1. A method for performing Montgomery arithmetic in a cryptographic operation executed on a Montgomery machine, said method implementing said Montgomery arithmetic in a uniform fashion to improve the resistance of said Montgomery machine to side-channel cryptographic attacks, said method comprising a processor of said Montgomery machine: selecting one of traditional Montgomery multiplication or signed capable Montgomery multiplication, according to an instruction; when the signed capable Montgomery multiplication is selected, the method comprising: representing operands in a Montgomery arithmetic operation as signed values; operating on said signed values using a signed-capable Montgomery arithmetic operation to produce a signed intermediate result; adjusting a Montgomery radix R of a signed-capable Montgomery multiplication operation to suit a bound of input operands comprising said signed intermediate result and another operand; operating on said input operands using said signed-capable Montgomery multiplication as tailored to suit said bound of said input operands; and, producing a result for use in said cryptographic operation.