Cryptography Hash Functions
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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. -
FIPS 140-2 Non-Proprietary Security Policy Oracle Linux 7 NSS
FIPS 140-2 Non-Proprietary Security Policy Oracle Linux 7 NSS Cryptographic Module FIPS 140-2 Level 1 Validation Software Version: R7-4.0.0 Date: January 22nd, 2020 Document Version 2.3 © Oracle Corporation This document may be reproduced whole and intact including the Copyright notice. Title: Oracle Linux 7 NSS Cryptographic Module Security Policy Date: January 22nd, 2020 Author: Oracle Security Evaluations – Global Product Security Contributing Authors: Oracle Linux Engineering Oracle Corporation World Headquarters 500 Oracle Parkway Redwood Shores, CA 94065 U.S.A. Worldwide Inquiries: Phone: +1.650.506.7000 Fax: +1.650.506.7200 oracle.com Copyright © 2020, Oracle and/or its affiliates. All rights reserved. This document is provided for information purposes only and the contents hereof are subject to change without notice. This document is not warranted to be error-free, nor subject to any other warranties or conditions, whether expressed orally or implied in law, including implied warranties and conditions of merchantability or fitness for a particular purpose. Oracle specifically disclaim any liability with respect to this document and no contractual obligations are formed either directly or indirectly by this document. This document may reproduced or distributed whole and intact including this copyright notice. Oracle and Java are registered trademarks of Oracle and/or its affiliates. Other names may be trademarks of their respective owners. Oracle Linux 7 NSS Cryptographic Module Security Policy i TABLE OF CONTENTS Section Title -
Extending NIST's CAVP Testing of Cryptographic Hash Function
Extending NIST’s CAVP Testing of Cryptographic Hash Function Implementations Nicky Mouha and Christopher Celi National Institute of Standards and Technology, Gaithersburg, MD, USA [email protected],[email protected] Abstract. This paper describes a vulnerability in Apple’s CoreCrypto library, which affects 11 out of the 12 implemented hash functions: every implemented hash function except MD2 (Message Digest 2), as well as several higher-level operations such as the Hash-based Message Authen- tication Code (HMAC) and the Ed25519 signature scheme. The vulnera- bility is present in each of Apple’s CoreCrypto libraries that are currently validated under FIPS 140-2 (Federal Information Processing Standard). For inputs of about 232 bytes (4 GiB) or more, the implementations do not produce the correct output, but instead enter into an infinite loop. The vulnerability shows a limitation in the Cryptographic Algorithm Validation Program (CAVP) of the National Institute of Standards and Technology (NIST), which currently does not perform tests on hash func- tions for inputs larger than 65 535 bits. To overcome this limitation of NIST’s CAVP, we introduce a new test type called the Large Data Test (LDT). The LDT detects vulnerabilities similar to that in CoreCrypto in implementations submitted for validation under FIPS 140-2. Keywords: CVE-2019-8741, FIPS, CAVP, ACVP, Apple, CoreCrypto, hash function, vulnerability. 1 Introduction The security of cryptography in practice relies not only on the resistance of the algorithms against cryptanalytical attacks, but also on the correctness and robustness of their implementations. Software implementations are vulnerable to software faults, also known as bugs. -
SELECTION of CYCLIC REDUNDANCY CODE and CHECKSUM March 2015 ALGORITHMS to ENSURE CRITICAL DATA INTEGRITY 6
DOT/FAA/TC-14/49 Selection of Federal Aviation Administration William J. Hughes Technical Center Cyclic Redundancy Code and Aviation Research Division Atlantic City International Airport New Jersey 08405 Checksum Algorithms to Ensure Critical Data Integrity March 2015 Final Report This document is available to the U.S. public through the National Technical Information Services (NTIS), Springfield, Virginia 22161. U.S. Department of Transportation Federal Aviation Administration NOTICE This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. The U.S. Government assumes no liability for the contents or use thereof. The U.S. Government does not endorse products or manufacturers. Trade or manufacturers’ names appear herein solely because they are considered essential to the objective of this report. The findings and conclusions in this report are those of the author(s) and do not necessarily represent the views of the funding agency. This document does not constitute FAA policy. Consult the FAA sponsoring organization listed on the Technical Documentation page as to its use. This report is available at the Federal Aviation Administration William J. Hughes Technical Center’s Full-Text Technical Reports page: actlibrary.tc.faa.gov in Adobe Acrobat portable document format (PDF). Technical Report Documentation Page 1. Report No. 2. Government Accession No. 3. Recipient's Catalog No. DOT/FAA/TC-14/49 4. Title and Subitle 5. Report Date SELECTION OF CYCLIC REDUNDANCY CODE AND CHECKSUM March 2015 ALGORITHMS TO ENSURE CRITICAL DATA INTEGRITY 6. Performing Organization Code 220410 7. Author(s) 8. Performing Organization Report No. -
