The GMR Signature Scheme was invented by Goldwasser et al. [2, 3]. In their landmark publication 2, they presented a formal framework of security definitions of cryptographic signature schemes (see digital signature schemes and public key cryptography) and they proposed the GMR Signature Scheme, which, under the assumption that integer factoring is hard, is provably secure by their strongest security definition, i.e., it resists existential forgery under an adaptive chosen message attack.
The value of the GMR Signature Scheme is not in its practical use, but in showing the existence of a provably secure signature scheme. Other more efficient signature schemes such as RSA digital signature scheme, DSA or ECDSA (see Digital Signature Standard) are memoryless, i.e., in order to produce a signature, one does not need to memorize any previously produced signatures (in whole or in part). Also, the computational effort of signing and verifying and the length of signatures are independent of...
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References
Merkle, Ralph (1982). “Secrecy authentication, and public-key systems.” PhD Dissertation, Electrical Engineering Department, ISL SEL 79-017k, Stanford University, Stanford, CA.
Goldwasser, Shafi, Silvio Micali, and Ronald L. Rivest (1984). “A “Paradoxical" solution to the signature problem.” 25th Symposium on Foundations of Computer Science (FOCS) 1984. IEEE Computer Society, 441–448.
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), 281–308.
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Bleumer, G. (2005). GMR Signature. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_176
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