Hash functions
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This document discusses hash functions and their uses in digital signatures and Bitcoin transactions. It explains that hash functions map arbitrary-length strings to fixed-length outputs and are used to sign transactions to prevent later modification. Common hash properties like collision resistance are described. The document also discusses the birthday problem as it applies to hash functions and estimates the number of trials needed to find collisions for different hash lengths. Examples of standardized hash functions and their security status over time are provided. Applications of hash functions like password storage, deduplication, and Merkle trees for partial verification in Bitcoin are also covered.
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The document provides an overview of the RSA public key encryption algorithm. It discusses how RSA uses a public key and private key pair, with the public key used to encrypt messages and the private key used to decrypt them. The security of RSA relies on the difficulty of factoring the product of two large prime numbers. The document outlines the RSA algorithm steps of key generation, encryption, and decryption. It also discusses RSA applications, standardization, speed, weaknesses, and history.
key distribution in network security
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Rsa Algorithm
The RSA algorithm document describes the steps to generate a public/private key pair for encryption and decryption. It involves selecting two large prime numbers p and q, computing n as their product, and using n along with the prime factors to calculate the private key exponent d that corresponds to the public key exponent e, such that ed = 1 mod φ(n). The example demonstrates computing the values for a specific case where p=3 and q=11.
The Diffie-Hellman key exchange document describes a protocol where Alice and Bob can establish a shared secret key over an insecure channel. It involves Alice generating a public value gx mod p and Bob generating a public value gy mod p, then each uses the other
Public Key Cryptography and RSA algorithm
Public Key Cryptography and RSA algorithm.Explanation and proof of RSA algorithm in details.it also describer the mathematics behind the RSA. Few mathematics theorem are given which are use in the RSA algorithm.
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Digital Signature, Electronic Signature, How digital signature works, Confidentiality of digital signature, Authenticity of digital signature, Integrity of digital signature, standard of digital signature, Algorithm of digital signature, Mathematical base of digital signature, parameters of digital signature, key computation of digital signature, key generation of digital signature, verification of of digital signature
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The document discusses hash functions and message authentication codes (MACs). It begins by defining hash functions and MACs, noting that hash functions generate a fingerprint for a message without a key while MACs use a keyed hash function. It then covers security requirements for hash functions like one-wayness and collision resistance. Popular hash functions are described like MD5, SHA-1, and the SHA-2 family. Constructions for hash functions based on block ciphers and iterated hash functions are also outlined. The document concludes by comparing hash functions and MACs and describing common MAC constructions.
Smart City Lecture 5 - Introduction to Encryption
This lecture gives an introduction to the field of cryptography for engineers. It provides an overview of hash algorithms, symmetric, asymmetric and hybrid ciphers, introduces Elliptic Curve Cryptography, and related algorithms (ECDH, ECDSA). It present Public Key Infrastructure (PKI), certificates (X.509), and how these can be automatically updated (ACME). It discusses Transport Encryption (TLS, DTLS), and End-to-End encryption, and when the latter is needed. Some common forms of attack are presented, to motivate the listener to implement the ubiquitous encryption policy (“Encrypt Everywhere”) in their solutions and organizations.
Bitcoin MOOC Lecture 1.pptx
This lecture introduces cryptocurrencies and the cryptographic concepts that enable them. It discusses hash functions and their properties like collision resistance. Digital signatures are explained as well as how public keys can represent identities. Simple cryptocurrency schemes are presented like GoofyCoin where a central party controls coin generation, and ScroogeCoin where a transaction history is published but one entity still controls validity. The goal of later lectures is to create a decentralized currency without a central trusted authority.
Cryptographic Hashing Functions
Cryptographic hashing functions are used to map data of arbitrary size to fixed-size values to facilitate data storage and transmission. They have properties such as preimage and collision resistance to make them unpredictable and secure. Popular cryptographic hashing algorithms include MD5, SHA-1, and SHA-2. Hashing functions are used for applications like digital signatures, password security, and message authentication. Techniques like salting hashes make them more resistant to brute force and pre-computed rainbow table attacks.
Webinar: MongoDB 2.4 Feature Demo and Q&A on Hash-based Sharding
In version 2.4, MongoDB introduces hash-based sharding, allowing the user to shard based on a randomized shard key to spread documents evenly across a cluster. Hash-based sharding is an alternative to range-based sharding, making it easier to manage your growing cluster. In this talk, we'll discuss provide an overview of this new feature and discuss the pros and cons of using a hash-based sharding vs. range-based approach.
Cryptography for Smalltalkers 2
Public Key Cryptography provides confidentiality, integrity, authentication, and non-repudiation through techniques like asymmetric encryption, digital signatures, hashes, and key exchange. It uses public/private key pairs based on hard mathematical problems like factoring and discrete logarithms. Common algorithms include RSA for encryption/signatures and Diffie-Hellman for key exchange. Signatures are generated with the private key and verified with the public key to authenticate messages and identities.
