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

, Tiger is a

cryptographic hash function A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with fixed size of n bits) that has special properties desirable for cryptography: * the probability of a particular n-bit output re ...

Eli Biham Eli Biham ( he, אלי ביהם) is an Israeli cryptographer and cryptanalyst, currently a professor at the Technion - Israel Institute of Technology Computer Science department. Starting from October 2008 and till 2013, Biham was the dean of t ...

in 1995 for efficiency on

64-bit In computer architecture, 64-bit Integer (computer science), integers, memory addresses, or other Data (computing), data units are those that are 64 bits wide. Also, 64-bit central processing unit, CPUs and arithmetic logic unit, ALUs are those ...

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" s ...

, 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. Goldwasser, S. and Bellare, M.b ...

. 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. The transformation is "one-way", meaning that it is difficult given a particular output to compute inputs which compre ...

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 Sha ...

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 The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...

) make implementations in hardware or

microcontroller A microcontroller (MCU for ''microcontroller unit'', often also MC, UC, or μC) is a small computer on a single VLSI integrated circuit (IC) chip. A microcontroller contains one or more CPUs (processor cores) along with memory and programmable i ...

s difficult.

Usage

Tiger is frequently used in

Merkle hash tree In cryptography and computer science, a hash tree or Merkle tree is a tree in which every "leaf" (node) is labelled with the cryptographic hash of a data block, and every node that is not a leaf (called a ''branch'', ''inner node'', or ''inode'') ...

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 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 partitio ...

standard, but was abandoned in favor of

RIPEMD RIPEMD (RIPE Message Digest) is a family of cryptographic hash functions developed in 1992 (the original RIPEMD) and 1996 (other variants). There are five functions in the family: RIPEMD, RIPEMD-128, RIPEMD-160, RIPEMD-256, and RIPEMD-320, of w ...

-160.

OID

refers to TIGER as having no

OID Oid or OID may refer to: * ''Oid'', a 2005 album by Space Manoeuvres * Object identifier, an object used in computing to name an object * Oracle Internet Directory, a directory service produced by Oracle Corporation * OpenID, a shared identity se ...

, whereas the GNU Coding Standards list TIGER as having OID 1.3.6.1.4.1.11591.12.2. In the

IPSEC In computing, Internet Protocol Security (IPsec) is a secure network protocol suite that authenticates and encrypts packets of data to provide secure encrypted communication between two computers over an Internet Protocol network. It is used in ...

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 ADC may refer to: Science and medicine * ADC (gene), a human gene * AIDS dementia complex, neurological disorder associated with HIV and AIDS * Allyl diglycol carbonate or CR-39, a polymer * Antibody-drug conjugate, a type of anticancer treatm ...

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 In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of 16. Unlike the decimal system representing numbers using 10 symbols, hexa ...

digits in

little-endian In computing, endianness, also known as byte sex, is the order or sequence of bytes of a word of digital data in computer memory. Endianness is primarily expressed as big-endian (BE) or little-endian (LE). A big-endian system stores the most si ...

byte order. The following demonstrates a 43-byte

ASCII ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because of ...

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 Stefan Lucks is a researcher in the fields of communications security and cryptography. Lucks is known for his attack on Triple DES, and for extending Lars Knudsen's Square attack to Twofish, a cipher outside the Square family, thus generalisi ...

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