A pair of functions f and g is said to be claw-free or claw-resistant if it is difficult to find inputs x, y to the functions such that
Such a pair of inputs is called a claw, describing the two-pronged inverse.
The concept of claw-resistance was introduced in the digital signature scheme of Goldwasser et al. [3], which was based on claw-free trapdoor permutations (see trapdoor one-way function and substitutions and permutations). Damgård [1] showed that claw-free permutations (without the trapdoor) could be employed to construct collision-resistant hash functions (see also collision resistance).
Recently, Dodis and Reyzin have shown that the claw-free property is essential to obtaining good security proofs for certain signature schemes [2].
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References
Damgård, Ivan Bjerre (1988). “Collision free hash functions and public key signature schemes.” Advances in Cryptology—EUROCRYPT'87, Lecture Notes in Computer Science, vol. 304, eds. D. Chaum and W.L. Price. Springer, Berlin, 203–216.
Dodis, Yevgeniy and Leonid Reyzin (2003). “On the power of claw-free permutations.” Security in Communications Networks (SCN 2002), Lecture Notes in Computer Science, vol. 2576, eds. S. Cimato, C. Galdi, and G. Persiano. Springer, Berlin, 55–73.
Goldwasser, Shafi, Silvio Micali, and Ronald L. Rivest (1988). “A digital signature scheme secure against adaptive chosen-message attacks.” SIAM Journal on Computing, 17 (2), 281–208.
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Kaliski, B. (2005). Claw-Free. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_63
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