Keccak
This document provides an overview of the Keccak hash function and sponge construction. It describes how Keccak was selected as the winner of the NIST hash function competition in 2012. The core of Keccak is the Keccak-f permutation, which applies 5 modules (Theta, Rho, Pi, Chi, Iota) over multiple rounds to diffuse bits across a 3D state array. Keccak offers flexibility in hash output size, parallelism for efficiency, and resistance to side-channel attacks. It finds applications in digital signatures, data integrity, password storage, and authenticated encryption.
notes.pdf
This document provides an overview of the Cryptocurrency Engineering and Design course at MIT. It introduces the instructors and discusses the course structure, which includes lectures, labs, and a final project. It then discusses some of the core concepts needed to build a cryptocurrency, including hash functions, signatures, and examples of early digital cash systems like Chaumian e-cash. The document outlines the first programming assignment, which involves implementing Lamport signatures using only hash functions.
Consistent hashing
This document discusses consistent hashing, an algorithm that provides better load balancing when keys are hashed and distributed across machines in a distributed system. It describes some limitations of traditional hashing algorithms, like all keys being relocated when a machine is added or removed. Consistent hashing assigns keys to machines while trying to minimize movement on machine changes. It works by hashing both keys and machines and allocating keys clockwise on a hash ring from their hash position. This allows easy horizontal scalability and better performance by clustering similar keys.
Secure hashing algorithm
This document discusses secure hashing algorithms used for authentication rather than encryption. It provides an overview of the requirements for authentication including preventing masquerading, content modification, sequence modification, and timing modification. It then describes the basic theory behind hashing including producing a message digest, ensuring it is computationally infeasible to find two messages with the same digest, and being unable to recreate a message from its digest. Finally, it details the framework of the SHA-1 hashing algorithm including preprocessing the message, initializing buffers, processing the message in blocks, and outputting the final digest.
introduction to cryptography
This document provides an introduction to cryptography. It defines key terms like cryptography, cryptanalysis, and cryptology. It describes the goals of encryption and authentication. It explains symmetric key cryptography where a shared secret key is used for both encryption and decryption. It also covers public key cryptography using key pairs, digital signatures to authenticate identity, and how public key encryption and signatures can be combined. The document discusses cryptographic attacks and principles like Kerckhoff's principle and provable security. It provides examples of cryptographic algorithms like block ciphers, stream ciphers, hash functions, and key exchange protocols.
crypto1.ppt
The document provides an introduction to cryptography, including definitions of key terms, goals of cryptography like encryption and authentication, and descriptions of common cryptographic techniques. It summarizes symmetric key encryption where a shared secret key is used for both encryption and decryption, public key encryption using key pairs, digital signatures to authenticate messages, and how public key encryption and signatures can be combined. It also discusses cryptographic attacks, Kerckhoffs' principle of secrecy depending on the key not the algorithm, provable security, block ciphers like AES and DES, encryption modes, stream ciphers, hash functions, message authentication codes, key exchange methods like Diffie-Hellman, and public key cryptosystems like RSA and ElGamal
crypto.ppt
The document provides an introduction to cryptography, including definitions of key terms, goals of cryptography like encryption and authentication, and descriptions of common cryptographic techniques. It summarizes symmetric key encryption where a shared secret key is used for both encryption and decryption, public key encryption using key pairs, digital signatures to authenticate messages, and how public key encryption and signatures can be combined. It also discusses cryptographic attacks, Kerckhoffs' principle of secrecy depending on the key not the algorithm, provable security, block ciphers like AES and DES, encryption modes, stream ciphers, hash functions, message authentication codes, key exchange methods like Diffie-Hellman, and public key cryptosystems like RSA and ElGamal
needed.ppt
This document provides an introduction to cryptography. It defines key terms like cryptography, cryptanalysis, and cryptology. It describes the goals of encryption and authentication. It explains symmetric key cryptography where a shared secret key is used for both encryption and decryption. It also covers public key cryptography using key pairs, digital signatures to provide authentication, and how public key encryption and signatures can be combined. It discusses cryptographic attacks and the importance of Kerckhoffs' principle. It provides an overview of common cryptographic algorithms like block ciphers, stream ciphers, hash functions, and key exchange methods. It also discusses concepts like encryption modes, password hashing, random number generation, and the security of algorithms like RSA and Diffie-
introduction to cryptography (basics of it)
This document provides an introduction to cryptography. It defines key terms like cryptography, cryptanalysis, and cryptology. It describes the goals of encryption and authentication. It explains symmetric key cryptography where a shared secret key is used for both encryption and decryption. It also covers public key cryptography using key pairs, digital signatures to provide authentication, and how public key encryption and signatures can be combined. It discusses cryptographic attacks and the importance of Kerckhoffs' principle. It provides an overview of common cryptographic algorithms like block ciphers, stream ciphers, hash functions, and key exchange methods. It also discusses concepts like encryption modes, password hashing, random number generation, and the security of algorithms like RSA and Diffie-
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Hash functions
- 1. Hash Functions CS4501, Fall 2015 David Evans and Samee Zahur University of Virginia
- 2. Hash("I, Alice, hereby pay Bob an amount of 23 mBTC") = 7abc39d0 2e0194bc d7e93192 bcdfe412
- 3. Hash Functions in Signatures signsk 𝑚 = 𝑠 Signature algorithms require a fixed-size 𝑚!
