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This paper presents algorithms for local inversion of maps and shows howseveral important computational problems such as cryptanalysis of symmetricencryption algorithms, RSA algorithm and solving the elliptic curve discretelog problem (ECDLP) can be addressed as local inversion problems. Themethodology is termed as the \emph{Local Inversion Attack}. It utilizes theconcept of \emph{Linear Complexity} (LC) of a recurrence sequence generated bythe map defined by the cryptanalysis problem and the given data. It is shownthat when the LC of the recurrence is bounded by a bound of polynomial order inthe bit length of the input to the map, the local inversion can be accomplishedin polynomial time. Hence an incomplete local inversion algorithm whichsearches a solution within a specified bound on computation can estimate thedensity of weak cases of cryptanalysis defined by such data causing low LC.Such cases can happen accidentally but cannot be avoided in practice and arefatal insecurity flaws of cryptographic primitives which are wrongly assumed tobe secure on the basis of exponential average case complexity. An incompletealgorithm is proposed for solving problems such as key recovery of symmetricencryption algorithms, decryption of RSA ciphertext without factoring themodulus, decrypting any ciphertext of RSA given one plaintext ciphertext paircreated with same public key in chosen ciphertext attack and solving thediscrete logarithm on elliptic curves over finite fields (ECDLP) as localinversion problems. It is shown that when the LCs of the respective recurrencesfor given data are small, solutions of these problems are possible inpractically feasible time and memory resources.

Local inversion of maps: A new attack on Symmetric encryption, RSA and ECDLP