The problem of computing an exponentiation occurs frequently in modern cryptography. In particular, it is the core operation in the three most popular families of public-key algorithms: integer factorization based schemes (e.g., RSA public key encryption); discrete logarithm problem based schemes (e.g., Digital Signature Standard or Diffie-Hellman key agreement); and elliptic curve cryptography. Exponentiation is defined as the repeated application of the group operation to a single group element. If we assume a multiplicative group, i.e., the group operation is called “multiplication”, and we denote the group element by g, we write an exponentation as
This case is in particular relevant for RSA and discrete logarithm schemes in finite fields. It should be kept in mind that the corresponding notation for additive groups, i.e., groups where the group operation is an addition, looks as follows:
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© 2005 International Federation for Information Processing
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Paar, C. (2005). Exponentiation Algorithms. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_150
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DOI: https://doi.org/10.1007/0-387-23483-7_150
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