Hash Functions and Message Authentication Codes
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FIPS 140-2 Non-Proprietary Security Policy
Kernel Crypto API Cryptographic Module version 1.0 FIPS 140-2 Non-Proprietary Security Policy Version 1.3 Last update: 2020-03-02 Prepared by: atsec information security corporation 9130 Jollyville Road, Suite 260 Austin, TX 78759 www.atsec.com © 2020 Canonical Ltd. / atsec information security This document can be reproduced and distributed only whole and intact, including this copyright notice. Kernel Crypto API Cryptographic Module FIPS 140-2 Non-Proprietary Security Policy Table of Contents 1. Cryptographic Module Specification ..................................................................................................... 5 1.1. Module Overview ..................................................................................................................................... 5 1.2. Modes of Operation ................................................................................................................................. 9 2. Cryptographic Module Ports and Interfaces ........................................................................................ 10 3. Roles, Services and Authentication ..................................................................................................... 11 3.1. Roles .......................................................................................................................................................11 3.2. Services ...................................................................................................................................................11 -
Fast Hashing and Stream Encryption with Panama
Fast Hashing and Stream Encryption with Panama Joan Daemen1 and Craig Clapp2 1 Banksys, Haachtesteenweg 1442, B-1130 Brussel, Belgium [email protected] 2 PictureTel Corporation, 100 Minuteman Rd., Andover, MA 01810, USA [email protected] Abstract. We present a cryptographic module that can be used both as a cryptographic hash function and as a stream cipher. High performance is achieved through a combination of low work-factor and a high degree of parallelism. Throughputs of 5.1 bits/cycle for the hashing mode and 4.7 bits/cycle for the stream cipher mode are demonstrated on a com- mercially available VLIW micro-processor. 1 Introduction Panama is a cryptographic module that can be used both as a cryptographic hash function and a stream cipher. It is designed to be very efficient in software implementations on 32-bit architectures. Its basic operations are on 32-bit words. The hashing state is updated by a parallel nonlinear transformation, the buffer operates as a linear feedback shift register, similar to that applied in the compression function of SHA [6]. Panama is largely based on the StepRightUp stream/hash module that was described in [4]. Panama has a low per-byte work factor while still claiming very high security. The price paid for this is a relatively high fixed computational overhead for every execution of the hash function. This makes the Panama hash function less suited for the hashing of messages shorter than the equivalent of a typewritten page. For the stream cipher it results in a relatively long initialization procedure. Hence, in applications where speed is critical, too frequent resynchronization should be avoided. -
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. -
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. -
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. -
Cryptanalysis of MD4
Cryptanalysis of MD4 Hans Dobbertin German Information Security Agency P. O. Box 20 03 63 D-53133 Bonn e-maih dobbert inQskom, rhein .de Abstract. In 1990 Rivest introduced the hash function MD4. Two years later RIPEMD, a European proposal, was designed as a stronger mode of MD4. Recently wc have found an attack against two of three rounds of RIPEMD. As we shall show in the present note, the methods developed to attack RIPEMD can be modified and supplemented such that it is possible to break the full MD4, while previously only partial attacks were known. An implementation of our attack allows to find collisions for MD4 in a few seconds on a PC. An example of a collision is given demonstrating that our attack is of practical relevance. 1 Introduction Rivest [7] introduced the hash function MD4 in 1990. The MD4 algorithm is defined as an iterative application of a three-round compress function. After an unpublished attack on the first two rounds of MD4 due to Merkle and an attack against the last two rounds by den Boer and Bosselaers [2], Rivest introduced the strengthened version MD5 [8]. The most important difference to MD4 is the adding of a fourth round. On the other hand the stronger mode RIPEMD [1] of MD4 was designed as a European proposal in 1992. The compress function of RIPEMD consists of two parallel lines of a modified version of the MD4 compress function. In [4] we have shown that if the first or the last round of its compress function is omitted, then RIPEMD is not collision-free. -
Efficient Collision Attack Frameworks for RIPEMD-160
Efficient Collision Attack Frameworks for RIPEMD-160 Fukang Liu1;6, Christoph Dobraunig2;3, Florian Mendel4, Takanori Isobe5;6, Gaoli Wang1?, and Zhenfu Cao1? 1 Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China [email protected],fglwang,[email protected] 2 Graz University of Technology, Austria 3 Radboud University, Nijmegen, The Netherlands [email protected] 4 Infineon Technologies AG, Germany [email protected] 5 National Institute of Information and Communications Technology, Japan 6 University of Hyogo, Japan [email protected] Abstract. RIPEMD-160 is an ISO/IEC standard and has been applied to gen- erate the Bitcoin address with SHA-256. Due to the complex dual-stream struc- ture, the first collision attack on reduced RIPEMD-160 presented by Liu, Mendel and Wang at Asiacrypt 2017 only reaches 30 steps, having a time complexity of 270. Apart from that, several semi-free-start collision attacks have been published for reduced RIPEMD-160 with the start-from-the-middle method. Inspired from such start-from-the middle structures, we propose two novel efficient collision at- tack frameworks for reduced RIPEMD-160 by making full use of the weakness of its message expansion. Those two frameworks are called dense-left-and-sparse- right (DLSR) framework and sparse-left-and-dense-right (SLDR) framework. As it turns out, the DLSR framework is more efficient than SLDR framework since one more step can be fully controlled, though with extra 232 memory complexi- ty. To construct the best differential characteristics for the DLSR framework, we carefully build the linearized part of the characteristics and then solve the cor- responding nonlinear part using a guess-and-determine approach. -