A (Second) Preimage Attack on the GOST Hash Function
A (Second) Preimage Attack on the GOST Hash Function Florian Mendel, Norbert Pramstaller, and Christian Rechberger Institute for Applied Information Processing and Communications (IAIK), Graz University of Technology, Inffeldgasse 16a, A-8010 Graz, Austria [email protected] Abstract. In this article, we analyze the security of the GOST hash function with respect to (second) preimage resistance. The GOST hash function, defined in the Russian standard GOST-R 34.11-94, is an iter- ated hash function producing a 256-bit hash value. As opposed to most commonly used hash functions such as MD5 and SHA-1, the GOST hash function defines, in addition to the common iterated structure, a check- sum computed over all input message blocks. This checksum is then part of the final hash value computation. For this hash function, we show how to construct second preimages and preimages with a complexity of about 2225 compression function evaluations and a memory requirement of about 238 bytes. First, we show how to construct a pseudo-preimage for the compression function of GOST based on its structural properties. Second, this pseudo- preimage attack on the compression function is extended to a (second) preimage attack on the GOST hash function. The extension is possible by combining a multicollision attack and a meet-in-the-middle attack on the checksum. Keywords: cryptanalysis, hash functions, preimage attack 1 Introduction A cryptographic hash function H maps a message M of arbitrary length to a fixed-length hash value h. A cryptographic hash function has to fulfill the following security requirements: – Collision resistance: it is practically infeasible to find two messages M and M ∗, with M ∗ 6= M, such that H(M) = H(M ∗). -
Linear-XOR and Additive Checksums Don't Protect Damgård-Merkle
Linear-XOR and Additive Checksums Don’t Protect Damg˚ard-Merkle Hashes from Generic Attacks Praveen Gauravaram1! and John Kelsey2 1 Technical University of Denmark (DTU), Denmark Queensland University of Technology (QUT), Australia. [email protected] 2 National Institute of Standards and Technology (NIST), USA [email protected] Abstract. We consider the security of Damg˚ard-Merkle variants which compute linear-XOR or additive checksums over message blocks, inter- mediate hash values, or both, and process these checksums in computing the final hash value. We show that these Damg˚ard-Merkle variants gain almost no security against generic attacks such as the long-message sec- ond preimage attacks of [10,21] and the herding attack of [9]. 1 Introduction The Damg˚ard-Merkle construction [3, 14] (DM construction in the rest of this article) provides a blueprint for building a cryptographic hash function, given a fixed-length input compression function; this blueprint is followed for nearly all widely-used hash functions. However, the past few years have seen two kinds of surprising results on hash functions, that have led to a flurry of research: 1. Generic attacks apply to the DM construction directly, and make few or no assumptions about the compression function. These attacks involve attacking a t-bit hash function with more than 2t/2 work, in order to violate some property other than collision resistance. Exam- ples of generic attacks are Joux multicollision [8], long-message second preimage attacks [10,21] and herding attack [9]. 2. Cryptanalytic attacks apply to the compression function of the hash function. -
Hash (Checksum)
Hash Functions CSC 482/582: Computer Security Topics 1. Hash Functions 2. Applications of Hash Functions 3. Secure Hash Functions 4. Collision Attacks 5. Pre-Image Attacks 6. Current Hash Security 7. SHA-3 Competition 8. HMAC: Keyed Hash Functions CSC 482/582: Computer Security Hash (Checksum) Functions Hash Function h: M MD Input M: variable length message M Output MD: fixed length “Message Digest” of input Many inputs produce same output. Limited number of outputs; infinite number of inputs Avalanche effect: small input change -> big output change Example Hash Function Sum 32-bit words of message mod 232 M MD=h(M) h CSC 482/582: Computer Security 1 Hash Function: ASCII Parity ASCII parity bit is a 1-bit hash function ASCII has 7 bits; 8th bit is for “parity” Even parity: even number of 1 bits Odd parity: odd number of 1 bits Bob receives “10111101” as bits. Sender is using even parity; 6 1 bits, so character was received correctly Note: could have been garbled, but 2 bits would need to have been changed to preserve parity Sender is using odd parity; even number of 1 bits, so character was not received correctly CSC 482/582: Computer Security Applications of Hash Functions Verifying file integrity How do you know that a file you downloaded was not corrupted during download? Storing passwords To avoid compromise of all passwords by an attacker who has gained admin access, store hash of passwords Digital signatures Cryptographic verification that data was downloaded from the intended source and not modified. Used for operating system patches and packages. -
