SHA-3 Family of Cryptographic Hash Functions and Extendable-Output Functions
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IMPLEMENTATION and BENCHMARKING of PADDING UNITS and HMAC for SHA-3 CANDIDATES in FPGAS and ASICS by Ambarish Vyas a Thesis Subm
IMPLEMENTATION AND BENCHMARKING OF PADDING UNITS AND HMAC FOR SHA-3 CANDIDATES IN FPGAS AND ASICS by Ambarish Vyas A Thesis Submitted to the Graduate Faculty of George Mason University in Partial Fulfillment of The Requirements for the Degree of Master of Science Computer Engineering Committee: Dr. Kris Gaj, Thesis Director Dr. Jens-Peter Kaps. Committee Member Dr. Bernd-Peter Paris. Committee Member Dr. Andre Manitius, Department Chair of Electrical and Computer Engineering Dr. Lloyd J. Griffiths. Dean, Volgenau School of Engineering Date: ---J d. / q /9- 0 II Fall Semester 2011 George Mason University Fairfax, VA Implementation and Benchmarking of Padding Units and HMAC for SHA-3 Candidates in FPGAs and ASICs A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science at George Mason University By Ambarish Vyas Bachelor of Science University of Pune, 2009 Director: Dr. Kris Gaj, Associate Professor Department of Electrical and Computer Engineering Fall Semester 2011 George Mason University Fairfax, VA Copyright c 2011 by Ambarish Vyas All Rights Reserved ii Acknowledgments I would like to use this oppurtunity to thank the people who have supported me throughout my thesis. First and foremost my advisor Dr.Kris Gaj, without his zeal, his motivation, his patience, his confidence in me, his humility, his diverse knowledge, and his great efforts this thesis wouldn't be possible. It is difficult to exaggerate my gratitude towards him. I also thank Ekawat Homsirikamol for his contributions to this project. He has significantly contributed to the designs and implementations of the architectures. Additionally, I am indebted to my student colleagues in CERG for providing a fun environment to learn and giving invaluable tips and support. -
The Order of Encryption and Authentication for Protecting Communications (Or: How Secure Is SSL?)?
The Order of Encryption and Authentication for Protecting Communications (Or: How Secure is SSL?)? Hugo Krawczyk?? Abstract. We study the question of how to generically compose sym- metric encryption and authentication when building \secure channels" for the protection of communications over insecure networks. We show that any secure channels protocol designed to work with any combina- tion of secure encryption (against chosen plaintext attacks) and secure MAC must use the encrypt-then-authenticate method. We demonstrate this by showing that the other common methods of composing encryp- tion and authentication, including the authenticate-then-encrypt method used in SSL, are not generically secure. We show an example of an en- cryption function that provides (Shannon's) perfect secrecy but when combined with any MAC function under the authenticate-then-encrypt method yields a totally insecure protocol (for example, ¯nding passwords or credit card numbers transmitted under the protection of such protocol becomes an easy task for an active attacker). The same applies to the encrypt-and-authenticate method used in SSH. On the positive side we show that the authenticate-then-encrypt method is secure if the encryption method in use is either CBC mode (with an underlying secure block cipher) or a stream cipher (that xor the data with a random or pseudorandom pad). Thus, while we show the generic security of SSL to be broken, the current practical implementations of the protocol that use the above modes of encryption are safe. 1 Introduction The most widespread application of cryptography in the Internet these days is for implementing a secure channel between two end points and then exchanging information over that channel. -
Lecture9.Pdf
