The total processing speed of microprocessors (based on clock rate and number of circuits) is doubling roughly every year. Today a symmetric session key needs to be 100 bits long to be considered strong. How long will a symmetric session key have to be in 30 years to be considered strong? (Hint: Consider how much longer decryption takes if the key length is increased by a single bit.) Explain.

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Yusen Luo says

In 30 years, to maintain the same level of security against brute force attacks, a symmetric session key will need to be 130 bits long.The security of a symmetric key encryption relies on the key length. If the key length is 𝑛 bits, there are 2 to the power of 𝑛 possible keys. Increasing the key length by one bit doubles the number of possible keys, making the decryption time (assuming brute force) also double. Conversely, increasing computational power allows more keys to be tested in the same amount of time.Given that computational power doubles every year, in 30 years, the computational power will have increased by a factor of 2 to the power of 30.Today, a 100-bit key is considered strong with 2 to the power of 100 possible combinations.To maintain the same level of security, the new key length 𝑘 must ensure that the time to brute force it remains proportional to the current time.For the decryption time to remain constant,a symmetric session key will need to be 100 + 30=130 bits long (taking the logarithm (base 2) of both sides).

Yifei Que says

The overall processing speed of microprocessors doubles every year, which is a common view based on technological progress and hardware development. However, the direct relationship between this growth rate and the length or required strength of the symmetric session key is not direct.

The length of a symmetric session key, such as 100 bits, is considered a powerful standard based on current security practices in cryptography and the ability to resist brute force attacks. The longer the key length, the longer the time required for brute force cracking, thereby improving security.

However, to predict how long it will take for symmetric session keys to be considered powerful within 30 years, we need to consider the development of encryption algorithms and attack techniques.

Jianan Wu says

The processing speed of microprocessors doubles every year, but the increase in key length does not directly correspond to the speed of technological progress. The strength of a symmetric session key is directly proportional to its length, and the longer the length, the more difficult it is to crack. Even if microprocessor performance significantly improves within 30 years, it cannot be simply inferred that the key length will increase exponentially. Because the increase in key length not only needs to consider technical feasibility, but also security and practical application needs. Therefore, within 30 years, a symmetric session key may need to exceed 100 bits to be considered powerful, but the specific length and time relationship are difficult to accurately predict.

Dongchang Liu says

In 30 years, a symmetric session key will need to be 130 bits long to be considered strong. The total processing speed of microprocessors is doubling roughly every year. Currently, a 100-bit key is considered strong, but as processing speeds increase by a factor of approximately 1 billion (2^30) over 30 years, the computational power available for decryption will significantly increase. Since decryption time doubles with each additional bit in the key length, to counteract this increase in processing speed, the key length must also increase. Therefore, adding 30 bits to the current 100-bit key, resulting in a 130-bit key, will maintain the same level of security against brute-force attacks in the future.

Ao Li says

Typically, in order to maintain security, the growth in key length needs to be at least proportional to the square root of the growth in computing power. This is because the complexity of cracking a key is usually exponentially proportional to the key length, while the growth of computing power is linear (doubling every year). Therefore, in order to maintain the same level of security, the key length needs to grow at a slower rate. Since the processing power doubles every year, after 30 years the processing power will be (2^{30}) times the original processing power. If we assume that the growth of the key length is proportional to the square root of the growth in computing power, then the length of the key will be (\sqrt{2^{30}}) times the original length in 30 years. This is equal to (2^{15}) times, or (32768) times.Converting the original length to the new length: since current symmetric session keys need to be 100 bits long to be considered secure, in 30 years the key length will need to be (100 \times 32768 = 3,276,800) bits in order to maintain the same level of security.

Tongjia Zhang says

The total processing speed of a microprocessor (based on the clock rate and the number of circuits) approximately doubles every year. Today, symmetric session keys need to be 100 bits long to be considered strong. How long would it take for a symmetric session key to be considered strong in 30 years? (Tip: Consider how long it takes to decrypt if the key length is increased by one bit.) Explain it. Assume that currently (0 years) a symmetric session key needs 100 bits to be considered strong. Considering that the processing speed of microprocessors doubles every year, the processing power in 30 years will be (2^{30}) times that of today. If the key length stays the same, the computing power in 30 years will be able to easily crack a 100-bit key.

