Left to right binary modular exponentiation in Javacard

Question

I am thinking to implement left to right binary modular exponentiation in Javacard.

I know that there are libraries which can perform RSA encryption etc. but in my case I just need to perform the modular exponentiation.

The only thing that I am confused is that as there is a restriction of usage of the data types as Javacard accepts at most the int data type. But in my case the numbers could also be in double.

Is is still possible to implement this algorithm using Javacard API for the big numbers.

Answer 1

Modular exponentiation in general can be used through raw RSA (RSA without padding) or Diffie-Hellman calculations on a Java Card. That way the co-processor - which is generally present on high end Java Card implementations - can be used directly. An hardware assisted Montgomery calculation in the cryptographic coprocessor will outperform any specific calculations by a very large margin. Performing calculations on very large numbers my not even be possible using a low end processor due to efficiency issues.

Usually int is not available in Java Card implementations - if just because the whole Java Card API doesn't use int anywhere. This goes double for double as the processor is extremely unlikely to contain a floating point processor (FPU). So generally you're stuck with (signed) short values. Of course you can perform any kind of calculations using short - see my answer here - but it won't be pretty nor fast.

In the end, the Java Card subset of Java is easily a Turing-complete machine. So yes, anything is possible until you run out of memory or - indeed - time.

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Note that security measures may make some tricks such as raw RSA impossible to use for generic modular arithmetic. I would recommend to try DH first and dig deep into the manuals to find out what the requirements of your particular platform may be.