Exponent

Exponentiation is a mathematical operation, written as b raised to the power of n, involving two numbers, the base b and the exponent (or power) n.

Modulo

The modulo (sometimes called modulus) operation finds the remainder of division of one number by another

Rsa shorter operations

Bit large number

Quality | Example |
---|---|

Smaller |
"In rsa signing a message m means exponentiation with the private exponent d the result r is the smallest integer 0 and smaller than the modulo n so that" from question "RSA signature size?" |

Lower |
"1024 bit private exponent large number lower than the modulo" from question "Checking RSA key pairs error" |

Others

Quality | Example |
---|---|

Normally shorter |
"Little wonder you get errors the exponent is normally shorter than the modulo which is always the same size as the key size" from question "RSA BadPaddingException when decrypting" |

Value faster |
"Using the pow function and passing a modulo value is faster than computing the full exponent and then taking the modulo because the modulo can be applied to the partial products at each stage of the calculation which stops the value from getting too large 10 6 to the power of 10 6 has 6 million decimal digits with a modulo applied at each step the values never have to grow larger than the size of the modulo - about 13 digits in this example" from question "Finding remainder mod involving exponent and division involving huge numbers" |