Xinyue Zhang says

The total processor speed of a microprocessor depends on the clock rate and the number of circuits. In general, this speed doubles roughly every year, which means that the processor’s performance doubles in the same time interval. If the symmetric session key length is increased by 1 bit, the time required for decryption will roughly double. If a symmetric session key needs to be 100 bits long to be considered a strong session key, then if we want a key strong enough to last 30 years, we need to consider decryption time. Assuming that the time to crack a bit is t, the time to crack a 100-bit key will be 2^100 * t. If we want this key to remain secure for 30 years, we need to make sure that this lasts much longer than 30 years. Therefore, we need to find a key length long enough to ensure that it will not be cracked for 30 years.

Zhichao Lin says

2^n=2^100×2^30

2^n=2^130

n=130

Thus, to maintain the same level of security in 30 years, a symmetric session key will need to be 130 bits long. This ensures that even with the increased processing power, brute-forcing the key remains computationally infeasible.

Qian Wang says

If a 100-bit key is considered strong today, in 30 years, the processing speed would be 2^30 times faster. To maintain the same level of security, we need to double the key length. Thus, the new key length required to be considered strong in 30 years will be:

2×100 = 200 bits.

A symmetric session key will need to be 200 bits long in 30 years to be considered strong.

Ruoyu Zhi says

To know how long it takes for a symmetric session key to be considered strong within 30 years, we first need to understand the concept of key length in symmetric encryption algorithms and its relationship with security. In symmetric encryption, the security of encryption largely depends on the length of the encryption key. The longer the length, the longer it takes to decrypt.

But based on the premise of the problem, Today a symmetric session key needs to be 100 bits long to be considered strong. However, with current computing power, it is computationally infeasible for attackers to decrypt data encrypted with a 100 bit key in a reasonable amount of time. Considering that the key length is increasing by a single bit, we can expect that computing power will increase exponentially over time.

If we consider increasing the key length by one bit, which is approximately twice the decryption time, we can estimate the required key length in 30 years:

[\ text {Decryption time with 100 bit key} \ times 2 ^ {30}]

This calculation assumes that due to the doubling of processing speed, the decryption time using a 100 bit key doubles annually.

Mengfan Guo says

In symmetric encryption, increasing the key length by one bit approximately doubles the work factor because the number of possible keys increases exponentially with key length.

If we assume that the processing speed doubles every year, then in 30 years, the processing speed would have increased by a factor of ( 2^{30} ). This means that a brute force attack would be ( 2^{30} ) times faster in 30 years than it is today.

To maintain the same level of security in the face of this increased processing power, a symmetric session key would need to be long enough that the work factor remains high enough to deter brute force attacks. If the processing power increases by ( 2^{30} ), the key length would need to increase by 30 bits

Therefore, if a 100-bit key is considered strong today, in 30 years, a key would need to be ( 100 + 30 = 130 ) bits long to be considered equally strong, assuming that the relationship between key length and computational effort remains constant and that the cryptographic algorithms do not change significantly in their resistance to attacks.

Yihan Wang says

In 30 years, a symmetric session key would need to be 130 bits long to offer the same level of strength as a 100-bit key does today,

In the case of symmetric encryption keys, each additional bit in the key length doubles the number of possible keys. This means that an attacker would need to try twice as many keys to brute force the encryption.

To determine how long a symmetric session key will need to be in 30 years to be considered strong, we need to consider the rate at which computational power increases and how that affects the time required to brute force a key of a given length. If we assume that processing power doubles every year (which is a more aggressive rate than Moore’s Law), then in 30 years, processors will be 2^30 (1,073,741,824) times more powerful.

Given that a 100-bit key is currently considered strong, we need to find out how many more bits would be required to maintain the same level of security against these much more powerful processors. Each bit added to the key length doubles the time required to brute force it. Therefore, to counteract the 2^30 increase in processing power, we would need to add 30 more bits to the key length.

