cryptography Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), ...

, Tiger is a

cryptographic hash function A cryptographic hash function (CHF) is a hash algorithm (a map (mathematics), map of an arbitrary binary string to a binary string with a fixed size of n bits) that has special properties desirable for a cryptography, cryptographic application: ...

Eli Biham Eli Biham () is an Israeli cryptographer and cryptanalyst who is a professor at the Technion - Israel Institute of Technology Computer Science department. From 2008 to 2013, Biham was the dean of the Technion Computer Science department, afte ...

in 1995 for efficiency on

64-bit In computer architecture, 64-bit integers, memory addresses, or other data units are those that are 64 bits wide. Also, 64-bit central processing units (CPU) and arithmetic logic units (ALU) are those that are based on processor registers, a ...

platforms. The size of a Tiger hash value is 192 bits. Truncated versions (known as Tiger/128 and Tiger/160) can be used for compatibility with protocols assuming a particular hash size. Unlike the

SHA-2 SHA-2 (Secure Hash Algorithm 2) is a set of cryptographic hash functions designed by the United States National Security Agency (NSA) and first published in 2001. They are built using the Merkle–Damgård construction, from a one-way compression ...

family, no distinguishing initialization values are defined; they are simply prefixes of the full Tiger/192 hash value. Tiger2 is a variant where the message is padded by first appending a byte with the hexadecimal value of 0x80 as in

MD4 The MD4 Message-Digest Algorithm is a cryptographic hash function developed by Ronald Rivest in 1990. The digest length is 128 bits. The algorithm has influenced later designs, such as the MD5, SHA-1 and RIPEMD algorithms. The initialism "MD" st ...

MD5 The MD5 message-digest algorithm is a widely used hash function producing a 128-bit hash value. MD5 was designed by Ronald Rivest in 1991 to replace an earlier hash function MD4, and was specified in 1992 as Request for Comments, RFC 1321. MD5 ...

and SHA, rather than with the hexadecimal value of 0x01 as in the case of Tiger. The two variants are otherwise identical.

Algorithm

Tiger is based on

Merkle–Damgård construction In cryptography, the Merkle–Damgård construction or Merkle–Damgård hash function is a method of building collision-resistant cryptographic hash functions from collision-resistant one-way compression functions. This construction was used in t ...

. The

one-way compression function In cryptography, a one-way compression function is a function that transforms two fixed-length inputs into a fixed-length output.Handbook of Applied Cryptography by Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone. Fifth Printing (August ...

operates on 64-bit words, maintaining 3 words of state and processing 8 words of data. There are 24 rounds, using a combination of operation mixing with XOR and addition/subtraction, rotates, and

S-box In cryptography, an S-box (substitution-box) is a basic component of symmetric key algorithms which performs substitution. In block ciphers, they are typically used to obscure the relationship between the key and the ciphertext, thus ensuring Clau ...

lookups, and a fairly intricate key scheduling algorithm for deriving 24 round keys from the 8 input words. Although fast in software, Tiger's large S-boxes (four S-boxes, each with 256 64-bit entries totaling 8 KiB) make implementations in hardware or

microcontroller A microcontroller (MC, uC, or μC) or microcontroller unit (MCU) is a small computer on a single integrated circuit. A microcontroller contains one or more CPUs (processor cores) along with memory and programmable input/output peripherals. Pro ...

s difficult.

Usage

Tiger is frequently used in Merkle hash tree form, where it is referred to as TTH ( Tiger Tree Hash). TTH is used by many clients on the Direct Connect and

Gnutella Gnutella is a peer-to-peer network protocol. Founded in 2000, it was the first decentralized peer-to-peer network of its kind, leading to other, later networks adopting the model. In June 2005, Gnutella's population was 1.81 million computer ...

file sharing networks, and can optionally be included in the

BitTorrent BitTorrent is a Protocol (computing), communication protocol for peer-to-peer file sharing (P2P), which enables users to distribute data and electronic files over the Internet in a Decentralised system, decentralized manner. The protocol is d ...

metafile for better content availability. Tiger was considered for inclusion in the

OpenPGP Pretty Good Privacy (PGP) is an encryption program that provides cryptographic privacy and authentication for data communication. PGP is used for signing, encrypting, and decrypting texts, e-mails, files, directories, and whole disk partit ...

standard, but was abandoned in favor of RIPEMD-160.

OID

refers to TIGER as having no OID, whereas the GNU Coding Standards list TIGER as having OID 1.3.6.1.4.1.11591.12.2. In the IPSEC subtree, HMAC-TIGER is assigned OID 1.3.6.1.5.5.8.1.3. No OID for TTH has been announced yet.

Byte order

The specification of Tiger does not define the way its output should be printed but only defines the result to be three ordered 64-bit integers. The "testtiger" program at the author's homepage was intended to allow easy testing of the test source code, rather than to define any particular print order. The protocols Direct Connect and ADC as well as the program tthsum use little-endian byte order, which is also preferred by one of the authors.

Examples

In the example below, the 192-bit (24-byte) Tiger hashes are represented as 48

hexadecimal Hexadecimal (also known as base-16 or simply hex) is a Numeral system#Positional systems in detail, positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbo ...

digits in

little-endian '' Jonathan_Swift.html" ;"title="Gulliver's Travels'' by Jonathan Swift">Gulliver's Travels'' by Jonathan Swift, the novel from which the term was coined In computing, endianness is the order in which bytes within a word (data type), word of d ...

byte order. The following demonstrates a 43-byte

ASCII ASCII ( ), an acronym for American Standard Code for Information Interchange, is a character encoding standard for representing a particular set of 95 (English language focused) printable character, printable and 33 control character, control c ...

input and the corresponding Tiger hashes: Tiger("The quick brown fox jumps over the lazy og") = 6d12a41e72e644f017b6f0e2f7b44c6285f06dd5d2c5b075 Tiger2("The quick brown fox jumps over the lazy og") = 976abff8062a2e9dcea3a1ace966ed9c19cb85558b4976d8 Even a small change in the message will (with very high probability) result in a completely different hash, e.g. changing to : Tiger("The quick brown fox jumps over the lazy og") = a8f04b0f7201a0d728101c9d26525b31764a3493fcd8458f Tiger2("The quick brown fox jumps over the lazy og") = 09c11330283a27efb51930aa7dc1ec624ff738a8d9bdd3df The hash of the zero-length string is: Tiger("") = 3293ac630c13f0245f92bbb1766e16167a4e58492dde73f3 Tiger2("") = 4441be75f6018773c206c22745374b924aa8313fef919f41

Cryptanalysis

Unlike MD5 or SHA-0/1, there are no known effective attacks on the full 24-round Tiger except for pseudo-near collision. While MD5 processes its state with 64 simple 32-bit operations per 512-bit block and SHA-1 with 80, Tiger updates its state with a total of 144 such operations per 512-bit block, additionally strengthened by large S-box look-ups. John Kelsey and Stefan Lucks have found a collision-finding attack on 16-round Tiger with a time complexity equivalent to about 2⁴⁴ compression function invocations and another attack that finds pseudo-near collisions in 20-round Tiger with work less than that of 2⁴⁸ compression function invocations. Florian Mendel et al. have improved upon these attacks by describing a collision attack spanning 19 rounds of Tiger, and a 22-round pseudo-near-collision attack. These attacks require a work effort equivalent to about 2⁶² and 2⁴⁴ evaluations of the Tiger compression function, respectively.

References

External links

* {{Cryptography navbox , hash Cryptographic hash functions