Abstract
We propose a signature scheme where the private key is a random (n, n)-matrix T with coefficients in ℤm=ℤ/mℤ, m a product of two large primes. The corresponding public key is A,m with A = T⊤T. A signature y of a message z ∈ ℤm is any y∈(ℤm)n such that y⊤ Ay approximates z, e.g. \(\left| z-{{y}^{T}}Ay \right|<4{{m}^{{{2}^{-n}}}}\). Messages z can be efficiently signed using the private key T and by approximating z as a sum of squares. Even tighter approximations | z− y⊤Ay| can be achieved by tight signature procedures. Heuristical arguments show that forging signatures is not easier than factoring m. The prime decomposition of m is not needed for signing messages, however knowledge of this prime decomposition enables forging signatures. Distinct participants of the system may share the same modulus m provided that its prime decomposition is unknown. Our signature scheme is faster than the RSA-scheme.
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© 1984 Plenum Press, New York
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Ong, H., Schnorr, C.P. (1984). Signatures Through Approximate Representations by Quadratic Forms. In: Chaum, D. (eds) Advances in Cryptology. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-4730-9_10
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DOI: https://doi.org/10.1007/978-1-4684-4730-9_10
Publisher Name: Springer, Boston, MA
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