Merkle- Suppose H is a Damgaord hash function built from a secure compression function : several to build a function ways keyed : m : = H Ilm 1 . end FCK ) (k ) Prep key , " " ↳ - Insecure due to structure of Merkle : can mount an extension attack: H (KH m) can Barnyard given , compute ' Hlkllmllm ) by extending Merkle- Danged chain = : m : 2 . FCK ) 11k) Append key , Hlm ↳ - - to : Similar to hash then MAC construction and vulnerable same offline attack adversary finds a collision in the - - > Merkle and uses that to construct a for SHA I used PDF files Barnyard prefix forgery f , they ↳ - Structure in SHA I (can matches exploited collision demonstration generate arbitrary collisions once prefix ) ' = : FCK m - H on h 3. method , ) ( K HMH K) for reasonable randomness ( both Envelope pseudo assumptions e.g , : = - = i - - : F ( m m } : h K m h m k 4. nest ( ki ) H Ck H (k m ( , and m ( ) is a PRF both Two , kz , ) (ka HH , )) F- , ) ) Falk , ) , ) key , - of these constructions are secure PRFS on a variable size domain hash- based MAC ✓ a the - nest with correlated : HMAC is PRF / MAC based on two key (though keys) : = m H H ka m HMACCK ( K H ( , )) , ) , where k ← k ④ and kz ← k to , ipad opad and and are fixed ( in the HMAC standard) ipad opad strings specified I 0×36 repeated %x5C repeated : k . a Since , and ka are correlated need to make on h remains under Sety , stronger assumption security leg , pseudorandom related attack) Instantiations : denoted HMAC- H where H is the hash function Typically , HMAC- SHAI %" - - HMAC SHA256 -
Authenticated Key-Exchange: Protocols, Attacks, and Analyses
The HMAC construction: A decade later Ran Canetti IBM Research What is HMAC? ● HMAC: A Message Authentication Code based on Cryptographic Hash functions [Bellare-C-Krawczyk96]. ● Developed for the IPSec standard of the Internet Engineering Task Force (IETF). ● Currently: - incorporated in IPSec, SSL/TLS, SSH, Kerberos, SHTTP, HTTPS, SRTP, MSEC, ... - ANSI and NIST standards - Used daily by all of us. Why is HMAC interesting? ● “Theoretical” security analysis impacts the security of real systems. ● Demonstrates the importance of modelling and abstraction in practical cryptography. ● The recent attacks on hash functions highlight the properties of the HMAC design and analysis. ● Use the HMAC lesson to propose requirements for the next cryptographic hash function. Organization ● Authentication, MACs, Hash-based MACs ● HMAC construction and analysis ● Other uses of HMAC: ● Pseudo-Random Functions ● Extractors ● What properties do we want from a “cryptographic hash function”? Authentication m m' A B The goal: Any tampering with messages should be detected. “If B accepts message m from A then A has sent m to B.” • One of the most basic cryptographic tasks • The basis for any security-conscious interaction over an open network Elements of authentication The structure of typical cryptographic solutions: • Initial entity authentication: The parties perform an initial exchange, bootstrapping from initial trusted information on each other. The result is a secret key that binds the parties to each other. • Message authentication: The parties use the key to authenticate exchanged messages via message authentication codes. Message Authentication Codes m,t m',t' A B t=FK(m) t' =? FK(m') • A and B obtain a common secret key K • A and B agree on a keyed function F • A sends t=FK(m) together with m • B gets (m',t') and accepts m' if t'=FK(m'). -
Hash Functions
Hash Functions A hash function is a function that maps data of arbitrary size to an integer of some fixed size. Example: Java's class Object declares function ob.hashCode() for ob an object. It's a hash function written in OO style, as are the next two examples. Java version 7 says that its value is its address in memory turned into an int. Example: For in an object of type Integer, in.hashCode() yields the int value that is wrapped in in. Example: Suppose we define a class Point with two fields x and y. For an object pt of type Point, we could define pt.hashCode() to yield the value of pt.x + pt.y. Hash functions are definitive indicators of inequality but only probabilistic indicators of equality —their values typically have smaller sizes than their inputs, so two different inputs may hash to the same number. If two different inputs should be considered “equal” (e.g. two different objects with the same field values), a hash function must re- spect that. Therefore, in Java, always override method hashCode()when overriding equals() (and vice-versa). Why do we need hash functions? Well, they are critical in (at least) three areas: (1) hashing, (2) computing checksums of files, and (3) areas requiring a high degree of information security, such as saving passwords. Below, we investigate the use of hash functions in these areas and discuss important properties hash functions should have. Hash functions in hash tables In the tutorial on hashing using chaining1, we introduced a hash table b to implement a set of some kind. -
