Exponentiation ladder for cryptography
AssigneeApple Inc.
InventorsMathieu Ciet, Augustin J. Farrugia, Gianpaolo Fasoli, Filip Paun
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Abstract
Method and apparatus for data security using exponentiation. This is suitable for public key cryptography authentication and other data security applications using a one-way function. A type of exponentiation is disclosed here where the bits of an exponent value expressed in binary form correspond to a course (path) in a given graph defining the one-way function. This uses an approach called here F sequences. Each value is in a ladder of a sequence of values, as defined from its predecessor values. This ladder satisfies certain algebraic identities and is readily calculated by a computer program or logic circuitry.
Claims11
A method of determining a cryptographic one-way function value, comprising the acts of:
- providing an initial value;
- calculating from the initial value a plurality of successive exponential function output values Fn, n representing a sequence of integers and Fin=(Fn)i, i being an integer greater than one, wherein a length of the output values is at least that of the initial value;
- storing the plurality of values Fn in a storage element;
- and
- using the successive stored values in a cryptographic process.
A cryptographic system for providing a one-way function value, comprising:
- a storage element for data to be protected;
- an assembler coupled to the storage for assembling an initial value including the data to be protected;
- a bit selector coupled to the assembler;
- a calculator portion coupled to the bit selector and which calculates using the initial value a plurality of successive exponential function output values Fn, n representing a sequence of integers and Fin=(Fi)n, i being an integer greater than 1, wherein a length of the output values is at least that of the initial value;
- and
- a second storage element coupled to the calculator portion for storing output values of the calculator portion, the calculator portion also being coupled to the assembler.
Dependencies are inferred from the claim text.