- 4. Hash Functions in Signatures signsk H 𝑚 = 𝑠 Signature algorithms can use a fixed-size H 𝑚
- 5. Verifying Hashed Signatures 1. Compute ℎ = H(𝑚) 2. Run verifyvk ℎ, 𝑠 3. Accept if verify passed
- 7. Hash("I, Alice, hereby pay Bob an amount of 23 mBTC") = 7abc39d0 2e0194bc d7e93192 bcdfe412
- 8. Arbitrary Strings Fixed-size numbers Infinitely large set Collisions Unavoidable Finite set
- 10. Common Hash Properties 1. Collision resistance “It is hard to find any two 𝑚1, 𝑚2 such that H 𝑚1 = H(𝑚2)” 2. Second preimage resistance “For given 𝑚1, it is hard to find 𝑚2 such that H 𝑚1 = H(𝑚2)” 3. Preimage resistance (such functions are also called one-way) “For a given ℎ, it is hard to find any 𝑚 such that H 𝑚 = ℎ” 1 ⇒ 2 ⇒ 3
- 11. Recap • Signing algorithms work on small inputs • We hash strings before signing them • We need collision-resistant hashes
- 13. Find smallest number of people such that E pairs of common birthdays ≥ 1 Ways to pair 4 people 3 + 2 + 1 = 6 Ways to pair 𝑛 people 𝑛 − 1 + ⋯ + 3 + 2 + 1 = 𝑛 𝑛 − 1 2 = 𝑛2 − 𝑛 2 E pairs of common birthdays = 𝑛2 − 𝑛 2 × 365
- 14. How many common pairs? E pairs = 𝑛2 − 𝑛 2 × 365 Using 𝑛 = 30: E pairs = 𝑛2−𝑛 2×365 = 900−30 2×365 = 1.192
- 15. I wish a year had more days … If we select 𝑛 items out of 𝑁, number of repeats expected = 𝑛2 − 𝑛 2𝑁 We expect first repeat in 𝑛 = Θ( 𝑁) trials
- 16. I was born on 0x8ca8294be… H(some input) looks like random 𝑘-bits How many trials before we find collision? 80-bit hashes have 280 possible outputs. On the order of 280 = 240 trials.
- 17. Real-life hash functions Name Output Length (bits) Security status MD5 128 Collisions found SHA1 160 Can be broken in ~261 iterations SHA2 → SHA-256 224-512 → 256 No known attacks SHA3 224-512 No known attacks Bitcoin typically uses SHA-256(SHA-256(transaction))
- 18. Hash-function life cycle New function proposed Security evaluated Function standardized Theoretical attacks proposed Attacks improved and are practical
- 19. “Typical” timelines MD5 • First proposed: 1991 • Published: 1992 • First signs of trouble: 1996 • Not collision resistant: 2004 • Chosen-prefix collision: by 2007 SHA3 • Competition started: 2007 • Submission deadline: 2008 • Elimination rounds: 2008-2010 • 5 finalists announced: 2010 • Kekkak algorithm selected as winner: 2012
- 20. Digital signatures JasonBenjamin Bitcoin transaction ID Deduplication Password storage
- 21. Password Databases Username Password Jack.Clough 12password Betty.Smith 8c2odkw Username “Salt” Scrypt(password+salt) Jack.Clough 150FE5Btiq… PaR6mPwHBj… Betty.Smith t1Y1B67ulN… QrUaLRqFvc… Insecure Better
- 22. Partial verification A block is a group of transactions in the Bitcoin ledger. Straightforward way: H 𝑇1 + 𝑇2 + ⋯ + 𝑇1000 = 0xa8c9239 … Verification requires me to inspect all 1000 transactions in the block.
- 23. Merkle Tree root = 0x220c04634a… p = H(a+b) = 0x2626113d5b… q = H(c+d) = 0x305e321c3e… H(T1) = a = 0x1763023d40… H(T2) = a = 0x1c1c3a3831… H(T3) = a = 0x2955461d31… H(T4) = a = 0x160b445b5e…
- 24. Recap • Hash functions used in lots of places: • Signatures • Unique global IDs: bitcoin transaction, Dropbox files • Password databases • File downloads • Birthday attacks: hashes with 𝑘-bit output can be expected to collide in 2 𝑘 2 iterations • Weak hashes can be broken faster: don’t use MD5, avoid SHA-1 • Merkle trees enable partial verification
- 25. Coming up… • Problemset 1 due tomorrow: (8:29 PM) • Ori has office hours today (5 PM – 6:30 PM) • Next class topic: Bitcoin mining