Cryptographic Checksum
Cryptographic checksum • A function that produces a checksum (smaller than message) • A digest function using a key only known to sender and recipient • Ensure both integrity and authenticity • Used for code-tamper protection and message-integrity protection in transit • The choices of hashing algorithms are Message Digest (MD) by Ron Rivest of RSA Labs or Secure Hash Algorithm (SHA) led by US government • MD: MD4, MD5; SHA: SHA1, SHA2, SHA3 k k message m tag Alice Bob Generate tag: Verify tag: ? tag S(k, m) V(k, m, tag) = `yes’ 4/19/2019 Zhou Li 1 Constructing cryptographic checksum • HMAC (Hash Message Authentication Code) • Problem to solve: how to merge key with hash H: hash function; k: key; m: message; example of H: SHA-2-256 ; output is 256 bits • Building a MAC out of a hash function: Paddings to make fixed-size block https://en.wikipedia.org/wiki/HMAC 4/19/2019 Zhou Li 2 Cryptoanalysis on crypto checksums • MD5 broken by Xiaoyun Input Output Wang et al. at 2004 • Collisions of full MD5 less than 1 hour on IBM p690 cluster • SHA-1 theoretically broken by Xiaoyun Wang et al. at 2005 • 269 steps (<< 280 rounds) to find a collision • SHA-1 practically broken by Google at 2017 • First collision found with 6500 CPU years and 100 GPU years Current Secure Hash Standard Properties https://shattered.io/static/shattered.pdf 4/19/2019 Zhou Li 3 Elliptic Curve Cryptography • RSA algorithm is patented • Alternative asymmetric cryptography: Elliptic Curve Cryptography (ECC) • The general algorithm is in the public domain • ECC can provide similar -
Advanced Meet-In-The-Middle Preimage Attacks: First Results on Full Tiger, and Improved Results on MD4 and SHA-2
Advanced Meet-in-the-Middle Preimage Attacks: First Results on Full Tiger, and Improved Results on MD4 and SHA-2 Jian Guo1, San Ling1, Christian Rechberger2, and Huaxiong Wang1 1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 2 Dept. of Electrical Engineering ESAT/COSIC, K.U.Leuven, and Interdisciplinary Institute for BroadBand Technology (IBBT), Kasteelpark Arenberg 10, B–3001 Heverlee, Belgium. [email protected] Abstract. We revisit narrow-pipe designs that are in practical use, and their security against preimage attacks. Our results are the best known preimage attacks on Tiger, MD4, and reduced SHA-2, with the result on Tiger being the first cryptanalytic shortcut attack on the full hash function. Our attacks runs in time 2188.8 for finding preimages, and 2188.2 for second-preimages. Both have memory requirement of order 28, which is much less than in any other recent preimage attacks on reduced Tiger. Using pre-computation techniques, the time complexity for finding a new preimage or second-preimage for MD4 can now be as low as 278.4 and 269.4 MD4 computations, respectively. The second-preimage attack works for all messages longer than 2 blocks. To obtain these results, we extend the meet-in-the-middle framework recently developed by Aoki and Sasaki in a series of papers. In addition to various algorithm-specific techniques, we use a number of conceptually new ideas that are applicable to a larger class of constructions. Among them are (1) incorporating multi-target scenarios into the MITM framework, leading to faster preimages from pseudo-preimages, (2) a simple precomputation technique that allows for finding new preimages at the cost of a single pseudo-preimage, and (3) probabilistic initial structures, to reduce the attack time complexity. -
Certicom Security Builder GSE Datasheet
Security Builder® GSE™ FIPS 140-2 VALIDATED CRYPTOGRAPHIC MODULE Build trusted, government-approved security into your products. Security Builder® GSE™ enables developers to quickly build client and server-side applications that require a FIPS 140-2 level 1 validation for the cryptographic module. Security Builder GSE acts as a software cryptographic provider within the Certicom® Security Architecture™ – a comprehensive, portable and modular solution designed to allow developers to quickly and cost-effectively embed security across multiple families and generations of devices and applications. MEETS GOVERNMENT SECURITY REQUIREMENTS REDUCES TIME TO MARKET A number of government regulations mandate the use of FIPS By building on Security Builder GSE, you can avoid the lengthy validated