So, in 30 years, a symmetric session key would need to be 130 bits long to offer the same level of strength as a 100-bit key does today, assuming that processing power doubles every year. It’s important to note that this is a simplified calculation and actual key strength requirements can be influenced by various factors, including advancements in cryptanalysis techniques and the availability of quantum computers, which could significantly affect the time required to break encryption keys.

Fang Dong says

In cryptography, the length of the key determines the strength of the encryption. As computing power improves, key lengths that were once considered secure may become easy to crack in the future. If the total processing speed of a microprocessor doubles every year, the amount of computing power needed to break encryption should, in theory, grow at a similar rate. Assuming that a symmetric session key needs to be 100 bits long to be considered strong, we want to know how long a key would need to be 30 years later to achieve the same level of security, and in cryptography, increasing the bit length of a key roughly doubles the difficulty of cracking the key because the size of the possible key space doubles. So if computing power doubles every year, the key length also needs to increase by one bit every year in order to maintain the same level of security. After 30 years, to maintain the same level of security, the number of bits the key length needs to increase is， 30 years x 1 bit/year =30 bits.

So, if today’s 100-bit symmetric key is considered strong, then in 30 years, to achieve the same level of security, the key length will need to be increased by 30 bits, that is, a 130-bit key will be required.

Menghe LI says

To determine how long a symmetric session key will need to be in 30 years to be considered strong, we can consider the impact of Moore’s Law on processing speed and its relation to encryption strength.

Moore’s Law states that the processing speed of microprocessors, based on clock rate and number of circuits, doubles roughly every year. Therefore, in 30 years, the processing speed would have doubled approximately 30 times.

Now, let’s consider the impact of increasing the key length by a single bit on decryption time. Generally, doubling the key length approximately doubles the time required for decryption, assuming all other factors remain constant.

If a 100-bit symmetric session key is considered strong today, in 30 years, with processing speed doubling approximately 30 times, decryption speed will have increased significantly. To maintain the same level of security, the symmetric session key length will need to be increased accordingly.

Since the processing speed doubles each year for 30 years, the decryption time will decrease by a factor of (2^ {30}) compared to today. To counterbalance this increased decryption speed and maintain the same level of security, the symmetric session key length will need to be increased by approximately the same factor.

If we denote (L) as the length of the symmetric session key required in 30 years, we can express this relationship as:

[2^ {L – 100} = 2^ {30}]，Solving for (L):，[L – 100 = 30]，[L = 30 + 100]

[L = 130]

Therefore, in 30 years, a symmetric session key will need to be approximately 130 bits long to be considered strong, assuming decryption time is the primary factor in determining key strength and Moore’s Law continues to hold true for processing speed advancements.

Chaoyue Li says

Since the processing speed doubles every year, this means that the processing speed doubles every year. I.e., the annual processing speed growth factor is 2. The processing speed after 30 years is 2^{30} times the current processing speed

As the speed grows, to maintain the same security, the key length needs to increase to offset the increase in processing speed so the decryption time increases 2^{(new length – 100)} times

As decryption time remains constant 2^{30} = 2^{(new length – 100)} times

The new length is about 130

So after 30 years, the symmetric session key needs to be 130 bits long to be considered appropriate

Weifan Qiao says

Due to the doubling of the total processing speed of microprocessors every year, we can use exponential growth to calculate the growth of encryption strength over time.

Assuming the initial symmetric key length is 100 bits and the encryption speed doubles every year. So in 30 years, the encryption speed will increase to (2 ^ {30}) times.

Ziyi Wan says

If the total processing speed of microprocessors doubles every year, then. Computing power is going to grow at this rate, and the potential rate of breaking encryption is going to grow, and in 30 years, there will be progress in all aspects. So I think it’s hard to predict

Wenhan Zhao says

The total processing speed of microprocessors is doubling roughly every year.

In 30 years, the processing speed would be 2^30 times.

When a key length is increased by just 1 bit, it effectively doubles the number of possible combinations, making decryption twice as difficult. (2^n, n=incremental bits)

To keep time the same, n=30.

In 30 years, a symmetric session key will need to be 130 bits long to be considered as strong as a 100-bit key today.