Permutation-Based Encryption, Authentication and Authenticated Encryption
Permutation-based encryption, authentication and authenticated encryption Permutation-based encryption, authentication and authenticated encryption Joan Daemen1 Joint work with Guido Bertoni1, Michaël Peeters2 and Gilles Van Assche1 1STMicroelectronics 2NXP Semiconductors DIAC 2012, Stockholm, July 6 . Permutation-based encryption, authentication and authenticated encryption Modern-day cryptography is block-cipher centric Modern-day cryptography is block-cipher centric (Standard) hash functions make use of block ciphers SHA-1, SHA-256, SHA-512, Whirlpool, RIPEMD-160, … So HMAC, MGF1, etc. are in practice also block-cipher based Block encryption: ECB, CBC, … Stream encryption: synchronous: counter mode, OFB, … self-synchronizing: CFB MAC computation: CBC-MAC, C-MAC, … Authenticated encryption: OCB, GCM, CCM … . Permutation-based encryption, authentication and authenticated encryption Modern-day cryptography is block-cipher centric Structure of a block cipher . Permutation-based encryption, authentication and authenticated encryption Modern-day cryptography is block-cipher centric Structure of a block cipher (inverse operation) . Permutation-based encryption, authentication and authenticated encryption Modern-day cryptography is block-cipher centric When is the inverse block cipher needed? Indicated in red: Hashing and its modes HMAC, MGF1, … Block encryption: ECB, CBC, … Stream encryption: synchronous: counter mode, OFB, … self-synchronizing: CFB MAC computation: CBC-MAC, C-MAC, … Authenticated encryption: OCB, GCM, CCM … So a block cipher -
Horner's Method: a Fast Method of Evaluating a Polynomial String Hash
Olympiads in Informatics, 2013, Vol. 7, 90–100 90 2013 Vilnius University Where to Use and Ho not to Use Polynomial String Hashing Jaku' !(CHOCKI, $ak&' RADOSZEWSKI Faculty of Mathematics, Informatics and Mechanics, University of Warsaw Banacha 2, 02-097 Warsaw, oland e-mail: {pachoc$i,jrad}@mimuw.edu.pl Abstract. We discuss the usefulness of polynomial string hashing in programming competition tasks. We sho why se/eral common choices of parameters of a hash function can easily lead to a large number of collisions. We particularly concentrate on the case of hashing modulo the size of the integer type &sed for computation of fingerprints, that is, modulo a power of t o. We also gi/e examples of tasks in hich strin# hashing yields a solution much simpler than the solutions obtained using other known algorithms and data structures for string processing. Key words: programming contests, hashing on strings, task e/aluation. 1. Introduction Hash functions are &sed to map large data sets of elements of an arbitrary length 3the $eys4 to smaller data sets of elements of a 12ed length 3the fingerprints). The basic appli6 cation of hashing is efficient testin# of equality of %eys by comparin# their 1ngerprints. ( collision happens when two different %eys ha/e the same 1ngerprint. The ay in which collisions are handled is crucial in most applications of hashing. Hashing is particularly useful in construction of efficient practical algorithms. Here e focus on the case of the %eys 'ein# strings o/er an integer alphabetΣ= 0,1,...,A 1 . 5he elements ofΣ are called symbols. -
BLAKE2: Simpler, Smaller, Fast As MD5
BLAKE2: simpler, smaller, fast as MD5 Jean-Philippe Aumasson1, Samuel Neves2, Zooko Wilcox-O'Hearn3, and Christian Winnerlein4 1 Kudelski Security, Switzerland [email protected] 2 University of Coimbra, Portugal [email protected] 3 Least Authority Enterprises, USA [email protected] 4 Ludwig Maximilian University of Munich, Germany [email protected] Abstract. We present the hash function BLAKE2, an improved version of the SHA-3 finalist BLAKE optimized for speed in software. Target applications include cloud storage, intrusion detection, or version control systems. BLAKE2 comes in two main flavors: BLAKE2b is optimized for 64-bit platforms, and BLAKE2s for smaller architectures. On 64- bit platforms, BLAKE2 is often faster than MD5, yet provides security similar to that of SHA-3: up to 256-bit collision resistance, immunity to length extension, indifferentiability from a random oracle, etc. We specify parallel versions BLAKE2bp and BLAKE2sp that are up to 4 and 8 times faster, by taking advantage of SIMD and/or multiple cores. BLAKE2 reduces the RAM requirements of BLAKE down to 168 bytes, making it smaller than any of the five SHA-3 finalists, and 32% smaller than BLAKE. Finally, BLAKE2 provides a comprehensive support for tree-hashing as well as keyed hashing (be it in sequential or tree mode). 