (AES) by NIST]
-* [https://www.cryptography.io/ Cryptography.io - Cryptography and its practices]
+* [https://csrc.nist.gov/publications/detail/sp/800-56ar4/final NIST Special Publication 800-56A Revision 4: Recommended Practice for Pair-Wise Key Establishment Schemes by NIST]
-* [https://www.ibm.com/security/cryptography IBM - Cryptography solutions]
+* [https://csrc.nist.gov/publications/detail/sp/800-90a/rev-1/final NIST Special Publication 800-90A: Recommendation for Random Number Generation Using Deterministic Random Bit Generators]
-* [https://www.eff.org/pages/cryptography Electronic Frontier Foundation - Cryptography resources]
 [[Category:Cryptography]]
+[[Category:Computer security]]
 [[Category:Information security]]
-[[Category:Mathematics]]