Luxiao Xue says

If the total processing speed of microprocessors is doubling roughly every year, then in 30 years, it will have increased by a factor of 2^30. This means that a microprocessor in 30 years will be able to process information much faster than it can today. If a symmetric session key needs to be 100 bits long to be considered strong today, then in 30 years, it will need to be longer to remain strong. We need to consider how much longer decryption takes if the key length is increased by a single bit. If decryption takes twice as long for a key that is one bit longer, then a key that is 100 bits long today will need to be 200 bits long in 30 years to remain strong.

This is because the increased processing speed of microprocessors will make it easier for attackers to crack shorter keys, and a longer key will provide more security. However, longer keys also require more processing power and time to encrypt and decrypt, which can impact the performance of the system.

Jingyu Jiang says

First, we need to understand the relationship between the symmetric session key length and the time required for decryption. Assuming the current 100-bit long key is considered a strong key, the number of keys needed to try will double the number of keys.

Since the total processing speed of the microprocessor doubles each year, this means that the annual computing power is twice that of the previous year. Therefore, if the key length increases one bit per year, the time required for the attacker to crack the key will remain unchanged, because the increased computational power just offset the difficulty caused by the increased key length.

Now, we have to calculate how long it would take for the key after 30 years to be considered a strong key. Since the processor speed doubles every year, 30 years later the processor will be at one times the current 2^30 . Therefore, to maintain the same level of security, the key length also needs to increase by 30 bits.

So, in 30 years, the strong key length will be:

100 + 30=130 bits

Therefore, after 30 years, the symmetric session key needs at least 130 bits long to be considered a strong key.

Yi Zheng says

If the number of bits in a symmetric encryption key increases by one bit, the time required for decryption will double. Assuming the processor speed doubles every year, then in 30 years, the processor speed will increase by 2 ^ 30 times. Therefore, in order to maintain the same security, the length of the symmetric session key also needs to be increased by 30 bits. Therefore, if today’s symmetric session key requires 100 bits to be considered secure, then 30 years later, a symmetric session key requires 130 bits to be considered secure.

Yuqing Yin says

In symmetric encryption, increasing the key length by one bit approximately doubles the work factor because the number of possible keys increases exponentially. If processing speed doubles every year, in 30 years, it would increase by a factor of \(2^{30}\), making brute force attacks \(2^{30}\) times faster. To maintain the same security level, the symmetric key length must increase by 30 bits. Thus, if a 100-bit key is strong today, a 130-bit key will be needed in 30 years to ensure the same level of security, assuming constant relationship between key length and computational effort, and no significant changes in cryptographic algorithm resistance.

Yucheng Hou says

Considering the trend of microprocessor processing speed doubling every year, it is expected that the processing speed will increase by about (2^30) times over the next 30 years. In order to maintain the security of symmetric encryption, the key length needs to be increased accordingly. Currently, 100-bit keys are considered secure, but with significant improvements in processing power, future key lengths will need to grow accordingly. Since decryption time roughly doubles with each bit increase in key length, in order to maintain the same level of security against brute-force attacks over the next 30 years, the key length needs to increase by the same number of bits as the processing power grows, that is, 30 bits. Therefore, it can be calculated that after 30 years, in order to maintain the same security strength, the length of the symmetric session key will need to be 100 + 30 = 130 bits.

Ao Zhou says

The processing of microprocessors doubles every year, but the certification time does not increase with the speed of the technology, because the strength of the symmetric connection is proportional to the length. The longer it takes, the harder it gets. Over the past 30 years, the performance of microprocessors has improved greatly, but the key length has increased exponentially, not only for technical reasons, but also for security reasons. Therefore, in 30 years, symmetric keys may require more than 100 digits. But the relationship between time and space is difficult to predict.

Kang Shao says

The overall processing speed of microprocessors is doubled every year, based on the common view of technological progress and hardware development. However, the direct relationship between this growth rate and the length or required strength of the symmetrical session key is not direct. Based on current security practices in encryption and the ability to resist violent attacks, the length of a symmetrical session key (e.g. 100 bits) is considered a strong standard. The longer the key length, the longer the time it takes to break raw force, and the better the safety. However, in order to predict how long it will take for symmetrical session keys to be considered strong within 30-years, it is necessary to consider the development of encryption algorithms and attack techniques.