Hash Functions and Thetitle NIST of Shapresentation-3 Competition
The First 30 Years of Cryptographic Hash Functions and theTitle NIST of SHAPresentation-3 Competition Bart Preneel COSIC/Kath. Univ. Leuven (Belgium) Session ID: CRYP-202 Session Classification: Hash functions decoded Insert presenter logo here on slide master Hash functions X.509 Annex D RIPEMD-160 MDC-2 SHA-256 SHA-3 MD2, MD4, MD5 SHA-512 SHA-1 This is an input to a crypto- graphic hash function. The input is a very long string, that is reduced by the hash function to a string of fixed length. There are 1A3FD4128A198FB3CA345932 additional security conditions: it h should be very hard to find an input hashing to a given value (a preimage) or to find two colliding inputs (a collision). Hash function history 101 DES RSA 1980 single block ad hoc length schemes HARDWARE MD2 MD4 1990 SNEFRU double MD5 block security SHA-1 length reduction for RIPEMD-160 factoring, SHA-2 2000 AES permu- DLOG, lattices Whirlpool SOFTWARE tations SHA-3 2010 Applications • digital signatures • data authentication • protection of passwords • confirmation of knowledge/commitment • micropayments • pseudo-random string generation/key derivation • construction of MAC algorithms, stream ciphers, block ciphers,… Agenda Definitions Iterations (modes) Compression functions SHA-{0,1,2,3} Bits and bytes 5 Hash function flavors cryptographic hash function this talk MAC MDC OWHF CRHF UOWHF (TCR) Security requirements (n-bit result) preimage 2nd preimage collision ? x ? ? ? h h h h h h(x) h(x) = h(x‘) h(x) = h(x‘) 2n 2n 2n/2 Informal definitions (1) • no secret parameters -
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. -
Hash Functions
11 Hash Functions Suppose you share a huge le with a friend, but you are not sure whether you both have the same version of the le. You could send your version of the le to your friend and they could compare to their version. Is there any way to check that involves less communication than this? Let’s call your version of the le x (a string) and your friend’s version y. The goal is to determine whether x = y. A natural approach is to agree on some deterministic function H, compute H¹xº, and send it to your friend. Your friend can compute H¹yº and, since H is deterministic, compare the result to your H¹xº. In order for this method to be fool-proof, we need H to have the property that dierent inputs always map to dierent outputs — in other words, H must be injective (1-to-1). Unfortunately, if H is injective and H : f0; 1gin ! f0; 1gout is injective, then out > in. This means that sending H¹xº is no better/shorter than sending x itself! Let us call a pair ¹x;yº a collision in H if x , y and H¹xº = H¹yº. An injective function has no collisions. One common theme in cryptography is that you don’t always need something to be impossible; it’s often enough for that thing to be just highly unlikely. Instead of saying that H should have no collisions, what if we just say that collisions should be hard (for polynomial-time algorithms) to nd? An H with this property will probably be good enough for anything we care about. -
Cryptography and Network Security Chapter 12
Chapter 12 – Message CryptographyCryptography andand Authentication Codes NetworkNetwork SecuritySecurity • At cats' green on the Sunday he took the message from the inside of the pillar and added Peter Moran's name to ChapterChapter 1212 the two names already printed there in the "Brontosaur" code. The message now read: “Leviathan to Dragon: Martin Hillman, Trevor Allan, Peter Moran: observe and tail. ” What was the good of it John hardly knew. He felt Fifth Edition better, he felt that at last he had made an attack on Peter Moran instead of waiting passively and effecting no by William Stallings retaliation. Besides, what was the use of being in possession of the key to the codes if he never took Lecture slides by Lawrie Brown advantage of it? (with edits by RHB) • —Talking to Strange Men, Ruth Rendell Outline Message Authentication • we will consider: • message authentication is concerned with: – message authentication requirements – protecting the integrity of a message – message authentication using encryption – validating identity of originator – non -repudiation of origin (dispute resolution) – MACs • three alternative approaches used: – HMAC authentication using a hash function – hash functions (see Ch 11) – DAA – message encryption – CMAC authentication using a block cipher – message authentication codes ( MACs ) and CCM – GCM authentication using a block cipher – PRNG using Hash Functions and MACs Symmetric Message Encryption Message Authentication Code • encryption can also provides authentication (MAC) • if symmetric encryption -
The First Cryptographic Hash Workshop
Workshop Report The First Cryptographic Hash Workshop Gaithersburg, MD Oct. 31-Nov. 1, 2005 Report prepared by Shu-jen Chang and Morris Dworkin Information Technology Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899 Available online: http://csrc.nist.gov/groups/ST/hash/documents/HashWshop_2005_Report.pdf 1. Introduction On Oct. 31-Nov. 1, 2005, 180 members of the global cryptographic community gathered in Gaithersburg, MD to attend the first Cryptographic Hash Workshop. The workshop was organized in response to a recent attack on the NIST-approved Secure Hash Algorithm SHA-1. The purpose of the workshop was to discuss this attack, assess the status of other NIST-approved hash algorithms, and discuss possible near-and long-term options. 2. Workshop Program The workshop program consisted of two days of presentations of papers that were submitted to the workshop and panel discussion sessions that NIST organized. The main topics for the discussions included the SHA-1 and SHA-2 hash functions, future research of hash functions, and NIST’s strategy. The program is available at http://csrc.nist.gov/groups/ST/hash/first_workshop.html. This report only briefly summarizes the presentations, because the above web site for the program includes links to the speakers' slides and papers. The main ideas of the discussion sessions, however, are described in considerable detail; in fact, the panelists and attendees are often paraphrased very closely, to minimize misinterpretation. Their statements are not necessarily presented in the order that they occurred, in order to organize them according to NIST's questions for each session. 3.