modules for the protection of data, especially in a and expensive FIPS validation process and get your product to wireless setting. FIPS also helps demonstrate adherence to market more quickly. Re-validation and re-branding options security best practices. In the US, for instance, compliance are also available if you wish for your product to be listed on with FIPS 140-2 can help manufacturers of network- the NIST Cryptographic Module Validation Program active connected devices and application software demonstrate best validation list. By using a pre-validated module you can meet practice encryption capabilities for protecting patient and user security requirements without diverting valuable resources and data. keep your developers focused on your core application. Security Builder GSE has been validated on a wide variety COMPREHENSIVE SECURITY SOLUTION of high-level and embedded operating systems, including QNX With support for leading client and server-side operating real-time OS, Android and iOS. -
Implementation of Hash Function for Cryptography (Rsa Security)
International Journal For Technological Research In Engineering Volume 4, Issue 6, February-2017 ISSN (Online): 2347 - 4718 IMPLEMENTATION OF HASH FUNCTION FOR CRYPTOGRAPHY (RSA SECURITY) Syed Fateh Reza1, Mr. Prasun Das2 1M.Tech. (ECE), 2Assistant Professor (ECE), Bitm,Bolpur ABSTRACT: In this thesis, a new method for expected to have a unique hash code and it should be implementing cryptographic hash functions is proposed. generally difficult for an attacker to find two messages with This method seeks to improve the speed of the hash the same hash code. function particularly when a large set of messages with Mathematically, a hash function (H) is defined as follows: similar blocks such as documents with common Headers H: {0, 1}* → {0, 1}n are to be hashed. The method utilizes the peculiar run-time In this notation, {0, 1}* refers to the set of binary elements configurability Feature of FPGA. Essentially, when a block of any length including the empty string while {0, 1}n refers of message that is commonly hashed is identified, the hash to the set of binary elements of length n. Thus, the hash value is stored in memory so that in subsequent occurrences function maps a set of binary elements of arbitrary length to of The message block, the hash value does not need to be a set of binary elements of fixed length. Similarly, the recomputed; rather it is Simply retrieved from memory, thus properties of a hash function are defined as follows: giving a significant increase in speed. The System is self- x {0, 1}*; y {0,1}n learning and able to dynamically build on its knowledge of Pre-image resistance: given y= H(x), it should be difficult to frequently Occurring message blocks without intervention find x. -
FIPS 198, the Keyed-Hash Message Authentication Code (HMAC)
ARCHIVED PUBLICATION The attached publication, FIPS Publication 198 (dated March 6, 2002), was superseded on July 29, 2008 and is provided here only for historical purposes. For the most current revision of this publication, see: http://csrc.nist.gov/publications/PubsFIPS.html#198-1. FIPS PUB 198 FEDERAL INFORMATION PROCESSING STANDARDS PUBLICATION The Keyed-Hash Message Authentication Code (HMAC) CATEGORY: COMPUTER SECURITY SUBCATEGORY: CRYPTOGRAPHY Information Technology Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899-8900 Issued March 6, 2002 U.S. Department of Commerce Donald L. Evans, Secretary Technology Administration Philip J. Bond, Under Secretary National Institute of Standards and Technology Arden L. Bement, Jr., Director Foreword The Federal Information Processing Standards Publication Series of the National Institute of Standards and Technology (NIST) is the official series of publications relating to standards and guidelines adopted and promulgated under the provisions of Section 5131 of the Information Technology Management Reform Act of 1996 (Public Law 104-106) and the Computer Security Act of 1987 (Public Law 100-235). These mandates have given the Secretary of Commerce and NIST important responsibilities for improving the utilization and management of computer and related telecommunications systems in the Federal government. The NIST, through its Information Technology Laboratory, provides leadership, technical guidance, and coordination of government efforts in the development of standards and guidelines in these areas. Comments concerning Federal Information Processing Standards Publications are welcomed and should be addressed to the Director, Information Technology Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Stop 8900, Gaithersburg, MD 20899-8900. William Mehuron, Director Information Technology Laboratory Abstract This standard describes a keyed-hash message authentication code (HMAC), a mechanism for message authentication using cryptographic hash functions.