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The speed of RSA hinges on the ability to do large modular exponentiations quickly. While e can be made small, d generally cannot. A popular method for fast modular exponentiation is the Square and Multiply algorithm. Suppose that N 8453 and d = 4961. We want to use the Square and Multiply algorithm to quickly decrypt y = 7475. a) Express d as a binary string (e. g. 10110110). = b) Supposing that initially r = y = 7475, enter the order of square operations (SQ) and multiply operations (MUL) that must be performed on r to compute yd mod N. Enter as a comma separated list, for example SQ, MUL, SQ, SQ, SQ, MUL, SQ, SQ, MUL, SQ, Sc c) What is x = yd mod N?

The speed of RSA hinges on the ability to do large modular exponentiations quickly. While e can be made small, d generally cannot. A popular method for fast modular exponentiation is the Square and Multiply algorithm. Suppose that N 8453 and d = 4961. We want to use the Square and Multiply algorithm to quickly decrypt y = 7475. a) Express d as a binary string (e. g. 10110110). = b) Supposing that initially r = y = 7475, enter the order of square operations (SQ) and multiply operations (MUL) that must be performed on r to compute yd mod N. Enter as a comma separated list, for example SQ, MUL, SQ, SQ, SQ, MUL, SQ, SQ, MUL, SQ, Sc c) What is x = yd mod N?

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**Educational Text on RSA and Fast Modular Exponentiation** The speed of RSA encryption hinges on the ability to perform large modular exponentiations quickly. While the exponent \( e \) can often be small, the exponent \( d \) generally cannot. A popular method for fast modular exponentiation is the Square and Multiply algorithm. **Example Problem:** Suppose we have: - \( N = 8453 \) - \( d = 4961 \) Our goal is to use the Square and Multiply algorithm to quickly decrypt \( y = 7475 \). **Tasks:** a) Express \( d \) as a binary string (e.g., 1011010). *Input Box* b) Assuming initially \( r = y = 7475 \), you need to determine the sequence of square operations (SQ) and multiply operations (MUL) that must be performed on \( r \) to compute \( y^d \mod N \). Enter this sequence as a comma-separated list. For example: \( \text{SQ, MUL, SQ, SQ, SQ, MUL, SQ, SQ, MUL, SQ, SQ} \). *Input Box* c) Compute the value of \( x = y^d \mod N \). *Input Box*
Transcribed Image Text:**Educational Text on RSA and Fast Modular Exponentiation** The speed of RSA encryption hinges on the ability to perform large modular exponentiations quickly. While the exponent \( e \) can often be small, the exponent \( d \) generally cannot. A popular method for fast modular exponentiation is the Square and Multiply algorithm. **Example Problem:** Suppose we have: - \( N = 8453 \) - \( d = 4961 \) Our goal is to use the Square and Multiply algorithm to quickly decrypt \( y = 7475 \). **Tasks:** a) Express \( d \) as a binary string (e.g., 1011010). *Input Box* b) Assuming initially \( r = y = 7475 \), you need to determine the sequence of square operations (SQ) and multiply operations (MUL) that must be performed on \( r \) to compute \( y^d \mod N \). Enter this sequence as a comma-separated list. For example: \( \text{SQ, MUL, SQ, SQ, SQ, MUL, SQ, SQ, MUL, SQ, SQ} \). *Input Box* c) Compute the value of \( x = y^d \mod N \). *Input Box*
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