1 Introduction The SHA-3 Competition succeeded in selecting a hash function that comple- ments SHA-2 and is much faster than SHA-2 in hardware [1]. There is nev- ertheless a demand for fast software hashing for applications such as integrity checking and deduplication in filesystems and cloud storage, host-based intrusion detection, version control systems, or secure boot schemes. -
Cryptographic Sponge Functions
Cryptographic sponge functions Guido B1 Joan D1 Michaël P2 Gilles V A1 http://sponge.noekeon.org/ Version 0.1 1STMicroelectronics January 14, 2011 2NXP Semiconductors Cryptographic sponge functions 2 / 93 Contents 1 Introduction 7 1.1 Roots .......................................... 7 1.2 The sponge construction ............................... 8 1.3 Sponge as a reference of security claims ...................... 8 1.4 Sponge as a design tool ................................ 9 1.5 Sponge as a versatile cryptographic primitive ................... 9 1.6 Structure of this document .............................. 10 2 Definitions 11 2.1 Conventions and notation .............................. 11 2.1.1 Bitstrings .................................... 11 2.1.2 Padding rules ................................. 11 2.1.3 Random oracles, transformations and permutations ........... 12 2.2 The sponge construction ............................... 12 2.3 The duplex construction ............................... 13 2.4 Auxiliary functions .................................. 15 2.4.1 The absorbing function and path ...................... 15 2.4.2 The squeezing function ........................... 16 2.5 Primary aacks on a sponge function ........................ 16 3 Sponge applications 19 3.1 Basic techniques .................................... 19 3.1.1 Domain separation .............................. 19 3.1.2 Keying ..................................... 20 3.1.3 State precomputation ............................ 20 3.2 Modes of use of sponge functions ......................... -
Why Simple Hash Functions Work: Exploiting the Entropy in a Data Stream∗
Why Simple Hash Functions Work: Exploiting the Entropy in a Data Stream¤ Michael Mitzenmachery Salil Vadhanz School of Engineering & Applied Sciences Harvard University Cambridge, MA 02138 fmichaelm,[email protected] http://eecs.harvard.edu/»fmichaelm,salilg October 12, 2007 Abstract Hashing is fundamental to many algorithms and data structures widely used in practice. For theoretical analysis of hashing, there have been two main approaches. First, one can assume that the hash function is truly random, mapping each data item independently and uniformly to the range. This idealized model is unrealistic because a truly random hash function requires an exponential number of bits to describe. Alternatively, one can provide rigorous bounds on performance when explicit families of hash functions are used, such as 2-universal or O(1)-wise independent families. For such families, performance guarantees are often noticeably weaker than for ideal hashing. In practice, however, it is commonly observed that simple hash functions, including 2- universal hash functions, perform as predicted by the idealized analysis for truly random hash functions. In this paper, we try to explain this phenomenon. We demonstrate that the strong performance of universal hash functions in practice can arise naturally from a combination of the randomness of the hash function and the data. Speci¯cally, following the large body of literature on random sources and randomness extraction, we model the data as coming from a \block source," whereby each new data item has some \entropy" given the previous ones. As long as the (Renyi) entropy per data item is su±ciently large, it turns out that the performance when choosing a hash function from a 2-universal family is essentially the same as for a truly random hash function. -
CSC 344 – Algorithms and Complexity Why Search?