Yifan Yang says

1. With the development of Moore’s Law, processing speed of processors doubles every 18 months.

2. The length of the encryption key is proportional to the time required to crack the key.

3. Each bit increase in the length of the encryption key doubles the time required to crack the key.

Based on these conclusions, we can calculate the length of the symmetric key after 30 years. Assuming a 100-bit symmetric key is considered secure today, 30 years from now, the time required to crack the key will be greatly reduced due to the increased processing speed of the processor. To maintain the same security, we need to increase the length of the key.

Assuming that the processing speed of the processor doubles every 18 months, in 30 years, the processing speed of the processor will be 2^15 times faster. Therefore, we need to increase the length of the key so that it takes the same amount of time to crack the key as it does today.

Since the length of the encryption key doubles the time it takes to crack it with each bit, we need to increase the length of the key so that it takes the same amount of time to crack the key as it does today. Therefore, we need to increase the length of the key so that it takes the same amount of time to crack the key as it does today.

So, after 30 years, a symmetric key needs at least 150 bits to be considered secure.

Zijian Tian says

This is my explanation of the question:

1. Understand key length and security:

Key strength is measured in bits. Each additional bit doubles possible keys, making brute force attacks twice as hard.

2. Consider processing power doubling:

If speed doubles yearly, in thirty years, processing power will be two to the power of thirty times greater.

Initial scenario:

Today, a one-hundred-bit key is strong, meaning it’s infeasible to break with current processing power.

Future scenario:

In thirty years, processors will be two to the power of thirty times more powerful, so today’s brute force attack time will be one divided by two to the power of thirty of the current time.

The new key must take the same time to brute force in thirty years as today to maintain security.

So, we can get the new key length:

Each added bit doubles brute force difficulty.

To counter two to the power of thirty increase in processing power, we must add thirty bits.

Given a one-hundred-bit key is strong today, in thirty years, the key length needs to be:

New key length=100 bits+30 bits=130 bits

New key length=100 bits+30 bits=130 bits

Thus, in thirty years, a symmetric session key will need to be at least one hundred thirty bits long to be considered strong.

Baowei Guo says

In 30 years, to maintain the same level of security against brute-force attacks given the exponential growth in processing power, a symmetric session key will need to be at least 130 bits long. This calculation assumes that the doubling of processing power continues consistently over the next 30 years and that no new cryptographic breakthroughs significantly alter the landscape of symmetric key cryptography.

Yimo Wu says

If the clock rate and the number of circuits persist in doubling annually for a span of thirty years, it becomes imperative that the 100-bit symmetric key be expanded to 130 bits (2^100/2) in order to maintain its robustness. Given that it currently takes one billion years to decrypt a 128-bit symmetric key with contemporary computational capabilities, it will indeed be intriguing to observe the decryption advancements adversaries might achieve in response to the ever-strengthening cryptography standards. Such developments not only underscore the evolving nature of cryptography but also highlight the ongoing challenge of safeguarding information in the face of advancing technological capabilities.

Yahan Dai says

The strength of encryption is determined by the key length. As computing capabilities advance, keys that were previously deemed secure may become vulnerable to attacks in the future. Given that a microprocessor’s overall processing speed doubles annually, the computational power required to compromise encryption should, theoretically, increase at a comparable rate. Imagine that currently, a symmetric session key needs to be 100 bits long to provide robust security. We are interested in knowing how long this key must be after 30 years to offer the same level of protection. In cryptography, each additional bit in the key approximately doubles the complexity of cracking it, owing to the doubling of the potential key space. Thus, if computational power increases by a factor of two each year, the key length must also grow by one bit per year to uphold the same security standard. Over 30 years, to sustain equivalent security, the key length would need to expand by 30 bits (30 years × 1 bit/year = 30 bits).

Therefore, if today’s standard for a strong symmetric key is 100 bits, then in 30 years, to achieve an equivalent level of security, the key length will need to be extended by 30 bits. This means that a 130-bit key will be necessary.