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Determining whether a given cryptographic function is a permutation of another given cryptographic function—A problem in intellectual property
تعیین اینکه آیا یک کارکرد رمزنگاری شده ، تغییر در عملکرد رمزنگاری داده شده دیگر است — مشکلی در مالکیت معنوی-2019 Imagine that, in order to avoid patent fees, licensing agreements, or export restrictions, someone permutes the plaintext bits, ciphertext bits, or key bits of a block cipher. All security properties of the block cipher would be preserved. There are many possible such permutations (e.g. 23116.32for the Advanced Encryption Standard, AES-256). It might seem infeasible to detect this fraud, and even harder to determine the permutation matrices used. Instead of a block cipher, it could be the compression function of a cryptographic hash, or any other cryptographic function.
This paper presents an algorithm whereby this fraud could be easily detected, by means of a SAT-Solver—a standard off-the-shelf software package that solves small-to-medium sized instances of the logical satisfiability problem. This paper also presents how this problem can be modeled in a system of polynomial equations (e.g. in the context of algebraic cryptanalysis). Moreover, this problem is related to the “isomorphism of polynomials” problem and that connection is explored at length. Keywords: Algebraic cryptanalysis | Block ciphers | Circuit equivalence | Intellectual property fraud detection | Isomorphism of polynomials | Logical satisfiability solvers (SAT-solvers) | Polynomials mod 2 |
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