Add a modexp example guest program + benchmark #1067

[Shubham1905s]

This PR adds a new guest program modexp-chain that performs repeated modular
exponentiation operations similar to EVM modexp.

✔ Configurable bitlengths for base, modulus, exponent
✔ Configurable number of iterations (similar to sha2-chain)
✔ Added corresponding benchmark entry in e2e_profiling.rs
✔ Uses fast modular exponentiation
✔ Randomized inputs for benchmarking

This closes issue #1067.

[graphite-app]

The current implementation of modexp_chain doesn't create a chain of operations - it repeatedly calculates the same modular exponentiation num_iters times without using the result of the previous calculation as input to the next one.

To create a proper chain where each result feeds into the next calculation, consider modifying the implementation to:

let mut out: u128 = base;
for _ in 0..num_iters {
    out = mod_pow(out, exp, modulus);
}

This way, each iteration will use the previous result as the base for the next modular exponentiation, creating a true chain of operations.

Suggested change

	let mut out: u128 = 0;
	for _ in 0..num_iters {
	out = mod_pow(base, exp, modulus);
	}
	let mut out: u128 = base;
	for _ in 0..num_iters {
	out = mod_pow(out, exp, modulus);
	}

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[graphite-app]

Critical overflow bug in mul_mod: When modulus > u128::MAX / 2 + 1, the operations res + a (line 11) and a << 1 (line 13) can overflow before the modulo is applied, causing either:

• Panic in debug builds
• Silent incorrect results in release builds due to wrapping

Example: If modulus = (u128::MAX / 2) + 2, then res and a can each be up to modulus - 1, making res + a > u128::MAX.

Fix by using checked arithmetic:

fn mul_mod(mut a: u128, mut b: u128, m: u128) -> u128 {
    if m == 0 {
        panic!("modulus cannot be zero");
    }
    let mut res: u128 = 0;
    a %= m;
    while b > 0 {
        if (b & 1) == 1 {
            res = (res + a) % m;
        }
        a = (a + a) % m;  // Use addition instead of shift to avoid overflow
        b >>= 1;
    }
    res
}

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[graphite-app]

Modulus validation missing: The mod_pow function doesn't validate that modulus != 0. Division by zero will occur on line 20 (1 % m) and line 21 (base %= m) if modulus is 0, causing a panic.

Add validation:

fn mod_pow(mut base: u128, mut exp: u128, m: u128) -> u128 {
    if m == 0 {
        panic!("modulus cannot be zero");
    }
    // rest of implementation
}

Suggested change

	fn mod_pow(mut base: u128, mut exp: u128, m: u128) -> u128 {
	let mut result: u128 = 1 % m;
	base %= m;
	while exp > 0 {
	if (exp & 1) == 1 {
	result = mul_mod(result, base, m);
	}
	base = mul_mod(base, base, m);
	exp >>= 1;
	}
	result
	}
	fn mod_pow(mut base: u128, mut exp: u128, m: u128) -> u128 {
	if m == 0 {
	panic!("modulus cannot be zero");
	}
	let mut result: u128 = 1 % m;
	base %= m;
	while exp > 0 {
	if (exp & 1) == 1 {
	result = mul_mod(result, base, m);
	}
	base = mul_mod(base, base, m);
	exp >>= 1;
	}
	result
	}

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