Patent Document ID: 8548161
Application ID: 12965689

Base Claim:
1. A method of cryptographically transforming data text c by a hardware processor comprising generating an integer representation m of the data text c according to 
 m=c d where d is a predetermined exponent, the step of generating the integer representation m including generating a sequence of intermediate numbers, each intermediate number being based on two or fewer earlier numbers in the sequence, the generating a sequence of intermediate numbers including retrieving a pre-stored instruction to determine which two or fewer earlier numbers in the sequence a given intermediate number is based on and a functional manipulation of the two or fewer earlier numbers required to generate the given intermediate number; wherein generating the integer representation m further includes deriving and storing a list of instructions, each instruction corresponding to the generation of a given intermediate number; wherein deriving and storing a list of instructions includes deriving the instructions from the predetermined exponent d; wherein deriving the instructions from the predetermined exponent includes: splitting the binary equivalent of the predetermined exponent d into first and second bit portions; executing a convergent sequence of operations on the first and second bit portions to reduce each bit portion to 1; and deriving an instruction at each step of the convergent sequence of operations, and wherein executing a convergent sequence of operations on the first and second bit portions includes: identifying the bit portion having the larger magnitude; halving the larger magnitude bit portion if the larger magnitude bit portion is even; and subtracting the smaller magnitude bit portion from the larger magnitude bit portion if the larger magnitude bit portion is odd; and repeating the identifying, halving and subtracting steps until each bit portion is 1.

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Claim 7:
7. A method according to claim 1 wherein executing a convergent sequence of operations on the first and second bit portions further includes halving the smaller magnitude bit portion if the larger magnitude bit portion is odd and the smaller magnitude bit portion is even and smaller than the larger magnitude bit portion by a predetermined factor.