Multiplicative inverse
A multiplicative inverse of an element is another element whose product with it equals the multiplicative identity.
Hacking Cryptography
A multiplicative inverse of an element is another element whose product with it equals the multiplicative identity in the relevant group.
- How it is used
- Recovers an LCG multiplier from outputs and derives the RSA private exponent from a public exponent.
- How deep it goes
- Works through modular inversion with a clock example and Go call, while deferring big-number-library detail and RSA correctness proof.
- Examples
- Uses 7 modulo 12, LCG output differences, Go’s ModInverse call, and an RSA keypair with p = 193 and q = 727.
- What you can do after
- Apply it via Go’s math/big library to recover an LCG multiplier or calculate an RSA private exponent.
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Modern C, Third Edition
A multiplicative inverse of a nonzero number is a number whose product with it equals one.
- How it is used
- Uses inverse approximation to demonstrate while, for, break, and continue iteration patterns.
- How deep it goes
- Explains the stopping test and update formula, but stops short of deriving Heron approximation mathematically.
- Examples
- Demonstrates inverses for 0.07, 5, and 6E+23, reporting approximations whose products approach one.
- What you can do after
- Build it from scratch in C using scaling, Heron updates, precision checks, and iteration safeguards.
Read how Modern C, Third Edition explains multiplicative inverse →
Related concepts
- Heron approximationproduced by · Heron approximation is an iterative numerical method that refines an estimate of a square root or related reciprocal quantity.
- inversekind of · An inverse is a value or operation that reverses the effect of another value or operation under a specified composition rule.
- matrix inverseincludes · A matrix inverse is a matrix that, when it exists, multiplies with a square matrix to produce the identity matrix.
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