CSC 344 – Algorithms and Complexity Lecture #5 – Searching Why Search? • Everyday life -We are always looking for something – in the yellow pages, universities, hairdressers • Computers can search for us • World wide web provides different searching mechanisms such as yahoo.com, bing.com, google.com • Spreadsheet – list of names – searching mechanism to find a name • Databases – use to search for a record • Searching thousands of records takes time the large number of comparisons slows the system Sequential Search • Best case? • Worst case? • Average case? Sequential Search int linearsearch(int x[], int n, int key) { int i; for (i = 0; i < n; i++) if (x[i] == key) return(i); return(-1); } Improved Sequential Search int linearsearch(int x[], int n, int key) { int i; //This assumes an ordered array for (i = 0; i < n && x[i] <= key; i++) if (x[i] == key) return(i); return(-1); } Binary Search (A Decrease and Conquer Algorithm) • Very efficient algorithm for searching in sorted array: – K vs A[0] . A[m] . A[n-1] • If K = A[m], stop (successful search); otherwise, continue searching by the same method in: – A[0..m-1] if K < A[m] – A[m+1..n-1] if K > A[m] Binary Search (A Decrease and Conquer Algorithm) l ← 0; r ← n-1 while l ≤ r do m ← (l+r)/2 if K = A[m] return m else if K < A[m] r ← m-1 else l ← m+1 return -1 Analysis of Binary Search • Time efficiency • Worst-case recurrence: – Cw (n) = 1 + Cw( n/2 ), Cw (1) = 1 solution: Cw(n) = log 2(n+1) 6 – This is VERY fast: e.g., Cw(10 ) = 20 • Optimal for searching a sorted array • Limitations: must be a sorted array (not linked list) binarySearch int binarySearch(int x[], int n, int key) { int low, high, mid; low = 0; high = n -1; while (low <= high) { mid = (low + high) / 2; if (x[mid] == key) return(mid); if (x[mid] > key) high = mid - 1; else low = mid + 1; } return(-1); } Searching Problem Problem: Given a (multi)set S of keys and a search key K, find an occurrence of K in S, if any. -
Hello, and Welcome to This Presentation of the STM32 Hash Processor
Hello, and welcome to this presentation of the STM32 hash processor. 1 Hash peripheral is in charge of efficient computing of message digest. A digest is a fixed-length value computed from an input message. A digest is unique - it is virtually impossible to find two messages with the same digest. The original message cannot be retrieved from its digest. Hash digests and Hash-based Message Authentication Code (HMAC) are widely used in communication since they are used to guarantee the integrity and authentication of a transfer. 2 The hash processor supports widely used hash functions including Message Digest 5 (MD5), Secure Hash Algorithm SHA-1 and the more recent SHA-2 with its 224- and 256- bit digest length versions. A hash can also be generated with a secrete-key to produce a message authentication code (MAC). The processor supports bit, byte and half-word swapping. It supports also automatic padding of input data for block alignment. The processor can be used in conjunction with the DMA for automatic processor feeding. 3 All supported hash functions work on 512-bit blocks of data. The input message is split as many times as needed to feed the hash processor. Subsequent blocks are computed sequentially. MD5 is the less robust function with only a 128-bit digest. The SHA standard has two versions SHA-1 and the more recent SHA-2 with its 224- and 256-bit digest length versions. 4 The hash-based message authentication code (HMAC) is used to authenticate messages and verify their integrity. The HMAC function consists of two nested Hash function with a secrete key that is shared by the sender and the receiver.